Subject Code : CSE002

Subject Title : Design of Shell Structure

Structure of the Course Content

Subject: Design of Shell Structure Structure of the Course

Content

BLOCK 1 Classification of ShellsUnit 1: Classification of shells, types of shellsUnit 2: Structural action, - Design of circular domesUnit 3: Conical roofsUnit 4: Circular cylindrical shells by ASCE Manual No.31BLOCK 2 Folded PlatesUnit 1: Folded Plate structuresUnit 2: Structural behaviour, typesUnit 3: Design by ACIUnit 4: ASCE Task Committee method – pyramidal roofBLOCK 3 Introductions to Space FrameUnit 1: Space framesUnit 2: Configuration - types of nodesUnit 3: General principles of design PhilosophyUnit 4: Behaviour of Space FramesBLOCK 4 Analysis and DesignUnit 1: Analysis of space framesUnit 2: Detailed design of Space framesUnit 3: Introduction to Computer Aided Design and Software PackagesUnit 4: Applications of Space FramesBLOCK 5 Special MethodsUnit 1: Introduction to Formex AlgebraUnit 2: Application of Formex AlgebraUnit 3: FORMIAN for generation of configurationUnit 4: Case Studies using Formex Algebra

BLOCK 1 Classification of Shells

The tusk shells or scaphopods are a class of shelled marine mollusks. The scientific name of this class is Scaphopoda, meaning "shovel-footed". Shells of species within this class range from about 0.5 to 15 cm in length. Members of the Order Dentaliida are generally significantly larger than those of the Order Gadilida.

These molluscs live on soft substrates offshore (usually not intertidally). Because of this subtidal habitat and the small size of most species, many beachcombers are unfamiliar with them; their shells are usually not nearly as common or as easily visible in the beach drift as the shells of sea snails and clams. Molecular data suggests that the scaphopods are a sister group to the cephalopods, although higher-level molluscan phylogeny remains somewhat unresolved.

A Unix shell is a command-line interpreter or shell that provides a traditional user interface for the Unix operating system and for Unix-like systems. Users direct the operation of the computer by entering command input as text for a command line interpreter to execute or by creating text scripts of one or more such commands.

The most influential Unix shells have been the Bourne shell and the C shell. The Bourne shell, sh, was written by Stephen Bourne at AT&T as the original Unix command line interpreter; it introduced the basic features common to all the Unix shells, including piping, here documents, command substitution, variables, control structures for condition-testing and looping and filename wildcarding. The language, including the use of a reversed keyword to mark the end of a block, was influenced by ALGOL 68

The C shell, csh, was written by Bill Joy while a graduate student at University of California, Berkeley. The language, including the control structures and the expression grammar, was modeled on C. The C shell also introduced a large number of features for interactive work, including the history and editing mechanisms, aliases, directory stacks, tilde notation, cdpath, job control and path hashing.

Both shells have been used as coding base and model for many derivative and work-alike shells with extended feature sets.

Unit 1: Classification of shells, types of shells

1.1Introduction1.2 Classification1.3 Seashells types1.4Types1.5 Glossary1.6 Check your Progress1.7 Reference1.8Answer to check your Progress

1.1 Introduction

A shell is a payload-carrying projectile, which, as opposed to shot, contains an explosive or other filling, though modern usage sometimes includes large solid projectiles properly termed shot (AP, APCR, APCNR, APDS, APFSDS and proof shot). Solid shot may contain a pyrotechnic compound if a tracer or spotting charge is used.

All explosive and incendiary filled projectiles, particularly for mortars, were originally called grenades, derived from the pomegranate due to its seeds being similar to grains of powder. Grenade is still used for an artillery or mortar projectile in some European languages

Shells are usually large calibre projectiles fired by artillery, armored fighting vehicles (including tanks), and warships.

Shells usually have the shape of a cylinder topped by an ogive-shaped nose for good aerodynamic performance, possibly with a tapering base; but some specialized types are quite different.

Many people collect seashells, creating large displays of various sizes, shapes and colors. The shells were probably found along an ocean shore and no longer contain the live creatures all shells at one time housed. Shells, or mollusks as the live creatures are scientifically called, have over 125,000 species; however, they are classified by three main types and three less common types. The seashells collected along beaches are the discarded external skeleton of these creatures.

1.2Classifications

• Discarded seashells and live mollusks range in size from that of a grain of rice up to almost 4 feet across. The three main classifications are bivalves, gastropods and cephalopods. These three groupings make up the most common and numerous of mollusks. Three less commonly found types are chitons, tusk shells and gastroverms.

Bivalves:

Various bivalve shells

Bivalves such as clams, oysters, scallops and mussels make up many of the most often found seashells. However, when found by beachcombers, these shells are often only half of the actual shell, as bivalves always contain two-part shells. Within this grouping,

there are pelecypods and brachiopods. Pelecypods contain two identical but mirror-imaged halves, while

brachiopods, which are very rare today, contain two very similar but not identical halves. The live creature lives between the two shells, with a muscle attaching the two halves tightly. Some mollusks bury themselves in the sand, and some attach to hard surfaces by burrowing or growing more shell to attach it to the surface. They commonly exist in salt-water oceans and seas as well as in freshwater streams, lakes and rivers.

Gastropods

Conch

Gastropods, which consist mostly of snail-like creatures, make up the largest and most varied group of mollusks. Live mollusks exist as a coiled animal inside a coiled shell with an extending foot, actually a stomach, by which they move. Gastropod shells include common types such as conchs, whelks, moon snails, cone snails and nautiluses. All contain a spiral-shaped shell and commonly live in both freshwater and salt water, as well as on land.

Cephalopods

Squid

Cephalopods include such creatures as squid, octopus and cuttlefish. This type of mollusk sometimes contains a shell but most often has evolved to a point of not needing a shell. Many fossilized shells of the ancestors of squid, octopus and cuttlefish have been found, demonstrating that this mollusk did once routinely contain a shell. Cephalopods evolved to be predatory, intelligent creatures with keen eyesight and tentacles containing suction cups for defending itself and attacking others.

Less common types

Chiton

Besides the most common shell types of bivalves, gastropods and cephalopods, three less common types of mollusks exist though are rarely found today. All are extremely small and often live in remote or deep waters. Chitons are tiny, with an armadillo-like shell that allows it to roll up into a ball to protect itself. Another type, tusk shells, resemble tiny elephant tusks open on both ends. These primitive creatures bury themselves in the sand with the smaller end sticking out. Gastroverms make up the last of the three less common shell and mollusk types. These are extremely primitive. Inside the shell lives a jointed, worm-like creature with vital organs repeated in every section of its body.

1.3 Seashells types

Welcome to the wonderful world of Seashells types collecting. Seashells types have been developing through this fascinating world of craft Seashells types, whose variety, complexity and areas of distribution seem infinite. Tropical Seashells types collect living in coral, reef, under rocks or in the beach. Craft seashells guide devoted to the answering your questions you might have about Seashells types, beach seashells, crafts seashells, wholesale seashells and more. Shells Treasures web site designed for craft seashells collectors with a variety of interests in the hobby Seashells types collection and for anyone who has ever been fascinated with the beauty and diversity of craft seashells. Seashells types boast many spectacular asia seashells types from shallow to very deep water. The great variation in color and sculpture of Seashells types make these jewels of the sea very popular with collectors. Seashells types is a web site for conchologists who want to purchase quality craft seashells and seashells jewelry that will entice beauty to their collections. A craft seashell collecting has practiced for thousands of years with craft seashells being used for trade and currency in the pacific region.

1.4 Types

• High-explosive o Mine shell

• Armor-piercing

• Armour-piercing, discarding-sabot • Armour-piercing, fin-stabilized, discarding-sabot • Armour-piercing, composite rigid • Armour-piercing, composite non-rigid (APCNR) • High-explosive, anti-tank • Discarding-sabot shell • High-explosive, squash-head or high-explosive plastic • Proof shot • Shrapnel shells • Cluster shells • Chemical • Non-lethal shells

Smoke Illumination Carrier Fireworks

There are many different types of shells. The principal ones include:

High-explosive

The most common shell type is high explosive, commonly referred to simply as HE. They have a strong steel case, a bursting charge, and a fuze. The fuse detonates the bursting charge which shatters the case and scatters hot, sharp case pieces (fragments, splinters) at high velocity. Most of the damage to soft targets such as unprotected personnel is caused by shell pieces rather than by the blast. The term "shrapnel" is sometimes incorrectly used to describe the shell pieces, but shrapnel shells functioned very differently and are long obsolete. Depending on the type of fuze used the HE shell can be set to burst on the ground (percussion), in the air above the ground (time or proximity), or after penetrating a short distance into the ground (percussion with delay, either to transmit more groun shock to covered positions, or to reduce the spread of fragments).

Early high explosives used before and during World War I in HE shells were Lyddite (picric acid), PETN, TNT. However, pure TNT was expensive to produce and most nations made some use of mixtures using cruder TNT and ammonium nitrate, some with other compounds included. These fills included Ammonal, Schneiderite and Amatol. The latter was still in wide use in World War II.

From 1944-5 RDX and TNT mixtures became standard. Notably "Composition B" (cyclotol). The introduction of 'insensitive munition' requirements, agreements and regulations in the 1990s caused modern western designs to use various types of plastic bonded explosives (PBX) based on RDX.

The percentage of shell weight taken up by its explosive fill increased steadily throughout the 20th Century. Less than 10% was usual in the first few decades, by World War II leading designs were around 15%. However, British researchers in that war identified 25% as being the optimal design for anti-personnel purposes, based on recognition that far smaller fragments than hitherto would give the required effects. This was achieved by 1960s designed 155mm L15 shell developed as part of the FH-70 program. The key requirement for increasing the HE content without increasing shell weight was to reduce the thickness of shell walls, this required improvements in high tensile steel.

Mine shell The mine shell is a particular form of HE shell developed for use in small caliber weapons such as 20 mm to 30 mm cannon. Small HE shells of conventional design can contain only a limited amount of explosive. By using a thin-walled steel casing of high tensile strength, a larger explosive charge can be used. Most commonly the explosive charge also was a more expensive but higher-detonation-energy type. The mine shell concept was invented by the Germans in the Second World War primarily for use in aircraft guns intended to be fired at opposing aircraft. Mine shells produced relatively little damage due to fragments, but a much more powerful blast. The aluminium structures and skins of Second World War aircraft were readily damaged by this greater level of blast.

Armor-piercing

The earliest naval and anti-tank shells had to withstand the extreme shock of punching through armor plate. Shells designed for this purpose sometimes had a greatly strengthened case with a small bursting charge, and sometimes were solid metal, i.e. shot. In either case, they almost always had a specially hardened and shaped nose to facilitate penetration. This resulted in armor-piercing (AP) projectiles.

A further refinement of such designs improved penetration by adding a softer metal cap to the penetrating nose giving APC (Armour piercing - capped). The softer cap dampens the initial shock that would otherwise shatter the round. The best profile for the cap is not the most aerodynamic; this can be remedied by adding a further hollow cap of suitable shape: APCBC (APC + Ballistic Cap)

AP shells with a bursting charge were sometimes distinguished by appending the suffix "HE". At the beginning of the Second World War, solid shot AP projectiles were common. As the war progressed, ordnance design evolved so that APHE became the more common design approach for anti-tank shells of 75 mm caliber and larger, and more common in naval shell design as well. In modern ordnance, most full caliber AP shells are APHE designs.

Armour-piercing, discarding-sabot

Armour-piercing, discarding-sabot (APDS) was developed by engineers working for the French Edgar Brandt company, and was fielded in two calibers (75 mm/57 mm for the Mle1897/33 75 mm anti-tank cannon, 37 mm/25 mm for several 37 mm gun types) just before the French-German armistice of 1940. The Edgar Brandt engineers, having been evacuated to the United Kingdom, joined ongoing APDS development efforts there, culminating in significant improvements to the concept and its realization. British APDS ordnance for their QF 6 pdr and 17 pdr anti-tank guns was fielded in March 1944.

The armor-piercing concept calls for more penetration capability than the target's armour thickness. Generally, the penetration capability of an armor piercing round is proportional to the projectile's kinetic energy. Thus an efficient means of achieving increased penetrating power is increased velocity for the projectile. However, projectile impact against armour at higher velocity causes greater levels of shock. Materials have characteristic maximum levels of shock capacity, beyond which they may shatter on impact. At relatively high impact velocities, steel is no longer an adequate material for armor piercing rounds due to shatter.

Tungsten and tungsten alloys are suitable for use in even higher velocity armour piercing rounds due to their very high shock tolerance and shatter resistance. However, tungsten is very dense, and tungsten rounds of full-caliber design are too massive to be accelerated to an efficient velocity for maximized kinetic energy. This is overcome by using a reduced-diameter tungsten shot, surrounded by a lightweight outer carrier, the sabot (a French word for a wooden shoe). This combination allows the firing of a smaller diameter (thus lower mass/aerodynamic resistance/penetration resistance) projectile with a larger area of expanding-propellant "push", thus a greater propelling force/acceleration/resulting kinetic energy.

Once outside the barrel, the sabot is stripped off by a combination of centrifugal force and aerodynamic force, giving the shot low drag in flight. For a given caliber the use of APDS ammunition can effectively double the anti-tank performance of a gun.

Armour-piercing, fin-stabilized, discarding-sabot

An Armour-Piercing, Fin-Stabilised, Discarding Sabot (APFSDS) projectile uses the sabot principle with fin (drag) stabilisation. A long, thin sub-projectile has increased sectional density and thus penetration potential. However, once a projectile has a length-to-diameter ratio greater than 10 (less for higher density projectiles), spin stabilisation becomes ineffective. Instead, drag stabilisation is used, by means of fins attached to the base of the sub-projectile, making it look like a large metal arrow.

Large calibre APFSDS projectiles are usually fired from smooth-bore (unrifled) barrels, though they can be and often are fired from rifled guns. This is especially true when fired from small to medium calibre weapon systems. APFSDS projectiles are usually made from high-density metal alloys such as tungsten heavy alloys (WHA) or depleted uranium (DU); maraging steel was used for some early Soviet projectiles. DU alloys are cheaper and have better penetration than others as they are denser and self-

sharpening, but they present radiological and toxic hazards that remain on the battlefield. The less toxic WHAs are preferred in most countries except the USA, UK, and Russia.

Armour-piercing, composite rigid

Armour-Piercing, Composite Rigid (APCR) is a British term, the US term for the design is High Velocity Armour Piercing (HVAP) and German, Hartkernmunition. The APCR projectile is a core of a high-density hard material such as tungsten carbide surrounded by a full-bore shell of a lighter material (e.g. an aluminium alloy). Most APCR projectiles are shaped like the standard APCBC shot (although some of the German Pzgr. 40 and some Soviet designs resemble a stubby arrow), but the projectile is lighter: up to half the weight of a standard AP shot of the same calibre. The lighter weight allows a higher velocity. The kinetic energy of the shot is concentrated in the core and hence on a smaller impact area, improving the penetration of the target armour. To prevent shattering on impact, a shock-buffering cap is placed between the core and the outer ballistic shell as with APC rounds. However, because the shot is lighter but still the same overall size it has poorer ballistic qualities, and loses velocity and accuracy at longer ranges. The APCR was superseded by the APDS which dispensed with the outer light alloy shell once the shot had left the barrel. The Germans used an APCR round, the Panzergranate 40 (Pzgr.40) "arrowhead" shot, for their 5 cm Pak 38 antitank guns in 1942, and it was also developed for their 75 and 88 mm antitank and tank guns, and for anti-tank guns mounted in German aircraft. Shortages of the key component, tungsten, led to the Germans dropping the use of APCR during late World War II because it was more efficiently used in industrial applications such as machine tools.

Armour-piercing, composite non-rigid (APCNR)

Armour-Piercing, Composite Non-Rigid (APCNR), the British term, but the more common terms are squeeze-bore and tapered bore and are based on the same projectile design as the APCR - a high density core within a shell of soft iron or other alloy, but it is fired by a gun with a tapered barrel, either a taper in a fixed barrel (Gerlich design in German use; original development efforts in the late 1930s in Germany, Denmark and France) or a final added section as in the British "squeeze -bore" (Littlejohn adaptor). The projectile is initially full-bore, but the outer shell is deformed as it passes through the taper. Flanges or studs are swaged down in the tapered section, so that as it leaves the muzzle the projectile has a smaller overall cross-section.[12] This gives it better flight characteristics with a higher sectional density and the projectile retains velocity better at longer ranges than an undeformed shell of the same weight. As with the APCR the kinetic energy of the round is concentrated at the core on impact. The initial velocity of the round is greatly increased by the decrease of barrel cross-sectional area toward the muzzle, resulting in a commensurate increase in velocity of the expanding propellant gases.

The Germans deployed their Schwere Panzerbüchse 41, their initial tapered barrel design, as a light anti-tank weapon early in the Second World War, but although HE projectiles were designed and put into service, the limiting of the shell diameter to the muzzle bore reduced their mass to only 85 grams and hence reduced their effectiveness. The British used the Littlejohn squeeze-bore adaptor which could be attached or removed as necessary, to extend the usefulness of their QF 2 pdr gun in armoured cars and light tanks which could not take a larger gun. Although a full range of shells and shot could be used, changing the adaptor in the heat of battle was highly impractical. The APCNR was superseded by the APDS design which was compatible with non-tapered barrels.

High-explosive, anti-tank

HEAT shells are a type of shaped charge used to defeat armoured vehicles. They are extremely efficient at defeating plain steel armour but less so against later composite and reactive armour. The effectiveness of the shell is independent of its velocity, and hence the range: it is as effective at 1000 metres as at 100 metres. The speed can even be zero in the case where a soldier simply places a magnetic mine onto a tank's armor plate. A HEAT charge is most effective when detonated at a certain, optimal, distance in front of the target and HEAT shells are usually distinguished by a long, thin nose probe sticking out in front of the rest of the shell and detonating it at the correct distance, e.g., PIAT bomb. HEAT shells are less effective if spun (i.e., fired from a rifled gun).

Discarding-sabot shell

A discarding-sabot shell (DSS) is (in principle) the same as the APDS shot but applied to high-explosive shells. It is a means to deliver a shell to a greater range. The design of the sub-projectile carried inside the sabot can be optimised for aerodynamic properties and the sabot can be built for best performance within the barrel of the gun. The principle was developed by a Frenchman, Edgar Brandt, in the 1930s. With the occupation of France, the Germans took the idea for application to anti-aircraft guns—a DSS projectile could be fired at a higher muzzle velocity and reach the target altitude more quickly, simplifying aiming and allowing the target aircraft less time to change course.

High-explosive, squash-head or high-explosive plastic

HESH is another anti-tank shell based on the use of explosive. Developed by the British inventor Sir Charles Dennistoun Burney in World War II for use against fortifications. A thin-walled shell case contains a large charge of a plastic explosive. On impact the explosive flattens, without detonating, against the face of the armour, and is then detonated by the fuze. Energy is transferred through the armour plate: when the compressive shock reflects off the air/metal interface on the inner face of the armour, it is

transformed into a tension wave which spalls a "scab" of metal off into the tank damaging the equipment and crew without actually penetrating the armour.

HESH is completely defeated by spaced armour, so long as the plates are individually able to withstand the explosion. It is still considered useful as not all vehicles are equipped with spaced armour, and it is also the most effective munition for demolishing brick and concrete. HESH shells, unlike HEAT shells, are best fired from rifled guns.

Another variant is the high-explosive plastic (HEP).

Proof shot

A proof shot is not used in combat but to confirm that a new gun barrel can withstand operational stresses. The proof shot is heavier than a normal shot or shell, and an oversize propelling charge is used, subjecting the barrel to greater than normal stress. The proof shot is inert (no explosive or functioning filling) and is often a solid unit, although water, sand or iron powder filled versions may be used for testing the gun mounting. Although the proof shot resembles a functioning shell (of whatever sort) so that it behaves as a real shell in the barrel, it is not aerodynamic as its job is over once it has left the muzzle of the gun. Consequently it travels a much shorter distance and is usually stopped by an earth bank for safety measures.

The gun, operated remotely for safety in case it fails, fires the proof shot, and is then inspected for damage. If the barrel passes the examination "proof marks" are added to the barrel. The gun can be expected to handle normal ammunition, which subjects it to less stress than the proof shot, without being damaged.

Shrapnel shells

Typical World War I shrapnel round

Main article: Shrapnel shell Shrapnel shells were an early (1784) anti-personnel munition which delivered

large numbers of bullets at ranges far greater than rifles or machine guns could attain - up to 6,500 yards by 1914. A typical shrapnel shell as used in World War I was streamlined, 75 mm (3 inch) in diameter and contained approximately 300 lead-antimony balls (bullets), each approximately 1/2 inch in diameter. Shrapnel used the principle that the bullets encountered much less air resistance if they travelled most of their journey packed together in a single streamlined shell than they would if they travelled individually, and could hence attain a far greater range.

The gunner set the shell's time fuze so that it was timed to burst as it was angling down towards the ground just before it reached its target (ideally about 150 yards before, and 60–100 feet above the ground). The fuze then ignited a small "bursting

charge" in the base of the shell which fired the balls forward out of the front of the shell case, adding approximately 200 – 250 ft/second to the existing velocity of 750–1200 ft/second. The shell case dropped to the ground and the bullets continued in an expanding cone shape before striking the ground over an area approximately 250 yards x 30 yards in the case of the US 3 inch shell. The effect was of a large shotgun blast just in front of and above the target, and was deadly against troops in the open. A trained gun team could fire 20 such shells per minute, with a total of 6,000 balls, which compared very favourably with rifles and machine-guns.

However, shrapnel's relatively flat trajectory (it depended mainly on the shell's velocity for its lethality, and was only lethal in a forward direction) meant that it could not strike trained troops who avoided open spaces and instead used dead ground (dips), shelters, trenches, buildings, and trees for cover. It was of no use in destroying buildings or shelters. Hence it was replaced during World War I by the high-explosive shell which exploded its fragments in all directions and could be fired by high-angle weapons such as howitzers, hence far more difficult to avoid.

Cluster shells

Cluster shells are a type of carrier shell or cargo munition. Like cluster bombs, an artillery shell may be used to scatter smaller submunitions, including anti-personnel grenades, anti-tank top-attack munitions, and landmines. These are generally far more lethal against both armor and infantry than simple high-explosive shells, since the multiple munitions create a larger kill zone and increase the chance of achieving the direct hit necessary to kill armor. Most modern armies make significant use of cluster munitions in their artillery batteries.

However, in operational use submunitions have demonstrated a far higher malfunction rate than previously claimed, including those that have self-destruct mechanisms. This problem, the 'dirty battlefield", led to the Ottawa Treaty.

Artillery-scattered mines allow for the quick deployment of minefields into the path of the enemy without placing engineering units at risk, but artillery delivery may lead to an irregular and unpredictable minefield with more unexploded ordnance than if mines were individually placed. Signatories of the Ottawa Treaty have renounced the use of cluster munitions of all types where the carrier contains more than ten submunitions.

Chemical

Chemical shells contain just a small explosive charge to burst the shell, and a larger quantity of a chemical agent such as a poison gas. Signatories of the Chemical Weapons Convention have renounced such shells.

Non-lethal shells

Not all shells are designed to kill or destroy. The following types are designed to achieve particular non-lethal effects. They are not completely harmless: smoke and illumination shells can accidentally start fires, and impact by the discarded carrier of all three types can wound or kill personnel, or cause minor damage to property.

Smoke:

The smoke shell is designed to create a smokescreen. The main types are bursting (those filled with white phosphorus WP and a small HE bursting charge are best known) and base ejection (delivering three or four smoke canisters, or material impregnated with white phosphorus). Base ejection shells are a type of carrier shell or cargo munition.

Base ejection smoke is usually white, however, coloured smoke has been used for marking purposes. The original canisters were non-burning, being filled with a compound that created smoke when it reacted with atmospheric moisture, modern ones use red phosphorus because of its multi-spectral properties. However, other compounds have been used, in World War II Germany used oleum (fuming sulphuric acid) and pumice.

Illumination

Modern illuminating shells are a type of carrier shell or cargo munition. Those used in World War I were shrapnel pattern shells ejecting small burning 'pots'.

A modern illumination shell has a fuze which ejects the "candle" (a pyrotechnic flare emitting white or infrared light) at a calculated altitude, where it slowly drifts down beneath a heat resistant parachute, illuminating the area below. These are also known as starshell or star shell.

Coloured flare shells have also been used for target marking purposes.

Carrier

The carrier shell is simply a hollow carrier equipped with a fuze which ejects the contents at a calculated time. They are often filled with propaganda leaflets (see external links), but can be filled with anything that meets the weight restrictions and is able to withstand the shock of firing. Famously, on Christmas Day 1899 during the siege of Ladysmith, the Boers fired into Ladysmith a carrier shell without fuze, which contained a Christmas pudding, two Union Flags and the message "compliments of the season". The shell is still kept in the museum at Ladysmith.

Fireworks

Aerial firework bursts are created by shells. In the United States, consumer firework shells may not exceed 1.75 inches in diameter.

1.5 Glossary

Acceleration - Securities cannot be sold unless a registration statement has become effective with the SEC, or a specific exemption applies. That effective date occurs automatically 20 days after it is filed, unless an SEC stop order or refusal order is in effect. In reality, however, each filing includes a 'delaying amendment' so that it cannot become effective automatically. Then the lawyers file a request for acceleration of the effective date to a selected day and time.

Aftermarket - The trading market that develops for shares after the public offering is over. Orders to buy or sell shares are matched in the over-the-counter (OTC) market by a securities firm acting as a market maker. For NYSE or American Stock Exchange shares, a specialist on the stock exchange will match orders. The quality of the aftermarket is measured by its ability to absorb bid price or asked price orders without major disruptions in the price. That ability is a function of the market's liquidity - the number of shares owned by the public, rather than by company insiders (called the float), and the extent to which the public is active in trading the shares, rather than holding them for the long term.

Affiliate - normally defined as an individual or corporation in a position to exert direct influence on the actions of a corporation. Among such persons are owners of 10% or more of the voting shares, directors, and senior elected officers and any persons or entities in a position to exert influence through them - such as members of their immediate family and other close associates.

All-or-none Offering - Each public offering will have a total number of shares that must be sold. Sometimes, in a direct public offering or a best efforts underwriting, a condition of the offering will be that all shares offered must be sold or the offering is cancelled and none of the shares will be sold; this is an all-or-none offering.

Allotment - In an underwritten public offering, each securities firm in the underwriting syndicate is allocated an allotment of shares to sell. As a practical matter there is very little relationship between the allotment and actual sales. Technically, the agreement among underwriters could force each member of the underwriting syndicate to take its allotment.

American Depositary Receipts (ADR) - A negotiable receipt representing a specific number of equity shares in a foreign corporation. ADRs trade in American dollars in the American securities market like domestic equities.

American Depositary Shares (ADS) - A trading unit for the issuer in the U.S. which may represent more or less than one underlying share of the issuer. ADSs are issued in

New York in registered form, eligible for trading and clearing in the U.S. markets, and may be made eligible for clearing outside the U.S. in Euroclear and CEDEL.

Angel Investors - Also known as informal, wealthy investors, these are people who invest money in the business at its start-up or "seed capital" stage, before other sources of capital are available. They are usually relatives or friends of the entrepreneur, or individuals with the wealth and experience to take significant risks for above-average long-term rewards.

Annual Report - Financial statements and management's discussion and analysis of the company's operations and condition. For companies with registered shares under the Securities Exchange Act of 1934, an annual report must be filed with the SEC, following a Form 10-K format. Most states require corporations to send annual reports to their shareowners. These usually require audited financial statements, but their form and content is left to management's preference.

Asked Price - Shares traded in the OTC market will have prices quoted by their market makers, either on NASDAQ, on the OTCBB? or in the Pink Sheets. The quotations are for the bid price (what the market maker will pay to buy at least 100 shares) and the asked price (what it will accept to sell at least 100 shares).

Bad Boys - Past offenders under securities fraud laws. When the SEC authorizes exemptions from full registration statements, such as Regulation A and SCOR, it prevents their use by a corporation affiliated with persons who have, within the previous five years, been convicted of securities fraud or who are subject to any enforcement order by a securities regulator. Filing under the securities laws requires disclosure of bad boy affiliations.

Best Efforts Underwriting - A type of underwriting, in which a securities firm agrees to use its "best efforts" to sell shares as an agent for the company. There is no minimum number of shares that the underwriter must sell.

Bid Price - The price at which the bidder will buy a specified number of shares (see asked price).

Big Five - The largest international independent public accounting and consulting firms.

Blind Pool - Public offerings also known as "blank check." These offerings are made without any specific business plan or purpose described for use of the offering proceeds. Normally, the business purpose of the company is to effectuate a merger or acquisition with an as-yet-to-be-specified company.

Blue Sky Laws - State securities laws.

Board of Directors - The governing body of a corporation, which sets policy and appoints major officers. Directors are elected by the shareholders.

Bonds - Debt securities generally for borrowings due to be repaid several years after they are issued. Bonds are legal instruments to evidence borrowed money.

Book Value - The amount of a corporation's shareholders' equity. Also called net worth. Literally, the company's assets minus liabilities.

Broker - Defined in the securities laws as a person in the business of buying and selling securities for the accounts of others. This may be a registered representative of a securities firm, an independent broker-dealer, or a financial planner.

1.6 Check your progress

1. Explain Classification of Shell2. Explain types of Shell

1.7 Reference

• Douglas T Hamilton, "High-explosive shell manufacture; a comprehensive treatise". New York: Industrial Press, 1916

• Douglas T Hamilton, "Shrapnel Shell Manufacture. A Comprehensive Treatise". New York: Industrial Press, 1915

• Hogg, OFG. 1970. “Artillery: its origin, heyday and decline”. London: C Hurst and Company.

• Catalog of recent and fossil turrids, John K. Tucker • A Catalogue of Nomenclature and Taxonomy in the Living Conidae, Mike

Filmer • Conchological Iconography - Harpidae, Ficidae, Strombidae • Oliva Shells, Bernard Tursch & Dietmar Greifeneder • Atlas of the Living Olive Shells of the World, Edward J. Petuch & Dennis M.

Sargent• Fauna of Australia, 1998 for Family to Class structure • Lorenz & Hubert for Cowries, • Röckel, Korn & Kohn for Cones, • Poppe & Goto for Volutes, • Bratcher & Cernohorsky for Terebrids • Kreipl for Cassids • Houart for various Muricids • Henning & Hemmen for Ranellidae & Personidae • Cossigniani for Bursidae • Lipe for Marginellidae

1.8 Check your progress Answer

1. Refer 1.12. Refer 1.3

Unit 2: Structural action, - Design of circular domes

2.1 Introduction2.2 Domes2.3 Properties of hyperboloid structures2.4 Types of Communication towers

2.4.1 Based on structural action2.4.2 Self supporting towers

2.4.2.1 Guyed towers2.4.2.2 Monopole

2.4.3 Based on cross section tower2.4.4 Based on the type of material sections2.4.5 Based on the number of segments

2.5 Characteristics2.6 Glossary2.7 Check your Progress2.8 Reference2.9 Answer to check your Progress

2.1 Introduction:

Hyperboloid structures are architectural structures designed with hyperboloid geometry. Often these are tall structures such as towers where the hyperboloid geometry's structural strength is used to support an object high off the ground, but hyperboloid geometry is also often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineer Vladimir Shukhov (1853–1939).[1]

The world's first hyperboloid tower is located in Polibino, Lipetsk Oblast, Russia.

The shapes are doubly ruled surfaces (hence can be built with a lattice of straight beams), which can be classed as:

• Hyperboloid of one sheet, such as cooling towers• Hyperbolic paraboloids, such as saddle roofs

Shells can be defined as curved structures capable of transmitting loads in more than two directions to supports. Loads applied to shell surfaces are carried to the ground by the development of compressive, tensile, and shear stresses acting in the in-plane direction of the surface. Thin shell structures are uniquely suited to carrying distributed

loads and find wide application as roof structures in building. They are, however, unsuitable for carrying concentrated loads.(Shodeck)

The behavior of any shell surface under the action of a load is analogous to a membrane, a surface element so thin that only tension forces can be developed (e.g. a soap bubble). Of primary importance is the existence of two sets of internal forces in the surface of a membrane that act in perpendicular directions. Also in existence is a type of tangential shearing stress which is developed within the membrane surface which helps carry the applied load. The shell tends to act in a fashion sim ilar to a two-way plate structure. (Schodeck)

2.2 Domes:

A dome is a structural element of architecture that resembles the hollow upper half of a sphere. Dome structures made of various materials have a long architectural lineage extending into prehistory.

Corbel domes and true domes have been found in the ancient Middle East in modest buildings and tombs. The construction of the first technically advanced true domes in Europe began in the Roman Architectural Revolution, when they were frequently used by the Romans to shape large interior spaces of temples and public buildings, such as the Pantheon. This tradition continued unabated after the adoption of Christianity in the Byzantine (East Roman) religious and secular architecture, culminating in the revolutionary pendentive dome of the 6th century church Hagia Sophia. Squinches, the technique of making a transition from a square shaped room to a circular dome, was most likely invented by the ancient Persians. The Sassanid Empire initiated the construction of the first large-scale domes in Persia, with such royal buildings as the Palace of Ardashir, Sarvestan and Ghal'eh Dokhtar. With the Muslim conquest of the Sassanid Empire, the Persian architectural style became a major influence on Muslim societies. Indeed the use of domes as a feature of Islamic architecture has gotten its roots from Persia (see gonbad, gongbei).

An original tradition of using multiple domes was developed in the church architecture in Russia, which had adopted Orthodox Christianity from Byzantium. Russian domes are often gilded or brightly painted, and typically have a carcass and an outer shell made of wood or metal. The onion dome became another distinctive feature in the Russian architecture, often in combination with the tented roof.

Domes in Western Europe became popular again during the Renaissance period, reaching a zenith in popularity during the early 18th century Baroque period. Reminiscent of the Roman senate, during the 19th century they became a feature of grand civic architecture. As a domestic feature the dome is less common, tending only to be a feature of the grandest houses and palaces during the Baroque period.

Construction of domes in the Muslim world reached its peak during the 16th – 18th centuries, when the Ottoman, Safavid and Mughal Empires, ruling an area of the

World compromising North Africa, the Middle East and South- and Central Asia, applied lofty domes to their religious buildings to create a sense of heavenly transcendence. The Sultan Ahmed Mosque, the Shah Mosque and the Badshahi Mosque are primary examples of this style of architecture.

Many domes, particularly those from the Renaissance and Baroque periods of architecture, are crowned by a lantern or cupola, a Medieval innovation which not only serves to admit light and vent air, but gives an extra dimension to the decorated interior of the dome.

Early history and primitive domesCultures from pre-history to modern times constructing domed dwellings using local materials. Although it is not known when the first dome was created, sporadic examples of early domed structures have been discovered.

The earliest discovered may be four small dwellings made of Mammoth tusks and bones. The first was found by a farmer in Mezhirich, Ukraine, in 1965 while he was digging in his cellar and

archaeologists unearthed three more. They date from 19,280 - 11,700 BC.

In modern times, the creation of relatively simple dome-like structures has been documented among various indigenous peoples around the world. The Wigwam was made by Native Americans using arched branches or poles covered with grass or hides. The Efé people of central Africa construct similar structures, using leaves as shingles. Another example is the Igloo, a shelter built from blocks of compact snow and used by the Inuit people, among others. The Himba people of Namibia construct "desert igloos" of wattle and daub for use as temporary shelters at seasonal cattle camps, and as permanent homes by the poor.

Drawing of an Assyrian bas-relief from Nimrud showing domed structures

The historical development from structures like these to more sophisticated domes is not well documented. That the dome was known to early Mesopotamia may explain the existence of domes in both China and the West in the first millennium BC. Another explanation, however, is that the use of the dome shape in construction did not

have a single point of origin and was common in virtually all cultures long before domes were constructed with enduring materials.

The recent discoveries of seal impressions in the ancient site of Chogha Mish (c. 6800 to 3000 BC), located in the Susiana plains of Iran, show the extentsive use of dome structures in mud-brick and adobe buildings. Other examples of mud-brick buildings, which also seemed to employ the "true" dome technique have been excavated at Tell Arpachiyah, a Mesopotamian site of the Halaf (c. 6100 to 5400 BC) and Ubaid (ca. 5300 to 4000 BC) cultures. Excavations at Tell al-Rimah have revealed brick domical vaults from about 2000 BC. At the Sumerian Royal Cemetery of Ur, a "complete rubble dome built over a timber centring" was found among the chambers of the tombs for Meskalamdug and Puabi, dating to around 2500 BC.[15] Set in mud mortar, it was a "true dome with pendentives rounding off the angles of the square chamber." Other small domes can be inferred from the remaining ground plans, such as one in the courtyard of Ur-Nammu's ziggurat, and in later shrines and temples of the fourteenth century BC.

Ancient tombs have been found from Oman to Portugal with stone corbel domes. The "Hafeet graves", also called "Mezyat graves", were structures built above ground, dating to the Bronze Age period between 3200 and 2700 BC in an area straddling the borders between Oman, UAE, and Bahrain. The larger Treasury of Atreus, a Mycenaean tomb covered with a mound of earth, dates to around 1250 BC. However, small corbel domes functioning as dwellings for poorer people appear to have remained the norm throughout the ancient Near East until the introduction of the monumental dome in the Roman period.[19]

A Neo-Assyrian bas-relief from Kuyunjik depicts domed buildings, although remains of such a structure in that ancient city have yet to be identified, perhaps due to the impermanent nature of sun-dried mudbrick construction..However, because the relief depicts the Assyrian overland transport of a carved stone statue, the background buildings most likely refer to a foreign village, such as those at the foothills of the Lebanese mountains. The relief dates to the eighth century BC, while the use of domical structures in the Syrian region may go back as far as the fourth millennium BC.[10]

Wooden domes were evidently used in Etruria on the Italian peninsula from archaic times. Reproductions were preserved as rock-cut Etruscan tombs produced until the Roman Imperial period, and paintings at Pompeii show examples of them in the third style and later. Wooden domes may also have been used in ancient Greece, over buildings such as the Tholos of Epidaurus, which is typically depicted with a conical roof.[10] Evidence for such wooden domes over round buildings in Ancient Greece, if they existed, has not survived and the issue is much debated

2.3 Properties of hyperboloid structures

Hyperbolic structures have a negative Gaussian curvature, meaning they curve inward rather than outward or being straight. As doubly ruled surfaces, they can be made

with a lattice of straight beams, hence are easier to build and, all else equal, stronger than curved surfaces that do not have a ruling and must instead be built with curved beams.

Hyperboloid structures are superior in stability towards outside forces than "straight" buildings, but have shapes often creating large amounts of unusable volume (low space efficiency) and therefore are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features, but their cross section is much more commonly seen in hyperbolic bridges.

With cooling towers, a hyperbolic structure is preferred. At the bottom, the widening of the tower provides higher surface area for water to boil in. As the water first boils and steam rises, the narrowing effect helps accelerate the laminar flow, and then as it widens out, contact between the heated air and atmospheric air supports turbulent mixing

Hyperboloid structures are architectural structures designed with hyperboloid geometry. Often these are tall structures such as towers where the hyperboloid geometry's structural strength is used to support an object high off the ground, but hyperboloid geometry is also often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineer Vladimir Shukhov (1853–1939).[1]

The world's first hyperboloid tower is located in Polibino, Lipetsk Oblast, Russia.

The shapes are doubly ruled surfaces (hence can be built with a lattice of straight beams), which can be classed as:

• Hyperboloid of one sheet, such as cooling towers• Hyperbolic paraboloids, such as saddle roof

2.4 Types of communication towers

The different types of communication towers are based upon their structural action, their cross-section, the type of sections used and on the placement of tower. A brief description is as given below:

2.4.1 Based on structural action.

Towers are classified into three major groups based on the structural action. They are: • Self supporting towers • Guyed towers • Monopole.

2.4.2 Self supporting towers.

The towers that are supported on ground or on buildings are called as self-supporting towers. Though the weight of these towers is more they require less base area

and are suitable in many situations. Most of the TV, MW, Power transmission, and flood light towers are self-supporting towers.

2.4.2.1 Guyed towers.

Guyed towers provide height at a much lower material cost than self supporting towers due to the efficient use of high-strength steel in the guys. Guyed towers are normally guyed in three directions over an anchor radius of typically 2/3 of the tower height and have a triangular lattice section for the central mast. Tubular masts are also used, especially where icing is very heavy and lattice sections would ice up fully. These towers are much lighter than self supporting type but require a large free space to anchor guy wires. Whenever large open space is available, guyed towers can be provided. There are other restrictions to mount dish antennae on these towers and require large anchor blocks to hold the ropes.

2.4.2.2 Monopole.

It is single self-supporting pole, and is generally placed over roofs of high raised buildings, when number of antennae required is less or height of tower required is less than 9m.

2.4.3 Based on cross section of tower.

Towers can be classified, based on their cross section, into square, rectangular, triangular, delta, hexagonal and polygonal towers. Open steel lattice towers make the most efficient use of material and enables the construction of extremely light-weight and stiff structures by offering less exposed area to wind loads. Most of the power transmission, telecommunication and broadcasting towers are lattice towers. Triangular Lattice Towers have less weight but offer less stiffness in torsion. With the increase in number of faces, it is observed that weight of tower increases. The increase is 10% and 20% for square and hexagonal cross sections respectively. If the supporting action of adjacent beams is considered, the expenditure incurred for hexagonal towers is somewhat less.

2.4.4 Based on the type of material sections.

Based on the sections used for fabrication, towers are classified into angular and hybrid towers (with tubular and angle bracings). Lattice towers are usually made of bolted angles. Tubular legs and bracings can be economic, especially when the stresses are low enough to allow relatively simple connections. Towers with tubular members may be less than half the weight of angle towers because of the reduced wind load on circular sections. However the extra cost of the tube and the more complicated connection details can exceed the saving of steel weight and foundations.

2.4.5 Based on the number of segments.

The towers are classified based on the number of segments as Three slope tower; Two slope tower; Single slope tower; Straight tower.

2.5 Characteristics

Comparison of a generic "true" arch (left) and a corbel arch (right).

A dome can be thought of as an arch which has been rotated around its central vertical axis. Thus domes, like arches, have a great deal of structural strength when properly built and can span large open spaces without interior supports. Corbel domes achieve their shape by extending each horizontal layer of stones

inward slightly farther than the previous, lower, one until they meet at the top. These are sometimes called false domes. True, or real, domes are formed with increasingly inward-angled layers of voussoirs which have ultimately turned 90 degrees from the base of the dome to the top.

A compound dome (red) with pendentives (yellow) from a sphere of greater radius than the dome.

Drums, also called tholobates or tambours, are cylindrical or polygonal walls supporting a dome which may contain windows. When the base of the dome does not match the plan of the supporting walls beneath it (for example, a circular dome on a square bay), techniques are employed to transition between the two. The simplest technique is to use diagonal lintels across the corners of the walls to create an octagonal base. Another is to use arches called squinchs to

span the corners, which can support more weight. The invention of pendentives, triangular segments of an even larger dome filling the spaces between the circular bottom of the dome and each of the four corners of the square base, superseded the squinch technique.

Domes can be divided into two kinds: simple and compound, depending on the use of pendentives. Pendentives are triangular sections of a sphere used to blend the curved surface of a dome with the flat surfaces of supporting walls. In the case of the simple dome, the pendentives are part of the same sphere as the dome itself; however, such domes are rare. In the case of the more common compound dome, the pendentives are

part of the surface of a larger sphere below that of the dome itself and form a circular base for either the dome or a drum section.

Domes have been constructed from a wide variety of building materials over the centuries: from mud to stone, wood, brick, concrete, metal, glass and plastic.

2.6 Glossary:

Acanthus. The acanthus leaf was used as a decorative motif on the Corinthian capital and later on the Composite capital. The form is a stylized version of the plant's long, slender leaves and pointed flowers.

Aedicule. Small structure intended to house a sacred image or statue. It may also be a niche set into the external wall of a building.

Altar frontal. Decoration of the front of an altar table, often either a relief sculpture or inlay. Usually made of marble but precious materials such as ivory or silver may also be used. Sometimes called antependium.

Altar panel. Large painting of a religious subject, situated above an altar in a church.

Alto-rilievo (High relief). Technique of sculpting in which the figures are considerably raised or detached from the background. In a bas-relief the figures are only slightly raised from the surface.

Amber. Derived from Arabic, amber is a fossilized resin, reddish-yellow in colour and more or less transparant. It has been used from ancient times to make trinkets and jewellery.

Antependium.*Altarfrontal.

Apse. A semi-circular or polygonal projection of a building, with a half dome or conch (bowl-shaped vault). In churches it is at the end of the central nave (sometimes also at the end of the side naves or transept) and houses the main altar and the choir. Two identical, facing apses are known as a double apse and where, as in some Romanesque churches, there are three, a triple apse.

Apsidiole. A small projecting apse forming part of the main apse. A typical element of Gothic and Cluniac architecture.

Arch. An architectural structure supported by columns or pilasters. The classical elements of an arch are: 1) intrados - the underside or soffit of an arch; 2) keystone - a central wedge-shaped block in the upper curved section; 3) extrados - the outer curve of the arch; 4) the impost - the blocks or bands on either side, from which the arch springs;

5) the span - the distance between the two sides. Various types of arches exist, according to the form of the curve: round arch - semicircular with the centre on the springing line; segmental arch - where the span is less than the diameter and the curve is semi-circular; drop arch - where the span is greater than the radii; pointed arch - having two arcs drawn from centres on the springing line; horseshoe -where the blocks at the springing line turn inwards; trefoil arch - rising from the apexes of two half arches; flying buttress - the two sides rest on staggered imposts.

Architrave. The lowest of the three main elements of an entablature. Also a moulded frame around a door or window.

Art Nouveau. Highly decorative artistic style, popular at the end of the 19th and beginning of the 20th century. Heavy use is made of ornamentally curving lines and shapes derived from flower and plant motifs.

Ashlar. Large square block of stone usually used as quoins on the outer corners of buildings decorated with rustication.

Atlas. Male version of a caryatide, a sculpted figure used instead of a column to support an entablature. Also called telamon.

Attic. Decorative architectural element situated above the cornice of a building and concealing the roof from view.

Baptismal font. Usually made of stone or marble and of various shapes, containing the holy water used during the ritual of baptism (* baptistery).

Baptistery. Religious building of circular design where the baptismal font is housed. Usually built beside or in front of a church or cathedral.

Baroque. Style of art popular in Italy and throughout Europe in the 17th century. It consisted of rich and elaborate detail and complex design. The term possibly derived from the Spanish barrueca (a rare type of pearl with an uneven shape) which later assumed the French form, baroque.

Base or basement. Lowest part of a building on which the entire structure rests. Also the lowest element of an order supporting the shaft of a column.

Basilica. In ancient Rome the basilica was a public building which served several purposes of an institutional nature, both civil and religious. The building was generally rectangular and was divided by colonnades. The wall at one end formed a semi-circular or rectangular apse. The term later came to mean a Christian church which adopted the same design as the Roman basilica.

Bas-relief. * Alto rilievo.

Baths. Roman baths consisted of a complex of buildings which were used as public baths and meeting place. They usually consisted of a series of rooms containing basins, baths and pools with warm, tepid and cold water (known as the calidarium, the tepidarium and the frigidarium); there was also a laconicum (a steam bath) and a apodyterium (changing room).

Battlements. A form of indented parapet around the top of castles and towers which may either be defensive or decorative. A Guelf battlement was rectangular while the solid upright blocks (merlons) of a Ghibelline battlement were further indented with a 'V' shape.

Bay. Space limited by two adjacent weight-bearing structures (columns, pilasters etc.). In churches the bay is also an area of the nave defined by four adjacent columns or pilasters in facing pairs. Here, the bay generally has a cross vault ( * vault).

Bell tower (Campanile). Structure in the shape of a tower, often incorporated into the outer wall of a church, though it may also be free-standing. The church bells are housed in the upper section.

Bottega (it.). Derived from the Latin apothèca, in turn derived from the Greek term apothèke. Room or rooms inside a building, opening onto the street and used for either a commercial activity or as an artist's or craftsman's workshop.

Bracket. * Corbel.

Bronze. Metal resulting from the fusion of copper and tin, occasionally with the addition of other metals. Used for figurines and statues.

Byzantine art. Figurative art which came into being around the 4th century A.D. in the eastern

Roman empire. The name derives from Byzantium, another name for Constantinople, the eastern capital. The style continued for over one thousand years, surviving until the fall of Constantinople to the Turks in 1453. The earliest works of art date from the 6th century when Byzantine art developed its own particular style (I Golden Age). Following a lengthy period of decline caused by the spread of iconoclasm which forbade the representation of religious subjects, it flourished once more during the reign of the Macedonian dynasty (867-1057, II Golden Age) and under the dynasty of the Palaeologus Emperors (1261-1453 Byzantine Renaissance). Byzantine art produced architectural works of art (Hagia Sophia in Constantinople, 7th-century, the Basilica of S. Apollinare Nuovo and S. Apollinare in Classe in Ravenna, 8th-9th century), magnificent mosaics (Ravenna, the cathedral of Monreale in Palermo), as well as icons and illuminated manuscripts.

Campanile. * Bell tower.

Cantoria. Choir gallery, usually raised, for the choir of singers in a church.

Cardo. Latin term for the main road running in a north-south direction through a town or city and crossing the decumanus which ran from west to east.

Carroccio (it.). In the 'free comunes' during the Middle Ages, the carroccio was a large wagon with four wheels drawn by oxen and symbolized the independence of the city. During periods of war, it was brought to the battlefield decorated with all the emblems and insignia of the city, the war bell and an altar.

Cartoon. A charcoal drawing made on card used in the making of large works of art, especially frescoes. The outline is then nicked out with a small knife or pricked out with an awl and placed on the surface to be painted. The form is then dusted with coal powder which leaves the outline of the picture to be painted on the surface.

Cathedral. The main church of a bishopric. The bishop officiates at the religious ceremonies and practices his spiritual teachings here.

2.7 Check your progress:

1. Explain Structural Action2. Explain Dome3. Explain Characteristics of Dome

2.8 Reference:

• "The Nijni-Novgorod exhibition: Water tower, room under construction, springing of 91 feet span", "The Engineer", № 19.3.1897, P.292-294, London, 1897.

• William Craft Brumfield, "The Origins of Modernism in Russian Architecture", University of California Press, 1991, ISBN 0-520-06929-3.

• Elizabeth Cooper English: “Arkhitektura i mnimosti”: The origins of Soviet avant-garde rationalist architecture in the Russian mystical-philosophical and mathematical intellectual tradition”, a dissertation in architecture, 264p., University of Pennsylvania, 2000.

• "Vladimir G. Suchov 1853-1939. Die Kunst der sparsamen Konstruktion.", Rainer Graefe, Jos Tomlow und andere, 192 S., Deutsche Verlags-Anstalt, Stuttgart, 1990, ISBN 3-421-02984-9.

• ^ Ricker, Nathan Clifford (1912) [1912]. A Treat on Design and Construction of Roofs. New York: J. Wiley & Sons. pp. 12. Retrieved 2008-08-15.

• ^ Maginnis, Owen Bernard (1903). Roof Framing Made Easy (2nd edition ed.). New York: The Industrial Publication Company. pp. 9. Retrieved 2008-08-16.

• ^ a b c Hibbeler, Russell Charles (1983) [1974]. Engineering Mechanics-Statics (3rd edition ed.). New York: Macmillan Publishing Co., Inc.. pp. 199–224. ISBN 0-02-354310-8.

• ^ Wingerter, R., and Lebossiere, P., ME 354, Mechanics of Materials Laboratory: Structures, University of Washington (February 2004), p.1

• ^ Merriman, Mansfield (1912) [192]. American Civil Engineers' Pocket Book. New York: J. Wiley & Sons. pp. 785. Retrieved 2008-08-16. "The Economic Depth of a Truss is that which makes the material in a bridge a minimum."

• ^ Bethanga Bridge at the NSW Heritage Office; retrieved 2008-Feb-06• ^ A Brief History of Covered Bridges in Tennessee at the Tennessee Department

of Transportation; retrieved 2008-Feb-06• ^ The Pratt Truss courtesy of the Maryland Department of Transportation;

retrieved 2008-Feb-6• ^ Tempe Historic Property Survey at the Tempe Historical Museum; retrieved

2008-Feb-06

2.9 Check your progress answers

1. Refer 2.12. Refer 2.33. Refer 2.4

Unit 3: Conical roofs

3.1 Introduction3.2 Location3.3 The listed historic monument3.4 Date of building3.5 Layout of the buildings3.6 Architecture3.7 Types of conical roofing

3.7.1 Corrugated fiber roofing3.7.2 Hi-tech roofing3.7.3 Everest Roofing3.7.4 Metal roofing

3.8 Roofs3.9 Types of roofs

3.9.1 Flat roof3.9.2 Earth roof3.9.3 Monopitched Roof3.9.4 Double-pitched (Gable) roof3.9.5 Hip roof3.9.6 Conical-shaped roof

3.10 Glossary3.11 Check your Progress3.12 Reference3.13 Answer to check your Progress

3.1 Introduction:

The designation Cabanes du Breuil is applied to the former agricultural dependencies of a farm located at the place known as Calpalmas at Saint-André-d'Allas, in the Dordogne department in France. Dating from the 19th century, if not the very early 20th century, these buildings share two distinguishing features, their being covered by a dry stone corbelled vault underneath a roofing of stone tiles and their being in clusters.

3.2 Location

The Cabanes du Breuil are located 9 km from Sarlat and 12 km from Les Eyzies, at a place called Calpalmas. They make up the outbuildings of a former agricultural farm comprising a single-storey house with a two-sided roof of stone tiles over wooden trusses, of a type commonly found in the Sarlat region. The farmyard gate bears an inscribed date: 1841.

How the designation originated

According to both Napoleonic and modern-day land registers, the name of the place is not "Le Breuil" but "Calpalmas". "Le Breuil" (also spelt "Le Breuilh") is, to be precise, the name of a nearby hamlet.

The designation "Cabanes du Breuil", although lacking in accuracy, was made popular - whether in its original form or under the variant "Bories du Breuil" - by the local monthly Périgord Magazine in the 1970s, and more generally by regional tourist brochures, not forgetting postcards from the 1980s onwards.

3.3 The Listed Historic Monument

Official protection was bestowed on the stone huts following a proposal made by a visitor who was struck with their beauty and uniqueness. First, the site was listed in 1968, then in May 1995, the huts themselves were declared listed buildings (together with the façades and stone roofs of the farmhouse and its bake house).

On several occasions, the stone huts underwent major restoration work (at the turn of the 1970s and again in the 1990s) (see Jean-Pierre Chavent in Bibliography). A number of alterations were made to roof ridges: the separate roofs of the huts in group 2 were merged together over two thirds of their height so as to mimick the ondulating ridge of group 1; likewise, the ridge line of the hut leaning against the gable of the bake house, originally a curve and countercurve, was straightened to be made parallel to the ridge of the bake house.

3.4 Date of Building

According to the Cabanes du Breuil's Internet site (see External Links), "In the Middle Ages, the cabanes du Breuil were inhabited by the Benedictine monks of Sarlat", a proof of this being a sale deed of "1449, the earliest written trace testifying to their presence". However, the alleged deed remains unpublished and its whereabouts and content are unknown. Besides, Calpalmas is a different place from Le Breuil.

In the book "Les cabanes en pierre sèche du Périgord" (The Dry Stone Huts of Périgord) published in 2002 (see Bibliography), the author states that "Le Breuil was once a possession of the Benedictines in the Chapter of Sarlat Bishopric, but nowhere is there any mention that the stone huts we see today already existed." He adds: "Twenty years ago, the landlady used to boast that the stone huts had been built or entirely rebuilt by her grandfather, at the beginning of the 20th century."

Again, according to the Cabanes du Breuil's website, rural craftsmen - a blacksmith, a harness maker and a weaver - are said to have rented some of the huts in order to practise their craft (see www.cabanes-du-breuil.com/histoire.htm). But the hut allegedly used by a blacksmith contains none of the requisite paraphernalia for that trade, and it was endowed with a faux chimney piece in 1988. Besides, a postcard from the 1970s shows the same building being used as a sheepfold: a dozen sheep are seen leaving it under the guidance of the then farmer and his wife.

3.5 Layout of the Buildings

A row of five huts arranged in an arc of circle line the uphill side of the farm:

• The first two huts are in fact one and the same building (presumably a hay store), of a rectangular ground plan with rounded corners; a smaller, circular hut abuts its far end; as all three roofs are connected by a curving ridge, one gets the impression of a single structure with threefold roofing.

• The next two huts are set at right angles to each other, the first one abutting on to the gable wall of the bake house, the second one leaning against the latter's side wall (the bake house is a small building with a two-sided roof clad in stone tiles, standing against the farmhouse's gable wall).

• A group of two conjoined huts, whose roofs are attached to each other, stands parallel to the first group a few metres up the hill.

• Lastly, further up the slope, two isolated huts, one small, the other bigger, plus a third, smaller one at the entrance to the site.

3.6 Architecture

From an architectural and morphological point of view, each hut consists of three different parts:

• a base of stones laid with earth mortar (not to be confused with dry stone walling);

• a vault of corbelled and outward-inclining stones;• over the vaulting, a bell-shaped roof of stone tiles with outward-flaring eaves.

Because of the slope, the uphill roof eaves are nearly at ground level.

Entrances look downhill and extend all the way up to the roof eaves. Their uprights are made of dressed stones alternating as headers and stretchers. They are capped by outer and inner wooden lintels, right under the eaves. They are fitted with a wooden door.

Each roof is adorned with a large dormer window (or hay window) with mortared stone jambs and a projecting roof supported by outer and inner wooden lintels. There is a break in the eaves right under each dormer. A number of windows can be accessed (presumably by poultry) through a flight of three or four projecting stones laid into the wall beneath.

Each roof is capped by a large, circularly carved stone slab. Inside the huts, at the height where corbelling starts, wooden beams serve as a rudimentary upper floor.

In their forms and techniques, the stone huts show an outstanding architectural unity, a likely hint that they belong to one and the same period or are the work of one and the same craftsman. Architecturally speaking, they are similar to the stone huts with conical or bell-shaped roofs that can be seen in other parts of the Sarlat region and hark back to a building campaign extending from the mid 18th century to the late 19th century..

3.7 Types of Conical roofing

One Billion Sq.m of Roofing in India. Everest Roofing Solutions include Everest AC Roofing and Everest Hi-Tech, Everest Rooflight and Metal Roofing Everest Roofing, which is fibre cement corrugated roofing sheets, is being used extensively throughout the country for factories, power plants, stadiums, schools, urban and rural houses, to name a few. Everest Hi-Tech is a high impact resistancenon-asbestos corrugated modern roofing system . Everest Rooflight -another high quality polycarbonate roofing sheet and Everest Metal roofing.

3.7.1Corrugated Fiber Roofing

Everest corrugated sheets are made from the finest quality of cement and fibre through a specially developed fibre orientation process. They undergo rigorous quality control - standards which are much higher than ISI - giving you a product of lasting value.

3.7.2 Hi-Tech Roofing

Everest Hi-Tech is a unique product manufactured in India. it is a corrugated cement roofing sheet reinforced with a blend of strong factory produced fibres including HIPP (High impact Polypropylene). These imported fibres replace asbestos and give your roof high impact resistance. Everst Hi-Tech provides high sound insulation from rain and thermal insulation from heat, saving you huge costs of additional insulation. Everest Hi--Tech is available in a range of colours.

3.7.3 Everest Rooflight Everest Rooflight - another quality product from the house of Everest - is a high quality polycarbonate roofing sheet manufactured using virgin polycarbonate resins through the co-extrusion process. This process of quality raw materials ensures uniform thickness, excellent UV resistance, optimum strength and long life of the product. Everest Rooflight's high impact strength and impressive physical properties, makes it an ideal choice to provide natural light and compliment the industrial, commercial and agricultural roofing systems.

3.7.4 Metal Roofing

With high precision roll forming and component forming machines you can be assured about the quality, reliability and integrity of Everest Metal Roofing Solutions. Everest Metal Roofing Solutions are available in Galvalume (Bare and coloured) and prepainted galvanised iron. These roofing solutions are available in a range of superior and aesthetic colours for roofing and wall cladding. These roofing solutions have excellent corrosion and weathering resistance thereby ensuring low maintenance and long durability of the roofing system.

3.8 Roofs

A roof is an essential part of any building in that it provides the necessary protection from rain, sun, wind, heat and cold. The integrity of the roof is important for the structure of the building itself as well as the occupants and the goods stored within the building.

The roof structure must be designed to withstand the dead load imposed by the roofing and framing as well as the forces of wind and in some areas, snow or drifting dust. The roofing must be leakproof, durable and perhaps satisfy other requirements such as being fire resistant, a good thermal insulator or high in thermal capacity.

There is a wide variety of roof shapes, frames and coverings from which to choose. The choice is related to factors such as the size and use of the building, its anticipated life and appearance, and the availability and cost of materials. Roofs may be classified in three ways:

• 1 According to the plane of the surface, i.e. whether it is horizontal or pitched.

• 2 According to the structural principles of the design, i.e. the manner in which the forces set up by external loads are resolved within the structure.

• 3 According to the span.

Flat and pitched roofs: A roof is called a flat roof when the outer surface is within 5° of horizontal whereas a pitched roof has a slope of over 5° in one or more directions. Climate and covering material affect the choice between a flat or pitched roof. The affect of climate is less marked architecturally in temperate areas than in those with extremes of climate. In hot, dry areas the flat roof is common because it is not exposed to heavy rainfall and it forms a useful out-of-doors living room. In areas of heavy rainfall a steeply pitched roof drains off rainwater more quickly.

Two-dimensional roof structures have length and depth only and all forces are resolved within a single vertical plane. Rafters, roof joists and trussers fall in this category. They fulfill only a spanning function and volume is obtained by using several two-dimensional members carrying secondary two-dimensional members (purling) in order to cover the required span.

Three-dimensional structures have length, depth and also breadth, and forces are resolved in three dimensions within the structure. These forms can fulfill a covering and enclosing function as well as that of spanning and are now commonly referred to as 'space structures'. Three dimensional or space structures include cylindrical and parabolic shells and shell domes, multi-curved slabs, folded slabs and prismatic shells, grid structures such as space frames, and suspended or tension roof structures.

Long and short span roofs: Span is a major consideration in the design and choice of a roof structure although functional requirements and economy have an influence as well.

Short spans, up to 8m, can generally be covered with pitched timber rafters or light-weight trusses either pitched or flat. Medium spans of 7 to 15 or 16m require truss frames designed of timber or steel.

Long spans of over 16m should, if possible, be broken into smaller units. Otherwise, these roofs are generally designed by specialists using girder, space deck or vaulting techniques.

In order to reduce the span and thereby reduce the dimensions of the members, the roof structure can be supported by poles or columns within the building or by internal walls. However, in farm buildings a free span roof structure will be advantageous if the farmer eventually wants to alter the internal arrangement of the building. The free space without columns allows greater convenience in maneuvering equipment as well.

Ring beam: In large buildings e.g. village stores, that have block or brick walls, a 150mm square reinforced concrete beam is sometimes installed on top of the external walls instead of a wall plate. The objective of this ring beam, which is continuous around

the building, is to carry the roof structure should part of the wall collaps in an earth tremor. It will also provide a good anchorage for the roof to prevent it lifting and reduce the effects of heavy wind pressure on the walls and unequal settlement.

3.9 Types of Roofs

3.9.1 Flat Roof

The flat roof is a simple design for large buildings in which columns are not a disadvantage. Simple beams can be used for spans up to about Sm. but with longer spans it is necessary to use deep beams, web beams or trusses for adequate support. Because farm buildings often need large areas free of columns, flat roofs with built-up roofing are not common. Flat roofs are prone to leak. To prevent pools of water from collecting on the surface they are usually built with a minimum slope of 1:20 to provide drainage.

The roof structure consists of the supporting beams, decking, insulation and a waterproof surface. The decking, which provides a continuous support for the insulation and surface, can be made of timber boards, plywood, chipboard, metal or asbestos-cement decking units or concrete slabs.

The insulation material improves the thermal resistance and is placed either above or below the decking.

The most common design for a waterproof surface is the built-up roof using roofing felt. This material consists of a fibre, asbestos or glass-fibre base which has been impregnated with hot bitumen. The minimum pitch recommended for built-up roofs is 1:20 or 3° which is also near the maximum if creeping of the felt layers is to be prevented.

For net roofs two or three layers of felt are used, the first being laid at right angles to the slope commencing at the eaves. If the decking is timber the first layer is secured with large flat-head felting nails and the subsequent layers are bonded to it with layers of hot bitumen compound. If the decking is of a material other than timber all three layers are bonded with hot bitumen compound. While it is still hot the final coat of bitumen is covered with a layers of stone chippings to protect the underlying felt, provide additional fire resistance and give increased solar reflection. An application of 20 kg/m² of 12.5mm chippings of limestone, granite or light-coloured gravel is suitable.

Where three layers of roofing felt are used and properly laid, flat roofs are satisfactory in rainy areas. However, they tend to be more expensive than other types and require maintenance every few years.

3.9.2 Earth Roof

Soil-covered roofs have good thermal insulation and high capacity for storing heat. The traditional earth roof is subject to erosion during rain, requires steady maintenance to prevent leakage. The roof is laid rather flat with a slope of 1:6 or less.

The supporting structure should be generously designed of preservative - treated or termite-resistant timber of poles, and inspected and maintained periodically, as a sudden collapse of this heavy structure could cause great harm. The durability of the mud cover can be improved by stabilizing the top soil with cement, and it can be waterproofed by placing a plastic sheet under the soil.

3.9.3 Monopitched Roof

Monopitch roofs slope in only one direction and have no ridge. They are easy to build, are comparatively inexpensive and are recommended for use on many farm buildings. The maximum span with timber members is about 5m, thus wider buildings will require intermediate supports. Also wide buildings with this type of roof will have a high front wall which increases the cost and leaves the bottom of that wall relatively unprotected by the roof overhang. When using corrugated steel or asbestos-cement sheets, the slope should not be less that 1:3(17 to 18°). Less slope may cause leakage as strong winds can force water up the slope.

The rafters can be of round or sawn timber or when wider spans are required, of timber or steel trusses which can be supported on a continuous wall or on posts. The inclined rafters of a pitched roof meet the wall plates at an angle and their load tends to make them slide off the plate. To reduce this tendency and to provide a horizontal surface through which the load may be transferred to the wall without excessively high compressive forces, the rafters in pitched roofs are notched over the plates. To avoid weakening of the rafter, the depth of the notch (seat cut) should not exceed one-third that of the rafter. When double rafters are used a bolted joint is an alternative. The rafters should always be thoroughly fixed to the walls or posts to resist the uplifting forces of the wind.

3.9.4 Double-pitched (Gable) Roof

A gable roof normally has a centre ridge with a slope to either side of the building. With this design a greater free span (7 to 8m) is possible with timber rafters than with a monopitch roof. Although the monopitch design may be less expensive in building widths up to 10m the inconvenience of many support columns favors the gable roof. The gable roof may be built in a wide range of pitches to suit any of several different roofing materials. A number of the elements that are associated with a gable roof. The following description is keyed to the figure:

• The bottom notch in the rafter that rests on the plate is called the seat cut or plate cut.

• The top cut that rests against the ridge board is called the ridge cut.

• The line running parallel with the edge of the rafter from the outer point of the seat cut to the centre of the ridge is called the work line.

• The length of the rafter is the distance along the work line from the intersection with the corner of the seat cut to the intersection with the ridge cut.

• If a ridge board is used, half the thickness of the ridge board must be removed from the length of each rafter.

• The rise of the rafter is the vertical distance from the top of the plate to the junction of the workline at the ridge.

• The run of the rafter is the horizontal distance from the outside of the plate to the centreline of the ridge.

• The portion of the rafter outside the plate is called the rafter tail.• The collar beam or cross tie prevents the load on the rafters from forcing the

walls apart which would allow the rafter to drop at the ridge. The lower the collar beam is placed, the more effective it will be. Occasionally small buildings with strong walls are designed without collar beams. The only advantage of this design is the clear space all the way to the rafters. Scissors trusses, as shown in Figure 5.51, at the same time allow some clear space.

• The right-hand rafter shows purlins spanning the rafters and supporting a rigid roofing material such as galvanized steel or asbestos-cement roofing.

• The left-hand rafter is covered with a tight deck made of timber boards plywood or chipboard. It would be covered with a flexible roofing material such as roll asphalt roofing.

• The left-hand cave is enclosed with a vertical facia board and a horizontal soffit board.

• The pitch is shown on the small triangle on the right side.

The angle of the ridge and seat cuts can be laid out on the rafter using a steel carpenter's square and the appropriate rise and run values both on the outside of the blades or both on the inside of the blades of the square, 30 and 20cm in the example in Figure 5.42. The length may be found with the pythagorean theorem using the rise and run of the rafter. The length is measured along the workline.

When a gable roof must span more than 7 to 8m, trusses are usually chosen to replace plain rafters. For large spans the trusses will save on total material used and provide a stronger roof structure. For solid roof decks the trusses are usually designed to be spaced approximately 600mm on centre, while for rigid roofing mounted on purling, a truss spacing of 1200mm or more is common.

The agricultural extension can provide designs for the spans, spacings and loads that are commonly found on farms.

3.9.5 Hip Roof

A hip roof has a ridge in the centre and four slopes. It is much more complicated in its construction, necessitating the cutting of compound angles on all of the shortened rafters and the provision for deep hip rafters running from the ridge to the wall plate to

carry the top ends of the jack rafters. The tendency of the inclined thrust of the hip rafters to push out the walls at the corners is overcome by tying the two wall plates together with an angle tie. At the hips and valleys the roofing material has to be cut at an angle to make it fit. The valleys are prone to leakage and special care has to be taken in the construction.

Four gutters are needed to collect the rain water from the roof, but that does not mean that there is any increase in the amount of water collected. Because this is an expensive and difficult way to roof a building, it should be recommended only where it is necessary to protect mud walls or unplastered brick walls against heavy driving rain and for wide buildings to reduce the height of the end walls.

3.9.6 Conical-shaped Roof

The conical roof is a three dimensional structure that is commonly used in rural areas. It is easy to assemble and can be built with locally available materials, making it inexpensive. It must be constructed with a slope appropriate to the roofing materials used to prevent it from leaking. The conical roof design is limited to rather short spans and to either circular or small square buildings. It does not allow for any extensions. If modern roofing materials are used there is considerable waste because of the amount of cutting necessary to obtain proper fit.

A conical-shaped roof structure requires rafters and purling, and in circular buildings, a wall plate in the form of a ring beam. This ring beam has three functions:

• a to distribute the load from the roof evenly to the wall, • b to supply a fixing point for the rafters, and• c to resist the tendency of the inclined rafters to press the walls outward radially

by developing tensile stress in the ring beam. If the ring beam is properly designed to resist these forces and secondary ring beams are installed closer to the center, a conical roof can be used on fairly large circular buildings.

In the case of square buildings, the outward pressure on the walls from the inclined rafters cannot be converted to pure tensile stress in the wall plate. Instead, it resembles the hip roof structure and should be designed with the angle ties across the wall plates at the corners.

3.10 Glossary

Aisled BarnA type of roof truss construction that has aisles down the side to increase the span;

Anti ponding stripIn roofing, tiles and slating. A flat strip of metal flashing material fixed to the top o the fascia and to the rafters to stop the sarking sagging so that no water can pond inside the fascia.;

Apron FlashingA flashing that seals the top edge of a roof against a wall or chimney etc.;

Arcade postA post at the side of a cruck truss to share the load and shorten the span. Usually seen in pairs in aisle barn construction.;

Arched braceA curved brace, normally out of naturally curved timbers used to stiffen a roof frame. Usually in pairs.;

Asbestos containing roofingAny roofing material containing asbestos fibres. Typically produced in corrugated sheets, imitation slates or imitation shingles. Banned as a new construction material since around 2000 in most countries.;

Ashlar pieceInside roof spaces, lofts and garrets, the short vertical pieces fixed between the floor and the rafters to form short walls. (Not to be confused with ashlar masonry).;

AshlaringThe short side wall frames in lofts, attics, garrets etc.;

Barge or Verge FlashingA flashing that seals the end of a roof against the verge or gable end.;

BargeboardA board or roll formed metal section fixed at the gable to finish and protect the roof to gable wall joint. ;

Barrel roofA roof with a semi-circular cross section;

Cambered Fink or Cambered Warren trussA Fink or Warren truss with a raised center bottom chord.;

Cantilever trussA truss where one end is allowed to run over the support. Part of the truss is said to be a cantilever.;

Ceiling battensSupported by and running at right angles to the ceiling-joists the battens typically timber or roll formed metal support the actual ceiling lining material.;

DendrochronologyIn old timber framed buildings it is used to date the time that trees were felled, and so the construction date, by various methods including study of the annual growth rings and carbon dating.;

DendrologyThe branch of botany involving the study of trees and shrubs. ;

EavesThe lower part of a sloping roof, the part of a roof which overhangs the walls. ;

Eaves braceA brace between a wall and the eaves to increase the overhang at the eaves.;

Eaves bracketA bracket between a wall and the eaves to increase the overhang at the eaves.;

Eaves lining

A sheeting or lining material to seal the underside of an overhanging eaves or verge. ;

Fabric roofsRoofs made from flexible membranes and tensioned cables. From simple shade structures to complex permanent structures.;

Fan trussSimilar to a W truss but with extra vertical ties added. Said that each sides web radiate like a fan.;

Fascia boardA horizontal board or roll formed metal fitting usually fixed vertically to the ends of the rafters ;

Fascia gutter1.) A rainwater gutter that is fixed to a fascia board.2.) A purpose made rainwater gutter that is fixed to the ends of the rafters and also performs the function of a fascia board.;

Fascia purlinUsually in steel shed roofs, a rolled formed comnination of a fascia and a purlin. Can be ordred to suit varying roof pitches.;

GableThe vertical triangular end of a pitched roof. It often is a continuation of the wall it is sat on or it can be made from different materials.;

Gable dormerA vertical window placed in a sloping gable roof. ;

Gable roofsA roof with two sloping surfaces from the ridge (usually in the center, joining at the side walls to form gable ends. ;

Gable VentA louvred vent in a gable wall.;

Gablet1). A small gable that projects from another roof surface, similar to a dormer but with no walls. It can indeed be sat at the top of a gable end but the term is rarely used in this respect any more. 2). A triangular coping to a wall or buttress.;

3.11 Check your progress:

1. Explain Type of Conical Roofs2. Explain Roofs3. Explain Type of roofs

3.12 Reference:

1. ^ Breuil is a frenchified form of the occitan word brueilh, meaning a clump of trees, a copse, a wooded river bank.

2. ^ "The name 'cabanes' was not deemed fit enough to attract tourists", the Sarlat Office de Tourisme website confesses.

3. ^ Curiously enough, no postcards of the site were made in the golden age of postcards (late 19th-century - early 20th century).

4. ^ In a 1971 article, Jean-Pierre Chavent reports that "In Marquay, he was told that the stone huts had been quite expensively restored by the Monuments Historiques office".

5. ^ Postcard published by Pierre Artaud & Cie, Les éditions du Gabier, BP 61, 27190 Conches. The caption says: "Quercy and Perigord boast a varied architecture of pigeon houses and sheep shelters that fit nicely with a landscape that is both unspoiled and soothing."

6. ^ A header has its smallest side as part of the facing while its greater part traverses the thickness of the wall; on the contrary, a stretcher has its full length sideways in the wall's stonework.

7. ^ In a photo taken in 1971, a bunch of hay can be seen sticking out of a dormer window.

8. ^ See Christian Lassure (text), Dominique Repérant (photos), Cabanes en pierre sèche de France, Edisud, 2004, in particular chapter entitled "La tradition constructive" (constructional tradition).

9. ^ With the exception of the interior of the huts bordering the uphill side of the farm yard.

10. ^ le site est ouvert à la visite tous les jours.

3.13 Check your progress answers

1. Refer 3.72. Refer 3.83. Refer 3.9

Unit 4: Circular cylindrical shells by ASCE Manual No.31

4.1 Introduction4.2 Fixed response impulse method4.3 Experimental cylinder4.4 Fixture Design4.5 Finite element analysis4.6 Instrumentation and experiment set-up4.7 Impact testing and data acquisition4.8 Glossary4.9 Check your progress4.10 Reference4.11 Answer to Check your progress

4.1 Introduction

A circular definition is one that uses the term(s) being defined as a part of the definition or assumes a prior understanding of the term being defined. Either the audience must already know the meaning of the key term(s), or the definition is deficient in including the term(s) to be defined in the definition itself. Such definitions lead to a need for additional information that motivated someone to look at the definition in the first place and, thus, violate the principle of providing new or useful information. If someone wants to know what a cellular phone is, telling them that it is a "phone that is cellular" will not be especially illuminating. Much more helpful would be to explain the concept of a cell in the context of telecommunications, or at least to make some reference to portability. Similarly, defining dialectical materialism as "materialism that involves dialectic" is unhelpful. For another example, we can define "oak" as a tree which has catkins and grows from an acorn, and then define "acorn" as the nut produced by an oak tree. To someone who does not know which trees are oaks, nor which nuts are acorns, the definition is inadequate. Consequently, many systems of definitions are constructed according to the vicious circle principle in such a way that authors do not produce viciously circular definitions.

A circular definition occurred in an early definition of the kilogram.[dubious – discuss] The kilogram was originally defined as the mass of one liter of water at standard pressure and the temperature at which it is densest (which is about 4 °C). The unit of pressure is the newton per square meter, where a newton is the force that accelerates one kilogram one meter per second squared. Thus the kilogram was defined in terms of itself. Since water is nearly incompressible, this circularity is of no consequence — with each iteration of the "circle," the resulting measure of a kilogram rapidly converges. Even so, to clear up

any confusion, the kilogram was later defined as the mass of a certain piece of metal in Sèvres.

A circular definition also crept into the classic definition of death that was once "the permanent cessation of the flow of vital bodily fluids", which raised the question "what makes a fluid vital?"

A branch of mathematics called non-well-founded set theory allows for the construction of circular sets. Circular sets are good for modelling cycles and, despite the field's name, this area of mathematics is well founded. Computer science allows for procedures to be defined by using recursion. Such definitions are not circular as long as they terminate.

Dictionaries are sometimes used erroneously as sources for examples of circular definition. Dictionary production, as a project in lexicography, should not be confused with a mathematical or logical activity, where giving a definition for a word is similar to providing an explanans for an explanandum in a context where practitioners are expected to use a deductive system.. While, from a linguistic prescriptivist perspective, any dictionary might be believed to dictate correct usage, linguists recognize that looking up words in dictionaries is not itself a rule-following practice independent of the give-and-take of using words in context..

Thus, the example of a definition of oak given above (something that has catkins and grows from acorns) is not completely useless, even if "acorn" and "catkin" are defined in terms of "oak", in that it supplies additional concepts (e.g., the concept of catkin) in the definition. While a dictionary might produce a "circle" among the terms, "oak", "catkin", and "acorn", each of these are used in contexts (e.g., those related to plants, trees, flowers, and seeds) that generate an ever-branching network of usages.

Definitions can be broadly or narrowly circular. Narrowly circular definitions simply define one word in terms of another. A broadly circular definition has a larger circle of words. For example, the definition of the primary word is defined using two other words, which are defined with two other words, etc., creating a definitional chain. This can continue until the primary word is used to define one of the words used in the chain, closing the wide circle of terms.

If all definitions rely on the definitions of other words in a very large, but finite chain, then all text-based definitions are ultimately circular. Extension (semantics) to the actual things that referring terms like nouns stand for, provided that agreement on reference is accomplished, is one method of breaking this circularity, but this is outside the capacity of a text-based definition.

Identification of the natural frequencies of a structure is normally done through Experimental Modal Analysis (EMA). EMA of a structure is used to obtain its modal characteristics i.e., natural frequency, damping coefficient and mode shape. In this paper,

a circular cylindrical shell under shear diaphragm boundary condition is investigated for its modal characteristics. The modal behavior is studied by exciting the cylinder at one or more points using an impact hammer and observing the response at certain points. The time domain data is collected then transformed in to frequency domain using Fast Fourier Transforms (FFT) to calculate the Frequency Response Function (FRF) of the structure. Peaks in the FRF represent resonances of the structure at the forcing frequencies, which helps in identifying the natural frequencies of the structure. The mode shape associated with a particular frequency can be obtained from the deformation pattern of the various points for which FRF data was collected. While various methods are being used to collect the excitation and response data in modal analysis, the modal characteristics study of a cylindrical shell uses the fixed response impulse method. This approach is found to be very efficient due to its simplicity and low cost.

4.2Fixed Response impulse method

In fixed response impulse [1] the excitation was applied to the cylinder by using an impact hammer at a number of predetermined points over the surface of the cylinder and the response was measured using an accelerometer at one fixed point. The transfer function i.e., the ratio of response to impact force was measured at each impact point by measuring both the force and the response at that impact point. The mode shape and its corresponding frequency were identified by schematically representing the geometry of the cylinder using the predetermined impact points on the cylinder both longitudinally and circumferentially as grids lying at their locations in a 3-dimensional space. Fitting the response data to the respective grid points helps in identifying the mode shape of the cylinder at a particular natural frequency using the representative shape formed due to thedisplacements of these grids.

4.3 Experimental Cylinder

A thin cylinder of known dimensions and material properties is chosen for the experimental study. The experimental cylinder is of length 28.845 in, radius of 9.94 in, thickness of 0.12 in, Young’s modulus of 3.0 E7 lb.f/in2 Poisson’s ratio of 0.29, and a mass density of 7.324 E-4 lb.sec2/in4.

4.4 Fixture Design

For shear diaphragm boundary condition, the cylinder is supported in the horizontal direction between two vertical octagonal plates mounted near the ends of a circular bar coaxial with the cylinder axis. Each octagonal plate has sixteen adjustable mounting clamps arranged circumferentially, eight internally and eight externally holding the ends of the cylinder at their sharp tip radii. These clamps support the cylinder ends both internally and externally all along its circumference allowing the cylinder to move only in the axial direction [2],

The circular bar rests on the test bed horizontally over two V-shaped supports at its ends This arrangement allows the cylinder together with the supporting discs and the circular bar to be rotated on its own axis. Rotation of the cylinder over the V- supports, aids in impacting the cylinder at the predetermined circumferential grid points without moving the impact hammer along the circumferential direction on the cylinder, while conducting the modal testing using fixed response impulse method.

4.5 Finite Element Analysis

Before setting up the experiment for modal analysis, the modal characteristics of the cylinder were examined using finite element analysis. The finite element mode shapes of various frequencies helps in understanding the cylinder’s vibration behavior and also assists in: choosing the frequency range and mode shapes of interest, selecting suitable accelerometer and impact hammer, selecting locations for accelerometer placement, etc. The placement of the accelerometer is very critical in obtaining valid data. The data obtained won’t be useful if the accelerometer is placed at a node point of the structure’s mode shape for any frequency within the frequency range of interest. The thin uniform circular cylindrical shell used for the Experimental Modal Analysis is modeled and analyzes for its frequencies using normal mode analysis in MSC.NASTRAN [3, 4]. The finite element model shown in Figure 4 has 2304 elements, arranged 64 elements along the cylinder circumference and 36 elements along its cylinder length.

The results for the normal mode analysis of the cylinder are listed in Table 1 are obtained for the first 20 modes in the frequency range 0 to 800 Hz. From the results it was found that, placing the accelerometer at points along the ircumference that is at a distance of ¼th of the cylinder length from the supporting plate would help in apturing all the modes and frequencies of our interest.

4.6 Instrumentation and Experiment set-up

A small and lighter compression type accelerometer is chosen for the purpose. Though light, the accelerometer’s sensitivity is compensated as the structure has modes of higher frequencies and the acceleration levels are higher. Wax is used in attaching the accelerometer to the cylinder because it is fast, clean, easy to use, lightweight and safe. The impact hammer selected for the test is a modally tuned one having an integral force transducer to measure the magnitude of the impact force.

The impact is measured by the compression of the piezoelectric force transducer in the hammer head. For the experiment cylinder a lighter hammer head and a hard tip are chosen to have short impulses with high peak force which provides sufficient energy to excite the frequencies between 0 to 800Hz. An SRS 785 dynamic signal analyzer is selected for our purpose to collect the Frequency Response Function (FRF) for each impact. The accelerometer and impact hammer are connected to the two channels of the analyzer through a signal conditioner.

The signal conditioner provides DC offset voltage to the piezoelectric transducers of the accelerometer and impact hammer, it also amplifies their output signal to connect to the input channels of analyzer. For FRF measurement, the display of the

analyzer is set for dual display format, displaying the forcetime data in the top window and the transfer function (FRF) in the bottom window.

The analyzer is set for manual overload data rejection; this lets the user to see the force time signals in the top window, and allows the user to accept or reject the data by verifying for overload or double hits. The transfer functions and computed FRF’s are stored to a floppy disk to use in further processing. On the experimental cylinder, a total of 153 grid points are marked over its outer surface along its circumference at two locations and along its length in longitudinal direction. Grids points 1 to 63 are marked at equal intervals over the circumference at a circumferential location at 1/4th distance of cylinder length between the two supporting discs.

Grid points 64 to 91 are marked between the supporting discs at equal intervals along the longitudinal direction. Grid points 92 to 153 are marked at equal intervals over the circumference at a circumferential location at 1/2 of the cylinder length. During the test, the accelerometer was placed at a fixed point (grid 1) and the impact will be applied at the 153 grid locations to record the resulting 153 transfer functions. The data stored by the analyzer has to be fed in to “STAR Modal 5.3.2” (Computer software by Spectral Dynamics) to identify the resonant frequencies and mode shapes.

Using Star Modal, the cylinder geometry is represented schematically using the grid points locations in a 3-dimensional space, the FRF collected using the analyzer are associated with their respective grid points to visualize the displacements of each grid location. The displacement of the grid points is used to visualize the mode shape and to identify frequency of each mode shape.

4.7 Impact testing and data acquisition

The frequency analyzer is set to measure the acceleration from the accelerometer signal and force from the impact hammer signal. The test is performed by gently hitting the cylinder at each grid point and measuring the frequency response function over the desired frequency range for each hit using the FFT analyzer. Before accepting the output data, the impact is verified for overloads or double hits by checking at the top window of the FFT analyzer. A total of 153 hits corresponding to 153 grid points were taken and the FRF data for each hit is stored. A schematic of the testing procedure. The FRF data stored is then transferred to the computer to analyze it for identifying the mode shapes and frequency. The measured data from the analyzer was associated to the cylinder geometry using the STAR Modal dynamic analysis software. A curve fit is made for the peaks of the FRF data collected at grid point 1. To sketch the mode shapes a quadrature fit is used to fit the frequency bands selected near each peak. The frequency for each mode is obtained by identifying the peak of each frequency band using a polynomial fit for the curve. The animation of the displaced geometry of each modes is used to identify the corresponding mode shapes.

4.8 Glossary

Strake:- Section of the cylindrical "shell" of the tank/vessel formed by rolling a piece of steel and joining at the seam.Shell:- The cylindrical section of the tank or vessel formed by 1 or more "strakes"Head:- A type of enclosure for the top, bottom or end of a tank. Can range in shape from hemispherical, to a very light dished depth. Heads are formed by pressing a dish in a circular blank and then rolling a "knuckle" around the perimeter to enable a butt weld to the "shell".Cone:- A conical section which is used to form either the bottom, top or end enclosures of the tank/vessel. Formed by rolling a circular pice of material with a segment removed. Once rolled and joined the shape is conical. This can be welded directly to the "shell" or can have a "knuckle" rolled onto it to enable a but weld connection to the "shell"Skirt:- A support system for a vertical vessel whereby a cylindrical section of material is attached to the shell of the tank such that it takes the load of the vessel and provides a level support mechanism.Legs:- An alternative support system whereby a number of sectional members are attached to the vessel shell in order to stand the vessel up.Circumferential weld:- The welded joint around the circumference of the tank/vessel that connects strakes to strakes or the end enclosures.Seam Weld:- The welded joint that joins the rolled "strake" material.Neck:- The opening in a top "cone" of a tank where it extends beyond a simple flange.Manway:- A large opening in the "shell" that enables access by personell to the inside of the tank/vessel.Cladding:- A second skin of material that covers any insulation material that is wrapped around the tank/vessel.Hydrostatic test:- A test for tank/vessel integrity that involves filling the tank/vessel with water to check for leakage.CIP:- Clean in Place system.Dimple plate:- A component of a tank that allows for heating or cooling of the tanks contents by running liquid through a cavity between the "shell" of the tank and a thinner outer skin which has been welded to the shell. After blowing the cavity with high pressure gas the thinner material blisters forming a dimple pattern.

4.9 Check your progress:

1. Explain Circular cylindrical shells2. Explain Experimental cylinder3. Explain fixture design

4.10 Reference:

1.Design and construction of concrete shell roofs by G.S. Rama Swamy - CBS Publishers 2. Fundamentals of the analysis and design of shell structures by Vasant S.Kelkar Robert

T.Swell - Prentice hall, Inc., englewood cliffs, new Jersy - 02632. 3. N.k. Bairagi, Shell analysis, Khanna Publishers, Delhi, 1990.

4. Billington, lthin shsell concrete structures, Mc Graw Hill Book company, New york, St. Louis, Sand Francisco, Toronto, London. 5. ASCE Manual of Engineering practice No.31, design of cylindrical concrete shell roofs ASC, Newyork.6. Construction Management and planning by B.Sengupata and H.Gula(Tata Mcgraw Hill) 7. Construction Management by Atkinson(Elseverir) 8. in principle land practice by EEC beech(Longman) 9. Robert Schultheis, Mary Summer (1999)” management Information Systems - The Mangament View. “ TATA mc Graw Hill Edition, New Delhi. 10. Kwakye, A.A. (1997), “construction Project Administration Adisson Wesley Longman, London 11. Keith Davis, Human Behaviour at work, Mc Graw Hill, USA, 1981. 12. Sehroeder, R.g., Operations Mangement, Mc Graw Hill, USA 1982. 13. james C.Van Horne, Financial Management and policy, prentice Hall of India Pvt. Ltd,, 4th Ed., New Delhi., 1979 14. Varshney R.L and Maheswari, K.l., managerial Economics, Sultan Chand, 1975 15. Frank Harrison, E., The Managerial Decision making process, Houghton Mifflin Co., Boston, 1975.

4.11 Check your progress Answers

1. Refer introduction2. Refer 4.33. Refer 4.4

BLOCK 2 Folded Plates

Geodesic Domes.

Geodesic domes are an example of a curved space frame. They were invented by R.Buckminster Fuller and as was seen in section 1 Structures in Nature examples of Geodesic domes can be found in nature. As was also discussed earlier, domes are not an new development, they have existed for hundreds of years. The geodesic dome is referred to as a braced dome due to the fact that there are bracing members present so that the dome keeps its shape.

The geodesic dome is made up of a network of triangles, this results in the maximum amount of strength and rigidity being obtained while using the minimum amount of materials.

The varying number of triangles is referred to as the frequency and the higher the frequency the greater the resistance of the structure to collapse. Click on the icon to see how the different frequencies change the shape of a Geodesic dome. Geodesic domes can be constructed from metals or plastics and they have many advantages.

Speed of construction - In 1955 he built domes for the air-force and they only took fourteen hours to erect.

Size - the clear span of a dome constructed by Fuller in 1958 was 117m and it had a total weight of 12MN. If you then compare this to St.Peter's Cathedral in Rome which has a diameter of 40m and weighed 100MN.

Using drinking straws and connections try and make a geodesic dome.

Unit 1: Folded Plate structures

1.1 Introduction1.2 Folded plate and barrel vault1.3 Preliminary design of shells1.4 Thickness of shells1.5 Types and forms of shells structure

1.5.1 Barrel shells1.5.2 Folded plates1.5.3 Umbrella shells

1.6 Four gabled hypars1.7 Domes of revolution

1.8 Translation shells1.9 Glossary1.10 Check your Progress1.11 Reference1.12 Answer to check your progress

1.1 Introduction

Throughout the centuries deployable structures have been used in the field of architecture. Their application started early, in mobile tents, deployable textile sunscreens in antiques arenas and is nowadays often used for example in temporary roofing of sport arenas. These constructions share the common general intention of an improved building adaptability through the possibility to react to different utilisation requests. Currently most deployed constructions are based on the use of textile materials as deployable elements or completely rigid building elements, which can be removed entirely. Deployable structures using folded plate constructions are rarely realized despite the fact that it is possible to create wide span high performances structures with enclosing and formative character. The articulated design of the folds furthermore allows the structure to provide kinematical properties. Thus a structure can be designed which combines the advantages of folded plate structures with the possibility of a reversible building element through folding and unfolding. Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures This idea is not new, but remains an attractive subject, as the multitude of publications on this theme confirm. Lots of different folding patterns had been developed and verified in thin-paper-models, differing in the number of folds meeting in one knot and the angle arrangements around the knots.

But in reality, where wide spans have to be taken, the paper-model has to be replaced by a model considering the existing plate thickness and associated stiffness. These considerations lead to several restraints in realizable foldable plate structures of which one important is the feasible compactness in the completely folded state, especially when the structure is supposed to disappear. Hence only three reasonable folded plate structure mechanisms remain: the one-fold, the four-fold and the six-fold-pattern. As the one-fold-mechanism represents a quit easy folding pattern to analyze, the four-fold mechanism becomes more difficult to handle in regards of the geometric, static and kinematical characteristics.

Most concrete shell structures are buildings, including storage facilities, commercial buildings, and residential homes. Concrete shell construction techniques are well suited for complex curves and are also used to build boat hulls (called ferroconcrete). Historically, it was used by the British to create the Mulberry Harbours for the 1944 D-Day invasion of Normandy.

Like the arch, the curved shapes often used for concrete shells are naturally strong structures, allowing wide areas to be spanned without the use of internal supports, giving an open, unobstructed interior. The use of concrete as a building material reduces both materials cost and construction costs, as concrete is relatively inexpensive and easily cast into compound curves. The resulting structure may be immensely strong and safe; modern monolithic dome houses, for example, have resisted hurricanes and fires, and are widely considered to be strong enough to withstand even F5 tornadoes.

Since concrete is a porous material, concrete domes often have issues with sealing. If not treated, rainwater can seep through the roof and leak into the interior of the building. On the other hand, the seamless construction of concrete domes prevents air from escaping, and can lead to buildup of condensation on the inside of the shell. Shingling or sealants are common solutions to the problem of exterior moisture, and dehumidifiers or ventilation can address condensation.

The oldest known concrete shell, the Pantheon in Rome, was completed about AD 125, and is still standing. It has a massive concrete dome 43m in diameter, with an oculus at its centre. A monolithic structure, it appears to have been sculpted in place by applying thin layers on top of each other in decreasing diameter. Massively thick at the bottom and thinning (with aerated volcanic pumice as part of the concrete mix) at the top, the Pantheon is a remarkable feat of engineering.

Modern thin concrete shells, which began to appear in the 1920s, are made from thin steel reinforced concrete, and in many cases lack any ribs or additional reinforcing structures, relying wholly on the shell structure itself.

Shells may be cast in place, or pre-cast off site and moved into place and assembled. The strongest form of shell is the monolithic shell, which is cast as a single unit. The most common monolithic form is the dome, but ellipsoids and cylinders (resembling concrete Quonset huts / Nissen huts) are also possible using similar construction methods.

Geodesic domes may be constructed from concrete sections, or may be constructed of a lightweight foam with a layer of concrete applied over the top. The advantage of this method is that each section of the dome is small and easily handled. The layer of concrete applied to the outside bonds the dome into a semi-monolithic structure.

Monolithic domes are cast in one piece out of reinforced concrete and date back to the 1960s. Advocates of these domes consider them to be cost-effective and durable structures, especially suitable for areas prone to natural disasters. They also point out the ease of maintenance of these buildings. Monolithic domes can be built as homes, office buildings, or for other purposes.

The Seattle Kingdome was the world's first (and only) concrete-domed multi-purpose stadium. It was completed in 1976 and demolished in 2000. The Kingdome was

constructed of triangular segments of reinforced concrete that were cast in place. Thick ribs provide additional support.

1.2 Folded plate and barrel vault

In this structure, a folded plate structure is combined with a barrel vault. For the same width of element, the transverse bending moments in the folded plates are usually larger than the barrel vault so it is important to keep the width of the plates so the slab will not be thick. The form is not especially suitable for long spans since the structural efficiency of the folded plate is not very great. However, it does provide a chance to develop an unusual form. A very interesting combination is the folded plate Z shell with the north light shell by making the upper end of the Z a smooth curve and the lower end a folded plate.

Folded plate design varied from that specified in the typical Code of Practice in the method of analysis, precautions against buckling instability, camber and deflexion controls, and permissible combined flexural, shear and axial stresses. Somewhat higher factors of safety were recommended than those normally required for other types of structure, and on most concrete folded plates a factor of safety of 3.5 to 5 was provided. Changes in stresses caused by geometrical displacements should be included in the design.

In cases where the plate width was narrow compared to the span, and the break in the surface at the connecting edges was small, strains in the plane of the plate might cause large local displacements, a smaller edge support, and consequent buckling of the member. While the cracking in the deep corrugated sections might be less than in slender conventional beams, the light reinforcement was rather more difficult to hold to fine tolerances, particularly on the sloped sections. At points of restraint, such as stiffener ribs, frames, and end-beams, special consideration should be given to the plate design. Although materials expanded uniformly as the temperature rose, structures did not. A structure would tend to deform or buckle until restraint was overcome.

Normally, folded plates were able to accommodatveo lumetric changes by small sidesways and flexural adjustments. However these thin plates were subject to quick and intensive volume changes and sections would invariably crack where these motions were restrained by thicker, slower-acting frames and rigid beams. At this point basic assumptions were no longer valid, unless at these restraining points the slab was reinforced at the juncture to resist and distribute cracking.

1.3 Preliminary design of shells

The principal purposes for preliminary design of any structure is: (1) To obtain quantities of materials for making estimates of cost. (2) Obtain a clear picture of the structural action, (3) Establish the dimensions of the structure, and, (4) Use the preliminary design as a check on the final design.

It is not expected that these preliminary design calculations be precise, but rather they should be within an accepted tolerance. The worst way to start a design is to immediately set up a finite element analysis. Any new type of structure requires an extended lead time to obtain a thorough understanding of the structural action.

The discussion of preliminary analysis here, has been restricted to principals rather than to presentation of calculations. Given these principals, the engineer should be able to set up his own calculations. Do not try to design shells without a thorough study of the relevant sections of the current American Concrete Association regulations. There are differences from the normal structures.

1.4 Thickness of shells

The thickness of the slab elements are normally governed by the number of layers of reinforcing bars. For shells of double curvature, there are usually only two layers so the minimum thickness could be: Two 3/8 in. bars, two 1/2 in. of cover equals 1.75 inches. However a little tolerance should be added. For a barrel shell or a folded plate:

Two 1/2 in. bars, one 3/4 in. bar, two 1/2 in. of cover equals 2.75 in. Of course, the concrete stresses should be checked, but they seldom control. Do not think that a shell will be stronger if it is thicker than required. For a description of the structural elements of the shells discussed here, the reader should first study the presentations in Mark Ketchum's

Shell Thickness

In a nutshell, the thicker the shell, the more higher it will sound. The thinner the shell, the lower it will sound. Don't get caught up in plies. You can't always judge a shell's thickness by how many plies it has. Some companies cut their plies thinner or thicker than others. The density of the wood also determines how thin a ply can be cut. Lauan plies will be much thicker than Birch, for example, because Birch is stronger and

can be cut thinner. Or one company's 9 ply shell could be thinner than another company's 6 ply shell. There are many variables.

Making shells from many plies, instead of one thick piece of wood, adds strength and stability to the shell. By alternating the grain of each ply, a thinner shell can be made that ends up being stronger than a thicker, solid piece of wood. It also will resist warping, as each ply has a different direction to the grain.

Gene Okamoto at Pearl Drums, provided the following information about how shell thickness effects the sound of a drum: The number of plies effects how readily energy is transferred from the heads to the shell. This single factor has a profound affect on the tonal characteristics and projection of the drum.

Thin-shell structures are light weight constructions using shell elements. These elements are typically curved and are assembled to large structures. Typical applications are fuselages of aeroplanes, boat hulls and roof structures in some buildings.

A thin shell is defined as a shell with a thickness which is small compared to its other dimensions and in which deformations are not large compared to thickness. A primary difference between a shell structure and a plate structure is that, in the unstressed state, the shell structure has curvature as opposed to plates structures which are flat. Membrane action in a shell is primarily caused by in-plane forces (plane stress), though there may be secondary forces resulting from flexural deformations. Where a flat plate acts similar to a beam with bending and shear stresses, shells are analogous to a cable which resists loads through tensile stresses. Though the ideal thin shell must be capable of developing both tension and compression.

Shell integration (the shell method in integral calculus) is a means of calculating the volume of a solid of revolution, when integrating along an axis perpendicular to the axis of revolution.

It makes use of the so-called "representative cylinder". Intuitively speaking, part of the graph of a function is rotated around an axis, and is modelled by an infinite number of hollow pipes, all infinitely thin.

The idea is that a "representative rectangle" (used in the most basic forms of integration – such as ∫ x dx) can be rotated about the axis of revolution; thus generating a hollow cylinder. Integration, as an accumulative process, can then calculate the integrated volume of a "family" of shells (a shell being the outer edge of a hollow cylinder) – as volume is the antiderivative of area, if one can calculate the lateral surface area of a shell, one can then calculate its volume.

The necessary equation, for calculating such a volume, V, is slightly different depending on which axis is serving as the axis of revolution. These equations note that the lateral surface area of a shell equals: 2 pi (π) multiplied by the cylinder's average radius, p(y), multiplied by the length of the cylinder, h(y). One can calculate the volume of a

representative shell by: 2π * p(y) * h(y) * dy, where dy is the thickness of the shell – that being some number approaching zero.

Shell integration can be considered a special case of evaluating a double integral in polar coordinates.

1.5 Types and Forms of Shell Structures

The shell structure is typically found in nature as well as in classical architecture. Its efficiency is based on its curvature (single or double), which allows a multiplicity of alternative stress paths and gives the optimum form for transmission of many different load types. Various different types of steel shell structures have been used for industrial purposes; singly curved shells, for example, can be found in oil storage tanks, the central part of some pressure vessels, in storage structures such as silos, in industrial chimneys and even in small structures like lighting columns. The single curvature allows a very simple construction process and is very efficient in resisting certain types of loads. In some cases, it is better to take advantage of double curvature. Double curved shells are used to build spherical gas reservoirs, roofs, vehicles, water towers and even hanging roofs.

Distributed loads due to internal pressure in storage tanks, pressure vessels or silos, or to external pressure from wind, marine currents and hydrostatic pressures are very well resisted by the in-plane behaviour of shells. Shell structures often need to be strengthened in certain problem areas by local reinforcement. Local reinforcement is also often required at connections between shell structures, such as commonly occur in general piping work and in the offshore industry. In contrast to local reinforcement, global reinforcement is generally used to improve the overall shell behaviour. In axisymmetric shells, the obvious location for the stiffeners is along selected meridians and parallel lines, creating in this way a true mesh which reinforces the pure shell structure.

There are two main mechanisms by which a shell can support loads. On the one hand, the structure can react with only in-plane forces, in which case it is said to act as a membrane. In practice, however, real structures have local areas where equilibrium or compatibility of displacements and deformations is not possible without introducing bending.

Local behaviour, however, is often critical in determining structural adequacy. Dimpling in domes, or the development of the so-called Yoshimura patterns in compressed cylinders, are phenomena related to local buckling that introduce a new level of complexity into the study of shells.

The theoretical limits of bifurcation of equilibrium that can be reached using mathematical models are upper limits to the behaviour of actual structures; as soon as any initial displacement or shape imperfection is present, the curve is smoothed.

Shell structures can usually be understood as a set of beams, arches and catenaries. Man-made shell structures as used in various branches. Engineering structures and/or architectural works whose structure is defined as Thin-shell structures from around the world. Finite Element Analyses of Buckling of Shell Structures. Numerical analysis of shell structures and elements. International Association of Shell and Spatial Structures (IASS). Thin shell structures are uniquely suited to carrying distributed loads and find wide application as roof structures in building. Equilibrium of shell structures (Oxford engineering science series). Design of Plate and Shell Structures. Shell structures are widely used in civil, mechanical, architectural, aeronautical, and marine engineering.

1.5.1 Barrel shells

First find the longitudinal and shear (diagonal tension) reinforcing required for a typical interior element of the structure.

1. A barrel shells acts as a beam in the long direction and as an arch in the curved area. The arch is supported by internal shears. Approximate values for the bending moments in the arch are summarized in the following sketch.

2. The area of reinforcing is obtained by estimating the effective depth of the beam element, from the center of reinforcing to the center of compression. The force in the reinforcing is equal to the bending moment divided by the effective depth. It may require several approximations to get a fair value. The area of reinforcing is, of course, the force divided by the allowable stress.

3. The tension in the diagonal direction is determined first by equating the longitudinal force to the shear forces.

4. The sum of the shearing forces equals the longitudinal forces. Let S equal the unit shear at the end of the beam. Then: S times the width of the shell times the length divided by 4 equals the longitudinal force.

If there are no other forces on an element at the neutral axis of the beam, then the diagonal tension equals the shear. From this information, a pattern of diagonal tension bars can be constructed.

5. The horizontal reaction of the arch elements of the shell must be contained by an rigid frame and a horizontal tie. Assume that this is simply a wide arch equal to half of the span. An approximation for the horizontal force would be equal to the load per foot on this arch times the arch span, squared divided by 8 and the rise. The thrust in the arch can be determined from this and the vertical reaction.

6. The edge spans of the shell should be supported by intermediate columns. The stiffness of a barrel shell at the outside edges is simply not stiff or strong enough to carry the required loads. The shell reinforcing at the edge members acts more like a typical arch and should be reinforced with two layers of bars.

1.5.2 FOLDED PLATES

The design of folded plate roof structures follows the design of barrel shells, but is much simpler because the elements are all essentially beams.

1. Support the folded plate at its longitudinal edges by frequent columns as was suggested for barrel shells.

2. Analyse and design the slab element as a continuous beam on fixed supports, including the first spans, normally a simple support. If it is haunched, then as a continuous haunched beam.

3. Design a typical longitudinal interior element as a beam by the usual methods.

4. Support the ends of the folded plates by rigid frames. In this case the frames are loaded by the shear forces from the slab element and are in the plane of the frame members.

A folded mountain is created when two tectonic plates come together . This causes them to rise out of the earth. These mountains are formed by compression. The process of mountain-building is called orogeny.

Fold mountains make up some of the highest mountains in the world. Folded mountains commonly form along borders, where two continents are colliding. They tend to look like an accordion. Some really complex folds can be found in parts of the Alps, Himalayas, Rockies, Appalachians, and Russia's Ural Mountains. These long mountain chains also show extensive signs of folding.

Fold mountains are created by uplift and folding of tectonic plates as they move towards each other and collide. This is known as a compressional plate margin. An example is the Andes Mountain range in South America (Nazca Plate colliding with the South American Plate).

The plates may be either 'continental and continental' or 'continental and oceanic'. The plates move towards each other, but there is not a free space for them to move into because they are already touching each other. With two massive plates of rock pushing against each other and continually moving, all that rock has to go somewhere!

The 2 plates push against each other and are continually moving At a destructive plate margin where oceanic and continental plates collide, the oceanic plate is subducted, pulled under the continental plate - whilst the continental plate is crumpled upwards to form a mountain range. The Andes are an example of fold mountains formed at a destructive plate margin.

When two continental plates move towards each other, both plates are forced upwards in a series of folds. This caused big problems for early geologists who struggled to explain why they were finding fossils of sea creatures high up in mountains such as the Himalayas! We now know that the fossils got there due to uplift of sedimentary rocks found along the edges of the plates.

You can simulate this process using two flat strips of modeling clay or old carpet. Put them side by side and push them together. One or both will crumple up and form a mini mountain range on your table top.

Folded mountains are created when tectonic plates are pushed together slowly and continueously with pressure and heat.

1.5.3 Umbrella shells

Following is a sketch of a typical inverted umbrella hypar. The principal elements are:

• The shell element with stresses predicted by the membrane equation. • The interior rib created by the intersection of the shell elements. • The exterior rib supporting the shell, particularly in the exterior corners • The cental column and the connection to the shell.

The membrane equation for a hypar gives the direct stresses in the shell:

Shear = Tension = wab/2f,where w = unit load, a and b = the dimensions of the individual panel, and f is the vertical height of the panel.

These loads are transfered directly to the supporting ribs through shear, and are used to design the ribs. The internal ribs are in compression and the external ribs are in tension. In both cases, the direct stress varies from zero at the edges to maximum at the center.

If the external ribs are placed above the shell then the edge member will be prestressed in positive moment and the edge of the shell will tend to deflect upward which is most desirable. It is also desirable to design this member for the additional weight of the edge member. The deflection at the end of the rib is critical.

The central column should be designed for some unbalanced load. The connection to the shell defies analysis, but tests by the Portland Cement Association have proved the strength of these types of joints. Be sure to include adequate reinforcing for any contingency.

Shellfish is a culinary and fisheries term for exoskeleton-bearing aquatic invertebrates used as food, including various species of molluscs, crustaceans, and echinoderms. Although most kinds of shellfish are harvested from saltwater environments, some kinds are found only in freshwater. In addition a few species of land crabs are eaten, for example Cardisoma guanhumi in the Caribbean.

The name "shellfish" is somewhat misleading, because shellfish are not related to fish in any way other than simply being animals. Many varieties of shellfish (crustaceans in particular) are actually closely related to insects and arachnids, making up one of the

main classes of the phylum Arthropoda. Cephalopods (squid, octopus, cuttlefish) and bivalves (clams, oysters) are molluscs, as are snails and slugs.

Familiar marine molluscs enjoyed as a food source by humans include many species of clams, mussels, oysters, winkles, and scallops. Some crustaceans commonly eaten are shrimp, prawn, lobster, crayfish, and crabs.[1] Echinoderms are not as frequently harvested for food as molluscs and crustaceans, however sea urchin roe is quite popular in many parts of the world.[2][3]

Most shellfish eat a diet composed primarily of phytoplankton and zooplankton.[4]

Shellfish are among the most common food allergens

1.6 Four gabled hypars

The design of this structure follows, with exceptions, the design of the umbrella hypar.

Please refer to the previous examp le. The sketch shows the essential elements:

The shell acts as an arch in one direction and as a catenary in the other. The membrane theory would predict that the stresses would be the same but of different sign. Studies by the finite element method have demonstrated that if the abutments are fixed, the compression stresses are greater, but if the abutments move because of, for example, a steel tie stretching, then the catenary stresses are larger. Which brings us to the conclusion that for the first case it would be advisable to increase the thickness of the shell near the supports to take the load off the rib elements.

The top ridge member is in compression and may require additional area above that of the shell. This is a long compression member and is free to deflect downward with the possibility of ultimate buckling, (Which has happened.) It is, therefore, advisable to camber this member upward to offset this tendency.

The slanting side ribs are also in compression and to some extent in bending, and sould be designed for some of the weight of the rib, say one quarter for a start.

1.7 Domes of Revolution

The rules described are suitable for domes of revolution of any configuration or variable thickness, not just cylindrical domes. The steps are as follows:

• Determine the total weight, P, above a series of horizontal sections • The total vertical stress,V, at any section will be equal to the vertical force, P. • The radial force at any section can be obtained for the freebody diagram for an

element as shown in the sketch. The symbol, Z, is perpendicular to the element. For a cylindrical dome the radial force can be obtained form the equation:

(T(vertical) + T(horizontal))/R = Z

• If the shell is not vertical, or nearly vertical, at the base, then a ring beam will be required. The force in the ring beam is obtained from the horizontal component, H, of the force at the base as shown in the sketch, and the cylinder formula: P = HR, where R is the horizontal radius of the shell.

• There will be some bending moment at the junction of the shell and the ring beam, so it is usual to gradually increase the thickness at this point and add moment reinforcing.

A dome is a space structure covering a more or less square or circular area. The best known example is the dome of revolution, and it is one of the earliest of the shell structures. Excellent examples are still in existence that were built in Roman times. They are formed by a surface generated by a curve of any form revolving about a vertical line. This surface has double curvature and the resulting structure is much stiffer and stronger than a single curved surface, such as a cylindrical shell. The simples dome of revolution is a portion of a sphere. However, other curves are also satisfactory, such as the ellipse, the parabola, other conic sections, or random curves.

Typical profiles for domes are shown later in the chapter and there are an infinite variety of possible shapes, each suitable for a particular purpose. Parts of domes of revolution, square or polygonal in plan with portions of the shell removed, are also considered in this chapter as domes of revolution. Their structural action is much more complex than the dome circular in plan.

1.8 Translation Shells

The translation shell is simply a square dome as shown by the sketch. The shape is generated by a curve moving along another curve. If the curves are circles, then every vertical section is the same. The dome is usually supported by arches. There are three principal design areas:

• The central dome area which is designed like a spherical dome. • The corners where there is considerable tension from the ring beam affect. • The arches which take their share of the total load. They are loaded in shear

including the weight of the arches themselves.

Laevistrombus canarium, commonly known as the dog conch and still better known under its synonym Strombus canarium, is a species of edible sea snail, a marine gastropod mollusk in the family Strombidae, the true conchs. An Indo-Pacific species, L. canarium lives on mud and sandy bottoms, grazing on algae and detritus. The shell of adult individuals is colored light yellowish-brown to golden to gray. It has a characteristic inflated body whorl, a flared and thick outer lip, and a shallow stromboid notch. Although it is considered to have value as an ornament, because the shell is heavy and compact it is also often used as sinker for fishing nets.

The external anatomy of the soft parts of this species is similar to that of other strombid snails; the animal has an elongate snout, thin eyestalks with well-developed eyes and sensory tentacles, and a narrow, strong foot with a sickle-shaped operculum attached. Among the predators of this snail are carnivorous gastropods such as cone snails and volutes, as well as humans, who consume the soft parts in a wide variety of dishes.

The dog conch is an economically important species in the Indo-West Pacific, and several studies indicate that it may be currently suffering population declines due to overfishing and overexploitation.[3][4] Malacologists and ecologists have recommended the reduction of the current exploitation rates; recent initiatives in Thailand are attempting to ensure the reproduction of younger individuals, as well as managing the natural populations in general.

Glossary:

against the grain - Printing at right angles to the direction of paper grain. This will cause folding problems. One way to work around folding against the grain is to score the paper before folding.

attachment - When referring to e-mail, an electronic file placed within an e-mail for the purpose of sending through the Internet.

banding - When the changes from screen percentage to screen percentage in a gradient can be seen, instead of a solid blending from dark to light or from color to color.

bind - To fasten sheets or signatures with wire, thread, glue, or by other means.

bindery - Where materials go for assembly. Cutting, folding, binding and boxing are some of the activities performed in bindery.

bleed - Ink which prints beyond the trim edge of the page, created for the purpose of allowing ink to extend to the edge of the page after trimming. Without bleed, cutting the product becomes extremely difficult and may sacrifice the quality of the product. For best results, create 1/8" (.125) bleed (past trim edge) on all edges where bleed is desired.

blueline - A blue photographic proof used to check position of all image elements. Similar to a blueprint. Universal does not utilize this type of proof; instead, a color, full-size, low-resolution proof is output for our clients.

camera-ready copy - An archaic term meaning print-ready, mechanical art.

carbonless - Pressure sensitive writing paper that does not use carbon paper.

ollate - A finishing term for gathering paper in a precise order.

color bar - A line of colored blocks in a row or a single color placed at the tail of a press sheet and used to measure the density of color across the width of a press sheet.

color correction - Improving color separations by altering either the electronic file or the amount of color burned onto a plate or the amount of ink applied to a press sheet.

color matching system - A system of formulated ink colors used for communicating color.

color separations - The process of preparing artwork, photographs, transparencies, or computer-generated art for printing by separating color into the four primary printing colors: cyan, magenta, yellow and black.

comb bind - To plastic comb bind by inserting the comb into punched holes.

computer-to-plate - Also known as CTP. The process by which plates are created using information sent to a direct-to-plate device from a computer, bypassing film. Click here to find out why this process is better.

crash number - Numbering paper by pressing an image on the first sheet which is transferred to all parts of the printed set.

crop - To cut off parts of a picture or image.

crop marks - Printed lines showing where to trim a printed sheet.

density - The degree of color or darkness of an image or photograph.

die - Metal rule or imaged block used to cut or place an image on paper in the finishing process.

die cutting - The process of using a die to cure images in or out of paper.

digital printing - Printing performed on a digital copier, such as a laser color copier or Docutech.

digital proof - A proof delivered electronically, as opposed to physically. The most typical example is a .pdf proof.

dot gain or spread - A term used to explain the difference in size between the dot on film versus the dot on paper.

double burn - Exposing a plate to multiple images.

duotone - A halftone picture made up of two printed colors.

e-commerce - The convenient process of ordering products and services online.

e-mail - Abbreviation for electronic mail.

ePrint - An abbreviation for electronic printing, this is what Universal calls their online ordering system which some customers can use to order products online.

embossing - Pressing an image into paper so that it creates a raised area.

emulsion - Light-sensitive coating found on printing plates and film.

flood - To cover a printed page with ink, varnish or plastic coating completely.

foil - A metallic or pigmented coating on plastic sheets or rolls used in foil stamping and foil embossing/debossing.

foil emboss/deboss - Foil stamping and embossing/debossing an image on paper with a die.

foil stamping - Using a die to place a metallic or pigmented image on paper.

Check your progress:

1. Explain Folded Plate structures2. Explain FOLDED PLATE AND BARREL VAULT3. Explain PRELIMINARY DESIGN OF SHELLS

Reference:

1. ^ Cumhuriyet Bilim Teknik Eki (Science and Technique Supplement of the Istanbul daily Cumhuriyet), August 20, 2010, p. 18.2. ^ "Introduction," Yapılar Fora / Buildings Ahoy p. 26.3. ^ His doctoral dissertation, which has so far remained unpublished, was titled “Analysis of Continuous Folded Plate Structures” (Yapılar Fora / Buildings Ahoy p. 338.4. ^ The article, titled "Analysis of Folded Plate Structures Continuous over Flexible Supports," was published in 1967 in the ASCE (American Society of Civil Engineers) Journal of the Structural Division.5. ^ Co-translated with Hasan Karataş, it came out in 1975 as Betonarme Kabuk Yapılar.6. ^ METU was governed by special legislation, and did not have to adhere to the rules and regulations the state universities in Turkey were subjected to. The September 12, 1980 military coup-d'etat led, among others, to the creation of Y.Ö.K. - Yüksek Öğretim Kurulu (Higher Education Council) and the promulgation of a concomitant law which took METU under its aegis and curtailed many of its prerogatives ("Introduction," Yapılar Fora / Buildings Ahoy p. 28).7. ^ Ali İhsan Ünay recounts the development at length in "Mimarlık Eğitiminde Yapı Sistemlerinin Tasarımı" (Design of Structural Systems in Architecture Education) p. 74.8. ^ Pultar was the (anonymous) editor of the first two copies, then handed over the editorship to Turan. The journal, currently under the editorship of Ali Cengizkan, has celebrated in 2010 its thirty-fifth year of publication ("Introduction," Yapılar Fora / Buildings Ahoy p. 30).9. ^ See Vacit Imamoğlu, "Bilim Insanı, Eğitimci, Çalışma Arkadaşım Mustafa Pultar" (Mustafa Pultar the Scholar, Educationist and Colleague) pp. 43-45; and "Introduction," Yapılar Fora / Buildings Ahoy p. 30.10. ^ See Emine O. Incirlioğlu, "Strüktür ve Yöntem Cinsinden Hayat Dersleri" (Lessons of Life in the Form of Structure and Method) p. 57.

11. ^ Özgüç, "Forty Years of Computer-aided Architectural Design," p. 122.12. ^ See Ali Doğramacı, "Çok Yönlü İnsan: Mustafa Pultar" (A Man of Many Talents: Mustafa Pultar), pp. 39-40 for details of his recruitment and appointment.

Check your progress answer:

1. Refer introduction2. Refer 1.23. Refer 1.3

Unit 2: Structural behavior, types

2.1 Structures and loads2.2 Classification of structures2.3 Loads

2.4 Analytical methods2.5 Limitations2.6 Strength of materials methods (classical

methods)2.7 Elasticity methods2.8 Methods using numerical approximation2.9 Time-line2.10 Structural behavior of model masonry shells2.11 Structural modeling2.12 Linearity of the structural system

Introduction

Structural analysis comprises the set of physical laws and mathematics required to study and predict the behavior of structures. The subjects of structural analysis are engineering artifacts whose integrity is judged largely based upon their ability to withstand loads; they commonly include buildings, bridges, aircraft, ships and cars. Structural analysis incorporates the fields of mechanics and dynamics as well as the many failure theories. From a theoretical perspective the primary goal of structural analysis is the computation of deformations, internal forces, and stresses. In practice, structural analysis can be viewed more abstractly as a method to drive the engineering design process or prove the soundness of a design without a dependence on directly testing it.

Adaptation is, first of all, a process, rather than a physical part of a body.[7] An internal parasite (such as a fluke) can illustrate the distinction: such a parasite may have a very simple bodily structure, but nevertheless the organism is highly adapted to its specific environment. From this we see that adaptation is not just a matter of visible traits: in such parasites critical adaptations take place in the life-cycle, which is often quite complex.[8]

However, as a practical term, adaptation is often used for the product: those features of a species which result from the process. Many aspects of an animal or plant can be correctly called adaptations, though there are always some features whose function is in doubt. By using the term adaptation for the evolutionary process, and adaptive trait for the bodily part or function (the product), the two senses of the word may be distinguished.

Adaptation is one of the two main processes that explain the diverse species we see in biology, such as the different species of Darwin's finches. The other is speciation (species-splitting or cladogenesis), caused by geographical isolation or some other mechanism.[9][10] A favourite example used today to study the interplay of adaptation and speciation is the evolution of cichlid fish in African lakes, where the question of reproductive isolation is much more complex.[11][12]

Adaptation is not always a simple matter, where the ideal phenotype evolves for a given external environment. An organism must be viable at all stages of its development and at all stages of its evolution. This places constraints on the evolution of development, behaviour and structure of organisms. The main constraint, over which there has been much debate, is the requirement that each genetic and phenotypic change during evolution should be relatively small, because developmental systems are so complex and interlinked. However, it is not clear what "relatively small" should mean, for example polyploidy in plants is a reasonably common large genetic change.[13] The origin of the symbiosis of multiple micro-organisms to form a eukaryota is a more exotic example.[14]

All adaptations help organisms survive in their ecological niches.[15] These adaptive traits may be structural, behavioral or physiological. Structural adaptations are physical features of an organism (shape, body covering, armament; and also the internal organization). Behavioural adaptations are composed of inherited behaviour chains and/or the ability to learn: behaviours may be inherited in detail (instincts), or a tendency for learning may be inherited (see neuropsychology). Examples: searching for food, mating, vocalizations. Physiological adaptations permit the organism to perform special functions (for instance, making venom, secreting slime, phototropism); but also more general functions such as growth and development, temperature regulation, ionic balance and other aspects of homeostasis. Adaptation, then, affects all aspects of the life of an organism.

Definitions

The following definitions are mainly due to Theodosius Dobzhansky.

1. Adaptation is the evolutionary process whereby an organism becomes better able to live in its habitat or habitats.[16]

2. Adaptedness is the state of being adapted: the degree to which an organism is able to live and reproduce in a given set of habitats.[17]

3. An adaptive trait is an aspect of the developmental pattern of the organism which enables or enhances the probability of that organism surviving and reproducing.[18]

Adaptedness and fitness

From the above definitions, it is clear that there is a relationship between adaptedness and fitness (a key population genetics concept). Differences in fitness between genotypes predict the rate of evolution by natural selection. Natural selection changes the relative frequencies of alternative phenotypes, insofar as they are heritable.[19] Although the two are connected, the one does not imply the other: a phenotype with high adaptedness may not have high fitness. Dobzhansky mentioned the example of the Californian redwood, which is highly adapted, but a relic species in danger of extinction.[16] Elliott Sober commented that adaptation was a retrospective concept since it implied something about the history of a trait, whereas fitness predicts a trait's future.[20]

1. Relative fitness. The average contribution to the next generation by a phenotype or a class of phenotypes, relative to the contributions of other phenotypes in the population. This is also known as Darwinian fitness, selective coefficient, and other terms.2. Absolute fitness. The absolute contribution to the next generation by a phenotype or a class of phenotypes. Also known as the Malthusian parameter when applied to the population as a whole.[19]

3. Adaptedness. The extent to which a phenotype fits its local ecological niche. This can sometimes be tested through a reciprocal transplant experiment.

2.1Structures and Loads

Dead load

Dead load

Imposed load

Live snow load

The dead load includes loads that are constant over time, including the weight of the structure acting with gravity on the foundations below, as well as other permanent loads, including weight of walls.

Live loads

Live loads, or imposed loads, are temporary, of short duration, or moving. Examples include snow, wind, earthquake, traffic, movements, water pressures in tanks, and occupancied loads. For certain specialized structures, vibro-acoustic loads may be considered.

Environmental loads

• Temperature changes leading to thermal expansion cause thermal loads• Loads caused by humidity or moisture induced expansion• Ice movements• Water waves• Shrinkage

Static loads

These are loads that build up gradually over time, or with negligible dynamic effects. Since structural analysis for static loads is much simpler than for dynamic loads, design codes usually specify statically-equivalent loads for dynamic loads caused by wind, traffic or earthquake.

Dynamic loads

These are loads that display significant dynamic effects. Examples include impact loads, waves, wind gusts and strong earthquakes. Because of the complexity of analysis, dynamic loads are normally treated using statically equivalent loads for routine design of static structures.

A structure refers to a system of connected parts used to support a load. Important examples related to Civil Engineering include buildings, bridges, and towers; and in other branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical systems, and electrical supporting structures are important. In order to design a structure, one must serve a specified function for public use, the engineer must account for its safety, esthetics, and serviceability, while taking into consideration economic and environmental constraints.

Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right. Structural engineers are most commonly involved in the design of buildings and large nonbuilding structures[2] but they can also be involved in the design of machinery, medical equipment,

vehicles or any item where structural integrity affects the item's function or safety. Structural engineers must ensure their designs satisfy given design criteria, predicated on safety (e.g. structures must not collapse without due warning) or serviceability and performance (e.g. building sway must not cause discomfort to the occupants). Buildings are made to endure massive loads as well as changing climate and natural disasters.

Structural engineering theory is based upon physical laws and empirical knowledge of the structural performance of different landscapes and materials. Structural engineering design utilises a relatively small number of basic structural elements to build up structural systems that can be very complex. Structural engineers are responsible for making creative and efficient use of funds, structural elements and materials to achieve these goals.

Structural engineers are responsible for engineering design and analysis. Entry-level structural engineers may design the individual structural elements of a structure, for example the beams, columns, and floors of a building. More experienced engineers would be responsible for the structural design and integrity of an entire system, such as a building.

Structural engineers often specialize in particular fields, such as bridge engineering, building engineering, pipeline engineering, industrial structures, or special mechanical structures such as vehicles or aircraft.

Structural engineering has existed since humans first started to construct their own structures. It became a more defined and formalised profession with the emergence of the architecture profession as distinct from the engineering profession during the industrial revolution in the late 19th Century. Until then, the architect and the structural engineer were usually one and the same - the master builder. Only with the development of specialised knowledge of structural theories that emerged during the 19th and early 20th centuries did the professional structural engineer come into existence.

The role of a structural engineer today involves a significant understanding of both static and dynamic loading, and the structures that are available to resist them. The complexity of modern structures often requires a great deal of creativity from the engineer in order to ensure the structures support and resist the loads they are subjected to. A structural engineer will typically have a four or five year undergraduate degree, followed by a minimum of three years of professional practice before being considered fully qualified.

Structural engineers are licensed or accredited by different learned societies and regulatory bodies around the world (for example, the Institution of Structural Engineers in the UK). Depending on the degree course they have studied and/or the jurisdiction they are seeking licensure in, they may be accredited (or licensed) as just structural engineers, or as civil engineers, or as both civil and structural engineers.

Structural building engineering includes all structural engineering related to the design of buildings. It is the branch of structural engineering that is close to architecture.

Structural building engineering is primarily driven by the creative manipulation of materials and forms and the underlying mathematical and scientific ideas to achieve an end which fulfills its functional requirements and is structurally safe when subjected to all the loads it could reasonably be expected to experience. This is subtly different from architectural design, which is driven by the creative manipulation of materials and forms, mass, space, volume, texture and light to achieve an end which is aesthetic, functional and often artistic.

The architect is usually the lead designer on buildings, with a structural engineer employed as a sub-consultant. The degree to which each discipline actually leads the design depends heavily on the type of structure. Many structures are structurally simple and led by architecture, such as multi-storey office buildings and housing, while other structures, such as tensile structures, shells and gridshells are heavily dependent on their form for their strength, and the engineer may have a more significant influence on the form, and hence much of the aesthetic, than the architect.

The structural design for a building must ensure that the building is able to stand up safely, able to function without excessive deflections or movements which may cause fatigue of structural elements, cracking or failure of fixtures, fittings or partitions, or discomfort for occupants. It must account for movements and forces due to temperature, creep, cracking and imposed loads. It must also ensure that the design is practically buildable within acceptable manufacturing tolerances of the materials. It must allow the architecture to work, and the building services to fit within the building and function (air conditioning, ventilation, smoke extract, electrics, lighting etc.). The structural design of a modern building can be extremely complex, and often requires a large team to complete.

Structural engineering specialties for buildings include:

• Earthquake engineering• Façade engineering• Fire engineering• Roof engineering• Tower engineering• Wind engineering

2.2 Classification of Structures

It is important for a structural engineer to recognize the various types of elements composing a structure and to be able to classify structures as to their form and function. Some of the structural elements are tie rods, rod, bar, angle, channel, beams, and columns. Combination of structural elements and the materials from which they are composed is referred to as a structural system. Each system is constructed of one or more

basic types of structures such as Trusses, Cables and Arches, Frames, and Surface Structures.

2.3 Loads

Once the dimensional requirement for a structure have been defined, it becomes necessary to determine the loads the structure must support. In order to design a structure, it is therefore necessary to first specify the loads that act on it. The design loading for a structure is often specified in codes. There are two types of codes: general building codes and design codes, engineer must satisfy all the codes requirements for a reliable structure. There are two types of loads that structure engineering must encounter in the design. First type of load is called Dead loads that consist of the weights of the various structural members and the weights of any objects that are permanently attached to the structure. For example, columns, beams, girders, the floor slab, roofing, walls, windows, plumbing, electrical fixtures, and other miscellaneous attachments. Second type of load is Live Loads which vary in their magnitude and location. There are many different types of live loads like building loads, highway bridge Loads, railroad bridge Loads, impact loads, wind loads, snow loads, earthquake loads, and other natural loads.

Genetic load is the reduction in selective value for a population compared to what the population would have if all individuals had the most favored genotype. It is normally stated in terms of fitness as the reduction in the mean fitness for a population compared to the maximum fitness.

Mathematics

Consider a single gene locus with the alleles , which have the fitnesses and the allele frequencies respectively. Ignoring frequency-

dependent selection, then genetic load (L) may be calculated as:

where wmax is the maximum value of the fitnesses and is mean fitness which is calculated as the mean of all the fitnesses weighted by their corresponding allele frequency:

where the ith allele is and has the fitness and frequency wi and pi respectively.

When the wmax = 1, then (1) simplifies to

Causes of genetic load

Load may be caused by selection and mutation.

Mutational load

Mutation load is caused when a mutation at a locus produces a new allele of either lesser or greater fitness. This lowers the average fitness of the population; a deleterious mutation has a lower relative fitness, lowering average load, while an advantageous mutation effectively increases the relative fitness of the existing allele, and thus also increases average fitness.

Selectional load

Selection occurs when the fitnesses of particular alleles are inequal, hence selection always exerts a load.

With directional selection, the allele frequencies will tend towards an equilibrium position with the fittest allele reaching a frequency in mutation-selection balance. As mutations are rare, this is effectively fixation. Consider two alleles and . If w1 >

w2, then at equilibrium, and , hence , and .

If the mean fitness is 0, the load is equal to 1, but the population goes extinct.

See also

• Haldane's dilemma

Segregational load

In contrast to directional selection, in which one homozygote has a higher fitness than both the heterozygote and other homozygote, heterozygote advantage (also called overdominance) always exerts a load against the less fit homozygotes at equilibrium.

2.4 Analytical methods

To perform an accurate analysis a structural engineer must determine such information as structural loads, geometry, support conditions, and materials properties. The results of such an analysis typically include support reactions, stresses and displacements. This information is then compared to criteria that indicate the conditions of failure. Advanced structural analysis may examine dynamic response, stability and non-linear behavior.

There are three approaches to the analysis: the mechanics of materials approach (also known as strength of materials), the elasticity theory approach (which is actually a special case of the more general field of continuum mechanics), and the finite element

approach. The first two make use of analytical formulations which apply mostly to simple linear elastic models, lead to closed-form solutions, and can often be solved by hand. The finite element approach is actually a numerical method for solving differential equations generated by theories of mechanics such as elasticity theory and strength of materials. However, the finite-element method depends heavily on the processing power of computers and is more applicable to structures of arbitrary size and complexity.

Regardless of approach, the formulation is based on the same three fundamental relations: equilibrium, constitutive, and compatibility. The solutions are approximate when any of these relations are only approximately satisfied, or only an approximation of reality.

An analytical technique is a method that is used to determine the concentration of a chemical compound or chemical element. There are a wide variety of techniques used for analysis, from simple weighing (gravimetric) to titrations (titrimetric) to very advanced techniques using highly specialized instrumentation. The most common techniques used in analytical chemistry are the following:

• titrimetry, based on the quantity of reagent needed to react with the analyte• Electroanalytical techniques, including potentiometry and voltammetry• Spectroscopy, based on the interaction of the analyte with electromagnetic

radiation• Chromatography, in which the analyte is separated from the rest of the sample so

that it may be measured without interference from other compounds• Microscopy• Bioanalysis• Radioanalytical chemistry

There are many more techniques that have specialized applications, and within each major analytical technique there are many applications and variations of the general techniques.

2.5 Limitations

Each method has noteworthy limitations. The method of mechanics of materials is limited to very simple structural elements under relatively simple loading conditions. The structural elements and loading conditions allowed, however, are sufficient to solve many useful engineering problems. The theory of elasticity allows the solution of structural elements of general geometry under general loading conditions, in principle. Analytical solution, however, is limited to relatively simple cases.

The solution of elasticity problems also requires the solution of a system of partial differential equations, which is considerably more mathematically demanding than the solution of mechanics of materials problems, which require at most the solution of an ordinary differential equation. The finite element method is perhaps the most restrictive and most useful at the same time. This method itself relies upon other structural theories

(such as the other two discussed here) for equations to solve. It does, however, make it generally possible to solve these equations, even with highly complex geometry and loading conditions, with the restriction that there is always some numerical error. Effective and reliable use of this method requires a solid understanding of its limitations.

Common law legal system might have a statute, for example, limiting the time for prosecution of crimes designated as misdemeanors to two years after the offense occurred. Under such a statute, if a person is discovered to have committed a misdemeanor three years ago, the time has expired for the prosecution of the misdemeanor.

While on one hand it may seem unfair to forbid prosecution of crimes that law enforcement can now prove to the standard required by law (cf., e.g., Beyond a reasonable doubt, Clear and convincing evidence, and Preponderance of the evidence), the purpose of a statute of limitations or its equivalent is to ensure that the possibility of punishment for an act committed sufficiently long ago cannot give rise to either a person's incarceration or the criminal justice system's activation. In short, unless the crime is exceptionally heinous in nature (for example, murder, which generally has no statute of limitations), social justice as enacted through law has compromised that lesser crimes from long ago are best let be rather than distract attention from contemporary serious crimes.

There is a statute of limitations for a few reasons. One is that over time evidence of all sorts can be corrupted or disappear. Memories fade, crime scenes are changed, and companies dispose of records. So, the best time to bring a lawsuit is while the evidence is not lost and as close to the alleged egregious behavior as possible. Another reason is that people want to get on with their lives and not have legal battles from their past come up unexpectedly. The injured party has a responsibility to quickly bring their charges so that the process can begin..

Note, however, that limitations periods may begin when the cause of action is deemed to have arisen, or when a plaintiff had reason to know of the harm, rather than at the time of the original event. This distinction is significant in cases in which an earlier event causes a later harm (e.g., a surgeon negligently operates on a patient, who subsequently suffers the consequences of that negligence years later).

In a related concept, contracts may also have a term under which they may be the basis of a suit, and after which a plaintiff is held to have waived any right to claim. Under Article VI of the United States Constitution, private contracts cannot be abridged; this provision has been held by the United States Supreme Court to mean that the federal government or a State can only vitiate a contract if it directly opposes an important public policy. Similarly, the Charter of Fundamental Rights, codified into law applicable to European Union countries by the passage civil lawsuit, is said to have accrued when the event beginning its time limitation occurs.

Sometimes this is the event itself that is the subject of the suit or prosecution (such as a crime or personal injury), but it may also be an event such as the discovery of a condition one wishes to redress, such as discovering a defect in a manufactured good, or in the case of controversial "repressed memory" cases where someone discovers memories of childhood sexual abuse long afterwards.

An idea closely related, but not identical, to the statute of limitations is a statute of repose. A statute of repose limits the time within which an action may be brought and is not related to the accrual of any cause of action; the injury need not have occurred, much less have been discovered. Unlike an ordinary statute of limitations, which begins running upon accrual of the claim, the period contained in a statute of repose begins when a specific event occurs, regardless of whether a cause of action has accrued or whether any injury has resulted.

This often applies to buildings and properties, and limits the time during which an action may lie based upon defects or hazards connected to the construction of the building or premises. An example of this would be that if a person is electrocuted by a wiring defect incorporated into a structure in, say, 1990, a state law may allow his heirs to sue only before 1997 in the case of an open (patent) defect, or before 2000 in the case of a hidden defect. Statutes of repose can also apply to manufactured goods. Manufacturers contend they are necessary to avoid unfairness and encourage consumers to maintain their property. Consumer groups argue that statutes of repose on consumer goods provide a disincentive for manufacturers to build durable products and to notify consumers of product defects as the manufacturers become aware of them. Consumer groups also argue that such statutes of repose disproportionately affect poorer people, since they are more likely to own older goods.

Once the time allowed for a case by a statute of limitations runs out, if a party raises it as a defense and that defense is accepted, any further litigation is foreclosed. Most jurisdictions provide that limitations are tolled under certain circumstances. Tolling will prevent the time for filing suit from running while the condition exists. Examples of such circumstances are if the aggrieved party (plaintiff) is a minor, or the plaintiff has filed a bankruptcy proceeding. In those instances, in most jurisdictions, the running of limitations is tolled until the circumstance (i.e., the injured party reaches majority in the former or the bankruptcy proceeding is concluded in the latter) no longer exists.

There may be a number of factors that will affect the tolling of a statute of limitations. In many cases, the discovery of the harm (as in a medical malpractice claim where the fact or the impact of the doctor's mistake is not immediately apparent) starts the statute running. In some jurisdictions the action is said to have not accrued until the harm is discovered; in others, the action accrues when the malpractice occurs, but an action to redress the harm is tolled until the injured party discovers the harm.

As discussed in Wolk v. Olson, the discovery rule does not apply to mass-media publications such as newspapers and the Internet; the statute of limitations begins to run at the date of publication.

An action to redress a tort committed against a minor is generally tolled in most cases until the child reaches the age of majority. A ten-year-old who is injured in a car accident might therefore be able to bring suit one, two, or three years after he turns 18.

It may also be inequitable to allow a defendant to use the defense of the running of the limitations period, such as the case of an individual in the position of authority over someone else who intimidates the victim into never reporting the wrongdoing, or where one is led to believe that the other party has agreed to suspend the limitations period during good faith settlement negotiations or due to a fraudulent misrepresentation.

Generally speaking, in the case of private, civil matters, the limitations period may be shortened or lengthened by agreement of the parties. Under the Uniform Commercial Code the parties to a contract for sale of goods may reduce the limitations period to not less than one year but may not extend it.

Although such limitations periods generally are issues of law, limitations periods known as laches may apply in situations of equity (i.e., a judge will not issue an injunction if the party requesting the injunction waited too long to ask for it), such periods are not clearly defined and are subject to broad judicial discretion.

For U.S. military cases, the Uniform Code of Military Justice states that all charges except for those facing general court martial (where a death sentence could be involved) have a five-year statute of limitation. This statute changes once charges have been prepared against the service member. In all supposed UCMJ violations except for those headed for general court martial, should the charges be dropped, there is a six-month window in which the charges can be reinstated. If those six months have passed and the charges have not been reinstated, the statutes of limitation have run out.

2.6 Strength of materials methods (classical methods)

The simplest of the three methods here discussed, the mechanics of materials method is available for simple structural members subject to specific loadings such as axially loaded bars, prismatic beams in a state of pure bending, and circular shafts subject to torsion. The solutions can under certain conditions be superimposed using the superposition principle to analyze a member undergoing combined loading. Solutions for special cases exist for common structures such as thin-walled pressure vessels.

For the analysis of entire systems, this approach can be used in conjunction with statics, giving rise to the method of sections and method of joints for truss analysis, moment distribution method for small rigid frames, and portal frame and cantilever method for large rigid frames. Except for moment distribution, which came into use in the 1930s, these methods were developed in their current forms in the second half of the nineteenth century. They are still used for small structures and for preliminary design of large structures.

The solutions are based on linear isotropic infinitesimal elasticity and Euler-Bernoulli beam theory. In other words, they contain the assumptions (among others) that the materials in question are elastic, that stress is related linearly to strain, that the material (but not the structure) behaves identically regardless of direction of the applied load, that all deformations are small, and that beams are long relative to their depth. As with any simplifying assumption in engineering, the more the model strays from reality, the less useful (and more dangerous) the result.

However, the term strength of materials most often refers to various methods of calculating stresses in structural members, such as beams, columns and shafts. The methods that can be employed to predict the response of a structure under loading and its susceptibility to various failure modes may take into account various properties of the materials other than material (yield or ultimate) strength. For example failure in buckling is dependent on material stiffness (Young's Modulus).

2.7 Elasticity methods

Elasticity methods are available generally for an elastic solid of any shape. Individual members such as beams, columns, shafts, plates and shells may be modeled. The solutions are derived from the equations of linear elasticity. The equations of elasticity are a system of 15 partial differential equations. Due to the nature of the mathematics involved, analytical solutions may only be produced for relatively simple geometries. For complex geometries, a numerical solution method such as the finite element method is necessary.

Many of the developments in the mechanics of materials and elasticity approaches have been expounded or initiated by Stephen Timoshenko.

Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are system of elastic springs embedded in the data space[1]. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering (zero elasticity) to the estimators located closely to linear PCA manifolds (very rigid springs). With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle" of data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and A.A. Pitenko in 1996–1998.

Let data set be a set of vectors S in a finite-dimensional Euclidean space. Elastic map is represented by a set of nodes Wj in the same space. For each datapoint a host node is the closest node Wj (if there are several closest nodes then one takes the node with the smallest number). The data set S is divided on classes

.

The approximation energy is distortion

this is the energy of the springs with unite elasticity which connect each data point with its host node.

On the set of nodes an additional structure is defined. Some pairs of nodes, (Wi,Wj), are connected by elastic edges. Let this set of pairs be E. Some triples of nodes, (Wi,Wj,Wk) are the bending ribs. Let this set of triples be G.

The stretching energy is

The bending energy is

where λ and μ are the stretching end bending modules.

For example, in the 2D rectangular grid the elastic edges are just vertical and horizontal edges (pairs of closest vertices) and the bending ribs are the vertical or horizontal triples of consecutive (closest) vertices.

The energy of the elastic map is U = D + UE + UG.

The elastic map should be in the mechanical equilibrium: it should minimise the energy U.

2.8 Methods Using Numerical Approximation

It is common practice to use approximate solutions of differential equations as the basis for structural analysis. This is usually done using numerical approximation techniques. The most commonly used numerical approximation in structural analysis is the Finite Element Method.

The finite element method approximates a structure as an assembly of elements or components with various forms of connection between them. Thus, a continuous system such as a plate or shell is modeled as a discrete system with a finite number of elements interconnected at finite number of nodes. The behavior of individual elements is characterized by the element's stiffness or flexibility relation, which altogether leads to the system's stiffness or flexibility relation. To establish the element's stiffness or flexibility relation, we can use the mechanics of materials approach for simple one-dimensional bar elements, and the elasticity approach for more complex two- and three-dimensional elements. The analytical and computational development is best effected throughout by means of matrix algebra.

Early applications of matrix methods were for articulated frameworks with truss, beam and column elements; later and more advanced matrix methods, referred to as "finite element analysis," model an entire structure with one-, two-, and three-dimensional elements and can be used for articulated systems together with continuous systems such as a pressure vessel, plates, shells, and three-dimensional solids. Commercial computer software for structural analysis typically uses matrix finite-element analysis, which can be further classified into two main approaches: the displacement or stiffness method and the force or flexibility method. The stiffness method is the most popular by far thanks to its ease of implementation as well as of formulation for advanced applications.

The finite-element technology is now sophisticated enough to handle just about any system as long as sufficient computing power is available. Its applicability includes, but is not limited to, linear and non-linear analysis, solid and fluid interactions, materials that are isotropic, orthotropic, or anisotropic, and external effects that are static, dynamic, and environmental factors. This, however, does not imply that the computed solution will automatically be reliable because much depends on the model and the reliability of the data input.

2.9 Time-line

• 1452-1519 Leonardo da Vinci made many contributions.• 1638: Galileo Galilei published the book "Two New Sciences" in which he

examined the failure of simple structures.• 1660: Hooke's law by Robert Hooke.• 1687: Isaac Newton published "Philosophiae Naturalis Principia Mathematica"

which contains the Newton's laws of motion.• 1750: Euler-Bernoulli beam equation.• 1700-1782: Daniel Bernoulli introduced the principle of virtual work.• 1707-1783: Leonhard Euler developed the theory of buckling of columns.• 1826: Claude-Louis Navier published a treatise on the elastic behaviors of

structures.• 1873: Carlo Alberto Castigliano presented his dissertation "Intorno ai sistemi

elastici", which contains his theorem for computing displacement as partial derivative of the strain energy. This theorem includes the method of least work as a special case.

• 1936: Hardy Cross' publication of the moment distribution method which was later recognized as a form of the relaxation method applicable to the problem of flow in pipe-network.

• 1941: Alexander Hrennikoff submitted his D.Sc thesis in MIT on the discretization of plane elasticity problems using a lattice framework.

• 1942: R. Courant divided a domain into finite subregions.• 1956: J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp's paper on the

"Stiffness and Deflection of Complex Structures". This paper introduces the name "finite-element method" and is widely recognized as the first comprehensive treatment of the method as it is known today.

2.10Structural Behaviour of Model Masonry Shells

According to the recent teaching reform at ETH Zurich, students are strongly encouraged to participate in experimental research. Within the scope of a research project on the structural behaviour of unreinforced masonry shells a load test on a conoid-type shell made of model clay bricks and thin layer mortar was performed at ETH’s Institute of Structural Engineering.

The results of the load test were analysed and allow a number of conclusions to be drawn:

• Curved unreinforced masonry structures, such as the tested shell are capable of resisting a considerable load by compressive membrane action.

• A simple structural model was successfully applied to analyse the structural behaviour of unreinforced masonry conoid-type shell subjected to (quasi) uniformly distributed load. This model divides the shell into two parts, i.e. the back part acting as a plate in bending and the front part carrying the load through arching action.

• Future research on unreinforced masonry shells should concentrate on large-scale, if possible full-scale tests. Furthermore, an effort should be made to find optimum shapes for unreinforced masonry shells. Finally, the numerical modelling of masonry deserves more study.

Structural System

Structural analysis is a process to analyze a structural system in order to predict the responses of the real structure under the excitation of expected loading and external environment during the service life of the structure. The purpose of a structural analysis is to ensure the adequacy of the design from the view point of safety and serviceability of the structure.

A structural system normally consists of three essential components as illustrated in (a) the structural model; (b) the prescribed excitations; and (c) the structural responses as the result of the analysis process. In all cases, a structure must be idealized by a mathematical model so that its behaviors can be determined by solving a set of mathematical equations

A structural system can be one-dimensional, two-dimensional or three-dimensional depending on the space dimension of the loadings and the types of structural responses that are of interest to the designer. Although any real-world structure is strictly three-dimensional, for the purpose of simplification and focus, one can recognize a specific pattern of loading under which the key structural responses will remain in just one or two-dimensional space.

2.11 Structural Modeling

A structural (mathematical) model can be defined as an assembly of structural members (elements) interconnected at the boundaries (surfaces, lines, joints). Thus, a structural model consists of three basic components namely, (a) structural members, (b) joints (nodes, connecting edges or surfaces) and (c) boundary conditions.

(a) Structural members: Structural members can be one-dimensional (1D) members (beams, bars, cables etc.), 2D members (planes, membranes, plates, shells etc.) or in the most general case 3D solids. (b) Joints: For one-dimensional members, a joint can be rigid joint, deformable joint or pinned joint, as shown in Figure 4. In rigid joints, both static and kinematics variables are continuous across the joint. For pinned joints, continuity will be lost on rotation as well as bending moment. In between, the deformable joint, represented by a rotational spring, will carry over only a part the rotation from one member to its neighbor offset by the joint deformation under the effect of the bending moment.

(c) Boundary conditions: To serve its purposeful functions, structures are normally prevented from moving freely in space at certain points called supports. As shown in Figure 5, supports can be fully or partially restrained. In addition, fully restrained components of the support may be subjected to prescribed displacements such as ground settlements.

2.12 Linearity of the Structural System

Assumptions are usually observed in order for the structural system to be treated as linear: (a) The displacement of the structure is so insignificant that under the applied loads, the

deformed configuration can be approximated by the un-deformed configuration in satisfying the equilibrium equations.

(b) The structural deformation is so small that the relationship between strain and displacement remains linear.

(c) For small deformation, the stress-strain relationship of all structural members falls in the range of Hooke’s law, i.e., it is linear elastic, isotropic and homogeneous.

Glossary:

Acceleration: A vector quantity equal to the rate that velocity changes with time.

Applied force: see external force.

Axial force: A system of internal forces whose resultant is a force acting along the longitudinal axis of a structural member or assembly.

Bending moment: A system of internal forces whose resultant is a moment. This term is most commonly used to refer to internal forces in beams.

Body force: An external force acting throughout the mass of a body. Gravity is a body force. An inertial force is a body force.

Brittle: A brittle structure or material exhibits low ductility, meaning that it exhibits very little inelastic deformation before complete failure.

Center of Gravity: The location of the resultant of gravity forces on an object or objects: sometimes called center of mass.

Centroid: Similar to the concept of center of gravity, except that it applies to a two dimensional shape rather than an object. For a given shape, the centroid location corresponds to the center of gravity for a thin flat plate of that shape, made from a homogeneous material.

Component (of a vector): Any vector can be expressed as a collection of vectors whose sum is equal to the original vector. Each vector in this collection is a component of the original vector. It is common to express a vector in terms of components which are parallel to the x and y axes.

Concentrated force: A force considered to act along a single line in space. Concentrated forces are useful mathematical idealizations, but cannot be found in the real world, where all forces are either body forces acting over a volume or surface forces acting over an area.

Concentrated load: An external force which a concentrated force.

Connection: Connection is similar to the concept of support, except that connection refers to a relationship between members in a structural model. A connection restrains degrees of freedom of one member with respect to another. For each restrained degree of freedom, there is a corresponding force transferred from one member to the other; forces associated with unrestrained degrees of freedom are zero. See fixed connection and pin connection.

Couple: A system of forces composed of two equal forces of opposite direction, offset by a distance. A couple is statically equivalent to a moment whose magnitude equals the magnitude of the force times the offset distance.

Deflection: This word usually carries the same meaning as displacement, although it is sometimes used in place of deformation.

Deformation: A change in the shape of an object or material.

Degree of Freedom: A displacement quantity which defines the shape and location of an object. In the two dimensional plane, a rigid object has three degrees of freedom: two translations and one rotation. In three dimensional space, a rigid object has six degrees of freedom (three translations and three rotations).

Displacement: A change in position. A displacement may be a translation a rotation or a combination of those.

Distributed load: An external force which acts over a region of length, surface, or area: essentially any external force which is not a concentrated force.

Ductility: Ductility generally refers to the amount of inelastic deformation which a material or structure experiences before complete failure. Quantitatively, ductility can be defined as the ratio of the total displacement or strain at failure, divided by the displacement or strain at the elastic limit.

Dynamic equilibrium: Equilibrium which includes inertial forces.

Check your progress:

1. Explain Classification of structures2. Explain Analytical methods3. Explain Elasticity methods

Reference

1. ^ McLennan, J. F. (2004), The Philosophy of Sustainable Design2. ^ Fan Shu-Yang, Bill Freedman, and Raymond Cote (2004). "Principles and

practice of ecological design". Environmental Reviews. 12: 97–112. link

3. ^ Anastas, P. L. and Zimmerman, J. B. (2003). "Through the 12 principles of green engineering". Environmental Science and Technology. March 1. 95-101A.

4. ^ [1] US DOE 20 yr Global Product & Energy Study.5. ^ Paul Hawken, Amory B. Lovins, and L. Hunter Lovins (1999). Natural

Capitalism: Creating the Next Industrial Revolution. Little, Brown.6. ^ Ryan, Chris (2006). "Dematerializing Consumption through Service

Substitution is a Design Challenge". Journal of Industrial Ecology. 4(1).7. ^ Ben-Gal I., Katz R. and Bukchin J., "Robust Eco-Design: A New Application

for Quality Engineering", IIE Transactions, Vol. 40 (10), p. 907 - 918. Available at: http://www.eng.tau.ac.il/~bengal/Eco_Design.pdf

8. ^ Various. " Guiding Principles of Sustainable Design." THE PRINCIPLES OF SUSTAINABILITY. Accessed at [2].

9. ^ JA Tainter 1988 The Collapse of Complex Societies Cambridge Univ. Press10. ^ [3] Buzz Holling 1973 Resilience and Stability of Ecological Systems11. ^ Waste and recycling, DEFRA12. ^ Household waste, Office for National Statistics.13. ^ Various. " Guiding Principles of Sustainable Design." Chapter 9: Waste

Prevention. Accessed at [4].14. ^ Ji Yan and Plainiotis Stellios (2006): Design for Sustainability. Beijing: China

Architecture and Building Press. ISBN 7-112-08390-715. ^ Holm, Ivar (2006). Ideas and Beliefs in Architecture and Industrial design:

How attitudes, orientations, and underlying assumptions shape the built environment. Oslo School of Architecture and Design. ISBN 82-547-0174-1.

16. ^ Rolf Disch Solararchitektur17. ^ Feenstra, G (December 1997). What Is Sustainable Architecture?. Retrieved

June 27, 2009, from UC SAREP Web site: [5]

Check your progress answer:1. Refer 2.22. Refer 2.43. Refer 2.7

Unit 3: Design by ACI

3.1 Introduction3.2 Limits on material strength

3.3 Beam design3.4 Design flexural reinforcement3.5 Determine factored moments3.6 Determine required flexural reinforcement3.7 Slab Design3.8 Design for flexure3.9 Determine factored moments for the strip3.10 Design flexural reinforcement for the strip3.11 Design punching shear reinforcement

Introduction

SAFE automates several slab and mat design tasks. Specifically, it integrates slab design moments across design strips and designs the required reinforcement; it checks slab punching shear around column supports and concentrated loads; and it designs beam flexural, shear, and torsion reinforcement. The design procedures are outlined in the chapter entitled "SAFE Design Features” in the Key Features and Terminology manual. The actual design algorithms vary based on the specific design code chosen by the user. This manual describes the algorithms used for the various codes.

It should be noted that the design of reinforced concrete slabs is a complex subject and the design codes cover many aspects of this process. SAFE is a tool to help the user in this process. Only the aspects of design documented in this manual are automated by SAFE design capabilities. The user must check the results produced and address other aspects not covered by SAFE.

Limits on Material Strength

The concrete compressive strength, f 'c , should not be less than 2500 psi (ACI 5.1.1). The upper limit of the reinforcement yield strength, fy, is taken as 80 ksi (ACI 9.4) and the upper limit of the reinforcement shear strength, fyt, is taken as 60 ksi (ACI 11.5.2). SAFE enforces the upper material strength limits for flexure and shear design of beams and slabs or for torsion design of beams. The input material strengths are taken as the upper limits if they are defined in the material properties as being greater than the limits. The user is responsible for ensuring that the minimum strength is satisfied. Strength Reduction Factors The strength reduction factors, φ, are applied to the specified strength to obtain the design strength provided by a member. The φ factors for flexure, shear, and torsion are as follows:φ = 0.90 for flexure (tension controlled) (ACI 9.3.2.1)φ = 0.75 for shear and torsion (ACI 9.3.2.3)These values can be overwritten; however, caution is advised.

Beam Design

In the design of concrete beams, SAFE calculates and reports the required areas of reinforcement for flexure, shear, and torsion based on the beam moments, shear forces, torsion, load combination factors, and other criteria described in this section. The reinforcement requirements are calculated at each station along the length of the beam. Beams are designed for major direction flexure, shear, and torsion only. Effects resulting from any axial forces and minor direction bending that may exist in the beams must be investigated independently by the user. The beam design procedure involves the following steps:

• Design flexural reinforcement• Design shear reinforcement• Design torsion reinforcement

Design Flexural Reinforcement

The beam top and bottom flexural reinforcement is designed at each station along the beam. In designing the flexural reinforcement for the major moment of a particular beam, for a particular station, the following steps are involved:

• Determine factored moments• Determine required flexural reinforcement

Determine Factored Moments

In the design of flexural reinforcement of concrete beams, the factored moments for each load combination at a particular beam station are obtained by factoring the corresponding moments for different load cases, with the corresponding load factors. The beam is then designed for the maximum positive and maximum negative factored moments obtained from all of the load combinations. Calculation of bottom reinforcement is based on positive beam moments. In such cases the beam may be designed as a rectangular or flanged beam. Calculation of top reinforcement is based on negative beam moments. In such cases the beam may be designed as a rectangular or inverted flanged beam.

Determine Required Flexural Reinforcement

In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding compression reinforcement by increasing the effective depth, the width, or the strength of the concrete. Note that the flexural reinforcement strength, fy , is limited to 80 ksi (ACI 9.4), even if the material property is

defined using a higher value. The design procedure is based on the simplified rectangular stress block, (ACI 10.2). Furthermore, it is assumed that the net tensile strain in the reinforcement shall not be less than 0.005 (tension controlled) (ACI 10.3.4) when the concrete in compression reaches its assumed strain limit of 0.003. When the applied moment exceeds the moment capacity at this design condition, the area of compression reinforcement is calculated assuming that the additional moment will be carried by compression reinforcement and additional tension reinforcement. The design procedure used by SAFE, for both rectangular and flanged sections (L- and T-beams), is summarized in the text that follows. It is assumed that the design ultimate axial force does not exceed (0.1 f ' c Ag) (ACI 10.3.5), hence all beams are designed for major direction flexure, shear, and torsion only.

Slab Design

Similar to conventional design, the SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The locations of the strips are usually governed by the locations of the slab supports. The moments for a particular strip are recovered from the analysis, and a flexural design is carried out based on the ultimate strength design method (ACI 318-08) for reinforced concrete as described in the following sections. To learn more about the design strips, refer to the section entitled "Design Strips" in the Key Features and Terminology manual.

Design for Flexure

SAFE designs the slab on a strip-by-strip basis. The moments used for the design of the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors. Those moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh. The design of the slab reinforcement for a particular strip is carried out at specific locations along the length of the strip. These locations correspond to the element boundaries. Controlling reinforcement is computed on either side of those element boundaries. The slab flexural design procedure for each load combination involves the following:

• Determine factored moments for each slab strip.• Design flexural reinforcement for the strip.

These two steps, described in the text that follows, are repeated for every load combination. The maximum reinforcement calculated for the top and bottom of the slab within each design strip, along with the corresponding controlling load combination, is obtained and reported.Determine Factored Moments for the Strip

For each element within the design strip, for each load combination, the program calculates the nodal reactive moments. The nodal moments are then added to get the strip moments.

Design Flexural Reinforcement for the Strip

The reinforcement computation for each slab design strip, given the bending moment, is identical to the design of rectangular beam sections described earlier (or to the flanged beam if the slab is ribbed). In some cases, at a given design section in a design strip, there may be two or more slab properties across the width of the design strip. In that case, the program automatically designs the tributary width associated with each of the slab properties separately using its tributary bending moment. The reinforcement obtained for each of the tributary widths is summed to obtain the total reinforcement for the full width of the design strip at the considered design section. This is the method used when drop panels are included. Where openings occur, the slab width is adjusted accordingly.

Design Punching Shear Reinforcement

The use of shear studs as shear reinforcement in slabs is permitted, provided that the effective depth of the slab is greater than or equal to 6 inches, and not less than 16 times the shear reinforcement bar diameter (ACI 11.11.3). If the slab thickness does not meet these requirements, the punching shear reinforcement is not designed and the slab thickness should be increased by the user. The algorithm for designing the required punching shear reinforcement is used when the punching shear capacity ratio exceeds unity. The Critical Section for Punching Shear and Transfer of Unbalanced Moment as described in the earlier sections remain unchanged. Glossary:

Server Platform: This refers to the type of computer server that will be used to push your site to the internet. When you purchase a web hosting solution from a company like GoDaddy.com, you will have to choose a server platform. Before you make this decision, make sure you discuss with your web designer which platforms he can use for development. You wouldn't want to purchase a PHP solution if your developer only works in ASP.Net or Cold Fusion.

HTML: HTML stands for Hypertext Markup Language, and is the defacto language of the internet. This markup language uses a simple tag structure to tell a web browser how to display a web page to the user.

CSS: CSS in an acronym for Cascading Style Sheets. CSS is used by web designers to define the look of a website by assigning style attributes (color, width, fonts, etc.) to its HTML tag structure. Using style sheets also allows a designer to easily unify the look of a website as it creates a template for page elements like paragraphs, headline text, buttons, and more.

ASP.Net: ASP.Net (.aspx) is Microsoft's web programming language. It is a robust development platform which allows your developer to do dynamic things with your web site like connect to a database, send an email, add a blog, or do complex math calculations.

PHP: PHP is a free general use scripting language that allows you to create dynamic websites, much like ASP.Net. Since no license is required to use PHP, it has become widely used throughout the internet development community.

Cold Fusion: Cold Fusion (.cfm) is Adobe Systems' web scripting language. While not as popular as ASP.Net or PHP, ColdFusion still maintains a strong presence as a valid server technology, and is often the choice of developers who work within design/marketing firms.

JavaScript: This scripting language is primarily used to provide enhanced user interfaces like rotating banners, and cool effects for buttons and banners.

JQuery: JQuery is an advanced JavaScript library that makes it easier for web developers to create some really awesome dynamic effects on a web site. JQuery is becoming widely accepted as a replacement for simple Flash functionality.

Flash: This is Adobe Systems' interactive development platform. It is most often used to create interactive graphical web applications, animations, and user interfaces.

ABX Comparator: A device that randomly selects between two components being tested. The listener doesn't know which device is being listened to.

AC3: See Dolby Digital

Acoustic suspension: A sealed or closed box speaker enclosure.

AES/EBU: Balanced digital connection. For example, used to connect a CD transport to a DAC. The AES/EBU standard uses XLR type connectors.

Alignment: A class of enclosure parameters that provides optimum performance for a woofer with a given value of Q.

Alpha: Term used in sealed enclosure designs to mean the ratio of Vas to Vb, where Vb is the volume of the box you will build.

Alternating Current (AC): An electrical current that periodically changes in magnitude and direction.

Ambience: The acoustic characteristics of a space with regard to reverberation. A room with a lot of reverb is said to be "live"; one without much reverb is "dead."

Ampere (A): The unit of measurement for electrical current in coulombs per second. There is one ampere in a circuit that has one ohm resistance when one volt is applied to the circuit. See Ohms Law.

Amplifier (Amp): A device which increases signal level. Many types of amplifiers are used in audio systems. Amplifiers typically increase voltage, current or both.

Amplifier classes: Audio power amplifiers are classified primarily by the design of the output stage. Classification is based on the amount of time the output devices operate during each cycle of signal swing. Also defined in terms of output bias current, (the amount of current flowing in the output devices with no signal).

Attenuate: To reduce in level.

Analog: Before digital, the way all sound was reproduced.

Aperiodic: Refers to a type of bass-cabinet loading. An aperiodic enclosure type usually features a very restrictive, (damped), port. The purpose of this restrictive port is not to extend bass response, but lower the Q of the system and reduce the impedance peak at resonance. Most restrictive ports are heavily stuffed with fiberglass, dacron or foam.

Audiophile: A person interested in sound reproduction.

AWS: Adaptive Woofer System, trademark of ACI. An active woofer system with built in user adjustable equalization capabilities.

Baffle: A surface used to mount a loudspeaker.

Balanced: Referring to wiring: Audio signals require two wires. In an unbalanced line the shield is one of those wires. In a balanced line, there are two wires plus the shield. For the system to be balanced requires balanced electronics and usually employs XLR connectors. Balanced lines are less apt to pick up external noise. This is usually not a factor in home audio, but is a factor in professional audio requiring hundreds or even thousands of feet of cabling. Many higher quality home audio cables terminated with RCA jacks are balanced designs using two conductors and a shield instead of one conductor plus shield.

Bandwidth: The total frequency range of any system. Usually specified as something like: 20-20,000Hz plus or minus 3 db.

Band-pass Enclosure: A multi-chambered ported system.

Band-pass filter: An electric circuit designed to pass only middle frequencies.

Bass Blockers: Commercial name for auto-sound first order high pass crossovers (non-polarized capacitors), generally used on midbass or dash speakers to keep them from trying to reproduce deep bass.

Bass Reflex: A type of loudspeaker that uses a port or duct to augment the low-frequency response. Opinions vary widely over the "best" type of bass cabinet, but much has to do with how well a given design, such as a bass reflex is implemented.

Beaming: A tendency of a loudspeaker to concentrate the sound in a narrow path instead of spreading it.

Bessel crossover: A type of crossover design characterized by having a linear or maximally flat phase response. Linear phase response results in constant time-delay (all frequencies within the passband are delayed the same amount). Consequently the value of linear phase is it reproduces a near-perfect step response with no overshoot or ringing. The downside of the Bessel is a slow roll-off rate. The same circuit complexity in a Butterworth response rolls off much faster.

Bi-amplify: The use of two amplifiers, one for the lows, one for the highs in a speaker system. Could be built into the speaker design or accomplished with the use of external amplifiers and electronic crossovers.

Bi-wiring: The use of two pairs of speaker wire from the same amplifier to separate bass and treble inputs on the speaker.

BNC: A type of connection often used in instrumentation and sometimes in digital audio. BNC connectors sometimes are used for digital connections such as from a CD Transport to the input of a DAC.

Boomy: Listening term, refers to an excessive bass response that has a peak(s) in it.

Bright: Listening term. Usually refers to too much upper frequency energy.

Bridging: Combining both left and right stereo channels on an automotive amplifier into one higher powered mono channel. When an amplifier is bridged, the impedance that the amplifier actually "sees" is calculated based upon the output of both stereo channels. Here is a simple formula to help define this:

Bridged Mono Impedance = (Y / X)/2

Y = impedance of driver(s) (both drivers should be identical)

X = # of drivers in circuit

One 4 ohm sub in bridged mono is equal to hooking up two 2 ohm subs in stereo, one to each channel.

Butterworth crossover: A type of crossover circuit design having a maximally flat magnitude response, i.e., no amplitude ripple in the passband. This circuit is based upon Butterworth functions, also know as Butterworth polynomials.

Cabin gain: The low frequency boost normally obtained inside a vehicle interior when subs are properly mounted.

Capacitor: A device made up of two metallic plates separated by a dielectric (insulating material). Used to store electrical energy in the electrostatic field between the plates. It produces an impedance to an ac current.

Center Channel: In home theater, sound decoded from the stereo signal sent to a speaker mounted in front of the listener, specially designed to enhance voices and sound effects from a movie soundtrack. Used in car audio to help offset skewed stereo imaging due to seating positions in the automotive environment.

Channel Balance: In a stereo system, the level balance between left and right channels. Properly balanced, the image should be centered between the left-right speakers. In a home-theater system, refers to achieving correct balance between all the channels of the system.

Check your progress:

1. Explain Design flexural reinforcement2. Explain Determine required flexural reinforcement3. Explain Slab Design

Reference:

[1] P. Berman, J. A. Garay, and K. J. Perry, “Optimal Early Stopping in DistributedConsensus”, Proc. 6th International Workshop on Distributed Algorithms (WDAG ’92),LNCS 647, Springer-Verlag, Nov. 1992, 221-237.[2] J. Blazewicz, P.W. Dell’Olmo, M. Drozdowski, and M.G. Speranza, “Scheduling MultiprocessorTasks on Three Dedicated Processors”, Information Processing Letters 41,pp. 275-280, 1992.[3] J. Blazewicz, J., P.W. Dell’Olmo, M. Drozdowski, and M.G. Speranza, “Scheduling Multiprocessor Tasks on Three Dedicated Processors: Corrigendum”, Information Processing Letters 49, pp. 269-270, 1994.13[4] Blazewicz, J., et.al., “Scheduling Computer and Manufacturing Processes”, Springer-Verlag, 1996.[5] CERT/CC Statistics 1988-2002, CERT Coordination Center,http://www.cert.org/stats/cert stats.html.

[6] M. Dror, Kubiak, W., and Dell’Olmo, P., “ ’Strong’ - ’Weak’ chain constrained scheduling,”Ricerca Operativa, Vol. 27, 1998, pp. 35-49.[7] E. Ellison, L. Linger, and M. Longstaff, Survivable Network Systems: An EmergingDiscipline, Carnegie Mellon, SEI, Technical Report CMU/SEI-97-TR-013, 1997.[8] Keynote Speech of the Information Survivability Workshop, part of the InternationalConference on Dependable Systems and Networks, DSN-2001, by Roy Maxion, CMU,Goteborg, Sweden, 2001.[9] D. Johansen, et al., Operating System Support for Mobile Agents, Proc. 5th IEEEWorkshop on Hot Topics in Operating Systems, 1995.[10] D. Johansen, et al., NAP: Practical Fault-Tolerance for Itinerant Computations, TechnicalReport TR98-1716, Department of Computer Science, Cornell University, USA,November, 1998.[11] A.W. Krings, and M.A. McQueen, “Distributed Agreement in a Security Application,”28th International Symposium on Fault-Tolerant Computing, Digest of FastAbstracts:FTCS-28, IEEE Computer Society Press, Munich, Germany, June 23 - 25, 1998, pp. 37-38.[12] A.W. Krings, et al., “A Two-Layer Approach to Survivability of Networked ComputingSystems”, Proc. International Conference on Advances in Infrastructure for ElectronicBusiness, Science, and Education on the Internet, L’Aquila, Italy, Aug 06 - Aug 12, pp.1-12, 2001.[13] A. Krings, et al., Attack Recognition Based on Kernel Attack Signatures, Proc. InternationalSymposium on Information Systems and Engineering, Las Vegas, pp. 413-419,2001.[14] A. Krings, et al., Scheduling Issues in Survivability Applications using Hybrid FaultModels, to appear in Parallel Processing Letters.

Check your progress Answer

1. Refer 3.42. Refer 3.63. Refer 3.7

Unit 4: ASCE Task Committee method – pyramidal roof

4.1 Introduction4.2 Definition of space frame4.3 Basic concepts4.4 Advantages of space frames4.5 Preliminary planning guidelines

4.1 Introduction

A growing interest in space frame structures has been witnessed worldwide over the last half century. The search for new structural forms to accommodate large unobstructed areas has always been the main objective of architects and engineers. With the advent of new building techniques and construction materials, space frames frequently provide the right answer and satisfy the requirements for lightness, economy, and speedy construction. Significant progress has been made in the process of the development of the space frame.

A large amount of theoretical and experimental research programs was carried out by many universities and research institutions in various countries. As a result, a great deal of useful information has been disseminated and fruitful results have been put into practice. In the past few decades, the proliferation of the space frame was mainly due to its great structural potential and visual beauty. New and imaginative applications of space frames are being demonstrated in the total range of building types, such as sports arenas, exhibition pavilions, assembly halls, transportation terminals, airplane hangars, workshops, and warehouses.

They have been used not only on long-span roofs, but also on mid- and short-span enclosures as roofs, floors, exterior walls, and canopies. Many interesting projects have been designed and constructed all over the world using a variety of configurations. Some important factors that influence the rapid development of the space frame can be cited as follows. First, the search for large indoor space has always been the focus of human activities. Consequently, sports tournaments, cultural performances, mass assemblies, and exhibitions can be held under one roof. The modern production and the needs of greater operational efficiency also created demand for large space with a minimum interference from internal supports. The space frame provides the benefit that the interior space can be used in a variety of ways and thus is ideally suited for such requirements. Space frames are highly statically indeterminate and their analysis leads to extremely tedious computation if by hand. The difficulty of the complicated analysis of such systems contributed to their limited use. The introduction of electronic computers has radically changed the whole approach to the analysis of space frames.

By using computer programs, it is possible to analyze very complex space structures with great accuracy and less time involved. Lastly, the space frame also has the problem of connecting a large number of members (sometimes up to 20) in space through different angles at a single point. The emergence of several connecting methods of proprietary systems has made great improvement in the construction of the space frame, which offered simple and efficient means for making connection of members. The exact tolerances required by these jointing systems can be achieved in the fabrication of the members and joints.

4.2 Definition of the Space Frame

If one looks at technical literature on structural engineering, one will find that the meaning of the space frame has been very diverse or even confusing. In a very broad sense, the definition of the space frame is literally a three-dimensional structure. However, in a more restricted sense, space frame means some type of special structure action in three dimensions. Sometimes structural engineers and architects seem to fail to convey with it what they really want to communicate.

Thus, it is appropriate to define here the term space frame as understood throughout this section. It is best to quote a definition given by a Working Group on Spatial Steel Structures of the International Association [11]. A space frame is a structure system assembled of linear elements so arranged that forces are transferred in a three-dimensional manner. In some cases, the constituent element may be two-dimensional. Macroscopically a space frame often takes the form of a flat or curved surface.

It should be noted that virtually the same structure defined as a space frame here is referred to as latticed structures in a State-of-the-Art Report prepared by the ASCE Task Committee on Latticed Structures [2] which states: A latticed structure is a structure system in the form of a network of elements (as opposed to a continuous surface). Rolled, extruded or fabricated sections comprise the member elements. Another characteristic of latticed structural system is that their load-carrying mechanism is three dimensional in nature. The ASCE Report also specifies that the three-dimensional character includes flat surfaces with loading perpendicular to the plane as well as curved surfaces.

The Report excludes structural systems such as common trusses or building frames, which can appropriately be divided into a series of planar frameworks with loading in the plane of the framework. In this section the terms space frames and latticed structures are considered synonymous. A space frame is usually arranged in an array of single, double, or multiple layers of intersecting members.

Some authors define space frames only as double layer grids. A single layer space frame that has the form of a curved surface is termed as braced vault, braced dome, or latticed shell. Occasionally the term space truss appears in the technical literature. According to the structural analysis approach, a space frame is analyzed by assuming rigid joints that cause internal torsions and moments in the members, whereas a space truss is assumed as hinged joints and therefore has no internal member moments.

The choice between space frame and space truss action is mainly determined by the joint-connection detailing and the member geometry is no different for both. However, in engineering practice, there are no absolutely rigid or hinged joints. For example, a double layer flat surface space frame is usually analyzed as hinged connections, while a single layer curved surface space frame may be analyzed either as hinged or rigid connections. The term space frame will be used to refer to both space frames and space trusses.

4.3 Basic Concepts

The space frame can be formed either in a flat or a curved surface. The earliest form of space frame structures is a single layer grid. By adding intermediate grids and including rigid connecting to the joist and girder framing system, the single layer grid is formed. The major characteristic of grid construction is the omni-directional spreading of the load as opposed to the linear transfer of the load in an ordinary framing system. Since such load transfer is mainly by bending, for larger spans, the bending stiffness is increased most efficiently by going to a double layer system.

The load transfer mechanism of curved surface space frame is essentially different from the grid system that is primarily membrane-like action. joist and girder framing system, the single layer grid is formed. The major characteristic of grid construction is the omni-directional spreading of the load as opposed to the linear transfer of the load in an ordinary framing system. Since such load transfer is mainly by bending, for larger spans, the bending stiffness is increased most efficiently by going to a double layer system. The load transfer mechanism of curved surface space frame is essentially different from the grid system that is primarily membrane-like action.

4.4 Advantages of Space Frames

1. One of the most important advantages of a space frame structure is its light weight. It is mainly due to fact that material is distributed spatially in such a way that the load transfer mechanism is primarily axial—tension or compression. Consequently, all material in any given element is utilized to its full extent. Furthermore, most space frames are now constructed with steel or aluminum, which decreases considerably their self-

weight. This is especially important in the case of long span roofs that led to a number of notable examples of applications.2. The units of space frames are usually mass produced in the factory so that they can take full advantage of an industrialized system of construction. Space frames can be built from simple prefabricated units, which are often of standard size and shape. Such units can be easily transported and rapidly assembled on site by semi-skilled labor. Consequently, space frames can be built at a lower cost.3. A space frame is usually sufficiently stiff in spite of its lightness. This is due to its three dimensional character and to the full participation of its constituent elements. Engineers appreciate the inherent rigidity and great stiffness of space frames and their exceptional ability to resist unsymmetrical or heavy concentrated load. Possessing greater rigidity, the space frames also allow greater flexibility in layout and positioning of columns.4. Space frames possess a versatility of shape and form and can utilize a standard module to generate various flat space grids, latticed shell, or even free-form shapes. Architects appreciate the visual beauty and the impressive simplicity of lines in space frames. A trend is very noticeable in which the structural members are left exposed as a part of the architectural expression. Desire for openness for both visual impact as well as the ability to accommodate variable space requirements always calls for space frames as the most favorable solution.

4.5 Preliminary Planning Guidelines

In the preliminary stage of planning a space frame to cover a specific building, a number of factors should be studied and evaluated before proceeding to structural analysis and design. These include not only structural adequacy and functional requirements, but also the aesthetic effect desired.1. In its initial phase, structural design consists of choosing the general form of the building and the type of space frame appropriate to this form. Since a space frame is assembled from straight, linear elements connected at nodes, the geometrical arrangement of the elements—surface shape, number of layers, grid pattern, etc.—needs to be studied carefully in the light of various pertinent requirements.2. The geometry of the space frame is an important factor to be planned which will influence both the bearing capacity and weight of the structure. The module size is developed from the overall building dimensions, while the depth of the grid (in case of a double layer), the size of cladding, and the position of supports will also have a pronounced effect upon it. For a curved surface, the geometry is also related to the curvature or, more specifically, to the rise of the span. A compromise between these various aspects usually has to be made to achieve a satisfactory solution.3. In a space frame, connecting joints play an important role, both functional and aesthetic, which is derived from their rationality during construction and after completion. Since joints have a decisive effect on the strength and stiffness of the structure and compose around 20 to 30% of the total weight, joint design is critical to space frame economy and safety. There are a number of proprietary systems that are used for space frame structures. A system should be selected on the basis of quality, cost, and erection efficiency. In addition, custom-designed space frames have been developed,

especially for long span roofs. Regardless of the type of space frame, the essence of any system is the jointing system.

4. At the preliminary stage of design, choosing the type of space frame has to be closely related to the constructional technology. The space frames do not have such sequential order of erection for planar structures and require special consideration on the method of construction. Usually a complete false work has to be provided so that the structure can be assembled in the high place. Alternatively, the structure can be assembled on the ground, and certain techniques can be adopted to lift the whole structure, or its large part, to the final position.

PED can also be expressed as (dQ/dP)/Q/P or the ratio of the marginal function to the average function for a demand curve Q = f( P). This relationship provides an easy way of determining whether a point on a demand curve is elastic or inelastic. The slope of a line tangent to the curve at the point is the marginal function. The slope of a secant drawn from the origin through the point is the average function.

If the slope of the tangent is greater than the slope of the secant (M > A) then the function is elastic at the point. If the slope of the secant is greater than the slope of the tangent then the curve is inelastic at the point. If the tangent line is extended to the horizontal axis the problem is simply a matter of comparing angles formed by the lines and the horizontal axis. If the marginal angle is numerically greater than the average angle then the function is elastic at the point. If the marginal angle is less than the average angle then the function is inelastic at that point.

If you follow the convention adopted by economist and plot the independent variable on the vertical axis and the dependent variable on the horizontal axis then the marginal function will be dP/dQ and the average function will be P/Q meaning that you are deriving the reciprocal of elasticity. Therefore opposite rules would apply. The tangency line slope would be dP/dQ and the slope of the secant would be the numerical value P/Q. This method is not limited to demand functions

it can be used with any functions. For example a linear supply curve drawn through the origin has unitary elasticity (if you use the method the marginal function is identical to the slope). If a linear supply function intersects the y axis then the marginal function will be less than the average and the function is inelastic at any point and becomes increasingly inelastic as one moves up the curve. With a supply curve that intersects the x axis then the slope of the curve will exceed the slope of the secant at all point meaning that the M > A the slope is elastic and will become increasingly elastic as one moves up the slope. Again this assumes that the dependent variable is drawn on the Y axis.

Glossary:

Dynamic range: The range between the loudest and the softest sounds that are in a piece of music, or that can be reproduced by a piece of audio equipment without distortion (a

ratio expressed in decibels). In speech, the range rarely exceeds 40 dB; in music, it is greatest in orchestral works, where the range may be as much as 75 dB.

EBP: Efficiency Bandwidth Product. A guide that helps a designer determine whether a driver is more suitable for a sealed or ported enclosure. EBP of less than 50 indicates the driver should be used in a sealed, 50 - 90 indicates flexible design options, over 90 indicates best for a ported enclosure. EBP = Fs / Qes

Efficiency rating: The loudspeaker parameter that gives the level of sound output when measured at a prescribed distance with a standard level of electrical energy fed into the speaker. The loudspeaker parameter that gives the level of sound output when measured at a prescribed distance with a standard level of electrical energy fed into the speaker.

Electronic Crossover: Uses active circuitry to send signals to appropriate drivers. More efficient than passive crossovers. Uses active circuitry to send signals to appropriate drivers. More efficient than passive crossovers.

Electrostatic Speaker: A speaker that radiates sound from a large diaphragm that is suspended between high-voltage grids.

Equalizer: Electronic set of filters used to boost or attenuate certain frequencies.

Euphonic: Pleasing. As a descriptive audio term, usually refers to a coloration or inaccuracy that non-the-less may be sonically pleasing.

Extension: How extended a range of frequencies the device can reproduce accurately. Bass extension refers to how low a frequency tone will the system reproduce, high-frequency extension refers to how high in frequency will the system play.

Farad: The basic unit of capacitance. A capacitor has a value of one farad when it can store one coulomb of charge with one volt across it.

Fb: The tuned frequency of a ported box.

Fc or Fcb:The system resonance frequency of a driver in a sealed box. The system resonance frequency of a driver in a sealed box.

Filter:An electrical circuit or mechanical device that removes or attenuates energy at certain frequencies. . An electrical circuit or mechanical device that removes or attenuates energy at certain frequencies. .

Flat Response:The faithful reproduction of an audio signal; specifically, the variations in output level of less than 1 dB above or below a median level over the audio spectrum.

F3: The roll-off frequency at which the driver's response is down -3dB from the level of it's midband response.

Fletcher-Munson curve: Our sensitivity to sound depends on its frequency and volume. Human ears are most sensitive to sounds in the midrange. At lower volume levels humans are less sensitive to sounds away from the midrange, bass and treble sounds "seem" reduced in intensity at lower listening levels.

Free Air Resonance: The natural resonant frequency of a driver when operating outside an enclosure.

Frequency: The range of human hearing is commonly given as 20-20,000Hz (20Hz-20kHz). One hertz (Hz) represents one cycle per second, 20Hz represents 20 cycles per second and so on. Lower numbers are lower frequencies

Fs: The frequency of resonance for a driver in free air.

Full-range: A speaker designed to reproduce all or most of the sound spectrum.

Fundamental: The lowest frequency of a note in a complex wave form or chord.

Gain: To increase in level. The function of a volume control.

Golden Ratio: The ratio of depth, width, and height based on the Greek Golden Rectangle. Often applied to speaker boxes or listening room design. The Ratio: W = 1.0, Depth = 0.618W, Height = 1.618W. The ratio of depth, width, and height based on the Greek Golden Rectangle. Often applied to speaker boxes or listening room design. The Ratio: W = 1.0, Depth = 0.618W, Height = 1.618W.

Grain: Listening term. A sonic analog of the grain seen in photos. A sort of "grittiness" added to the sound.

Ground: Refers to a point of (usually) zero voltage, and can pertain to a power circuit or a signal circuit. In car audio, the single most important factor to avoid unwanted noise is finding and setting a good ground.

Haas effect: If sounds arrive from several sources, the ears and brain will identify only the nearest. In other words, if our ears receive similar sounds coming from various sources, the brain will latch onto the sound that arrives first. If the time difference is up to 50 milliseconds, the early arrival sound can dominate the later arrival sound, even if the later arrival is as much as 10 dB louder. The discovery of this effect is attributed to Halmut Haas in 1949.

Harmonics: Also called overtones, these are vibrations at frequencies that are multiples of the fundamental. Harmonics extend without limit beyond the audible range. They are characterized as even-order and odd-order harmonics. A second-order harmonic is two times the frequency of the fundamental; a third order is three times the fundamental; a fourth order is four times the fundamental; and so forth. Each even-order harmonic: second, fourth, sixth, etc.-is one octave or multiples of one octave higher than the

fundamental; these even-order overtones are therefore musically related to the fundamental. Odd-order harmonics, on the other hand: third, fifth, seventh, and up-create a series of notes that are not related to any octave overtones and therefore may have an unpleasant sound. Audio systems that emphasize odd-order harmonics tend to have a harsh, hard quality.

HDCD: High-Definition Compact Disc. A proprietary system by Pacific Microsonics that requires special encoding during the recording process. Some observers report HDCD discs as having better sound. To gain the benefits requires having special HDCD in your CD player.

Headroom: The ability of an amp to go beyond its rated power for short durations in order to reproduce musical peaks without distortion. This capability is often dependent on the power supply used in the design.

Head Unit: The in dash control center of a car audio system, usually consisting of an internal low powered amp, AM/FM receiver, and either a tape or CD player (or both).

Hearing Sensitivity: The human ear is less sensitive at low frequencies than in the midrange. Turn your volume knob down and notice how the bass seems to"disappear". To hear low bass requires an adequate SPL level. To hear 25Hz requires a much higher SPL level than to hear 250Hz. In the REAL world, low frequency sounds are reproduced by large objects; bass drums, string bass, concert grand pianos, etc. Listen to the exhaust rumble of a 454 cubic inch V8 engine vs. the whine of the little four banger. The growl of a lion vs. the meow of your favorite kitty. As frequency decreases we perceive more by feel than actual hearing and we lose our ability to hear exact pitch.

Hertz (Hz): A unit of measurement denoting frequency, originally measured as Cycles Per Second, (CPS): 20 Hz = 20 CPS. Kilohertz (kHz) are hertz measured in multiples of 1,000.

High-Pass Filter: A circuit that allows high frequencies to pass but rolls off the low frequencies. When adding a subwoofer it is often desirable to roll-off the low frequencies to the main amplifiers and speakers. This will allow the main speakers to play louder with less distortion. High-pass filters used at speaker level are usually not very effective unless properly designed for a specific main speaker (see impedance below).

Hiss: Audio noise that sounds like air escaping from a tire.

Home Theater: An audio system designed to reproduce the theater sound experience while viewing film at home. Minimally consisting of a Dolby Pro Logic® surround sound receiver, left and right front speakers, a center channel speaker, and two surround speakers. These plus optional subwoofer(s), surround speaker(s), and digital formats such as Dolby Digital® can enhance the viewing experience by drastically improving the sound quality of movie soundtracks.

Hum: Audio electronic noise that has a steady low frequency pitch.

Imaging: Listening term. A good stereo system can provide a stereo image that has width, depth and height. The best imaging systems will define a nearly holographic re-creation of the original sound

Impedance: Impedance is a measure of electrical resistance specified in ohms. Speakers are commonly listed as 4 or 8 ohms but speakers are reactive devices and a nominal 8 ohm speaker might measure from below 4 ohms to 60 or more ohms over its frequency range. This varying impedance curve is different for each speaker model and makes it impossible to design a really effective "generic" speaker level high-pass filter. Active devices like amplifiers typically have an input impedance between about 10,000-100,000 ohms and the impedance is the same regardless of frequency.

Inductance (L): The capability of a coil to store energy in a magnetic field surrounding it. It produces an impedance to an ac current. Inductors are commonly used in audio as low pass crossovers.

Infinite Baffle: A baffle that completely isolates the back wave of a driver from the front without a standard enclosure.

Infrasonic (Subsonic) Filter: A filter designed to remove extremely low frequency (25Hz or lower) noise from the audio signal. Useful for Ported box designs.

Interconnects: Cables that are used to connect components at a low signal level. Examples include CD player to receiver, pre-amplifier to amplifier, etc. Most interconnects use a shielded construction to prevent interference. Most audio interconnects use RCA connections although balanced interconnects use XLR connections.

Isobarik Enclosure: A trade name for a compound enclosure.

Jitter: A tendency towards lack of synchronization caused by electrical changes. Technically the unexpected (and unwanted) phase shift of digital pulses over a transmission medium. A discrepancy between when a digital edge transition is supposed to occur and when it actually does occur - think of it as nervous digital, or maybe a digital analogy to wow and flutter.

Kevlar: Material developed by Dupont that is has an exceptional strength to weight ratio. Used extensively in bullet-proof vests, skis, sailboat hulls, etc. In audio, used in many variations for speaker cones.

Kilohertz (kHz): One thousand hertz.

Le: The inductance of a driver's voice coil, typically measured at 1 kHz in millihenries (mH).

Line Level: CD players, VCRs, Laserdisc Players etc., are connected in a system at line level, usually with shielded RCA type interconnects. Line level is before power amplification. In a system with separate pre-amp and power-amp the pre-amp output is line level. Many surround sound decoders and receivers have line level outputs as well.

Line-Source: A speaker device that is long and tall. Imagine a narrow dowel dropped flat onto the water's surface. The line-source has very limited vertical dispersion, but excellent horizontal dispersion.

Lobing: Any time more than one speaker device covers the same part of the frequency range there will be some unevenness in the output. (Picture the waves from one pebble dropped into a calm pool vs. two pebbles dropped several inches apart.) Lobing means that the primary radiation pattern(s) is at some angle above or below the centerline between the two drivers. Good crossover design takes this into account.

Low Frequency Extension: Manufacturers, writers and salespeople toss around all kinds of numbers and terminology that can be very confusing and misleading. "This $300 shoebox sized sub is flat to 20Hz". Right, in your dreams . . . How is that cheap, tiny box and driver going to reproduce a 56 foot wavelength with enough power to be heard? It will not to it. Good bass reproduction requires moving a lot of air and playback at realistic volumes. Remember the rule of needing to move four times the air to go down one octave. Example: You have a pair of good quality tower speakers with 10" woofers that produce good bass down to around 40Hz. The salesman is telling you that his little subwoofer with a single 10" woofer will extend your system down to 20Hz. If you've been paying attention, you know that his woofer will have to move eight times as much air as each of your 10" woofers, not likely. Adding that subwoofer to your system might give you more apparent bass energy, and in fact may help a little with movie special effects, but it is unlikely to extend bass response significantly.

Low-Pass Filter: A circuit that allows low frequencies to pass but rolls off the high frequencies. Most subwoofers have low-pass filters built in and many surround sound decoders have subwoofer outputs that have been low-pass filtered.

Loudness: Perceived volume. Loudness can be deceiving. For example, adding distortion will make a given volume level seem louder than it actually is.

Check your progress:1. Explain Basic concepts of Space frame2. Explain Advantages of space frames3. Explain Preliminary planning guidelines

Reference:

1 A. W. Krings, “Agent Survivability: An Application for Strong and Weak Chain Constrained Scheduling”, to appear as paper STSSM01, 37th Hawaii International

Conference on System Sciences, (HICSS-37), Minitrack on Security and Survivability in Mobile Agent Based Distributed Systems, January, 2004.2. L. Lamport, M. Pease, R. Shostak, The Byzantine Generals Problem, ACM Transactions on Programming Languages and Systems, Vol. 4, No. 3, July 1982, 382-401.143. Critical Foundations, The President’s Commission on Critical Infrastructure Protection, Government Printing Office, Washington, DC, Oct. 1997.4. K. Rothermel, and M. Strasser, A Fault-Tolerant Protocol for Providing the Exactly- Once Property of Mobile Agents, Proc. IEEE Symposium on Reliable Distributed Systems (SRDS’98), West Lafayette, USA, October, 1998, pp. 100-108.5. F.B. Schneider, Towards Fault-tolerant and Secure Agentry, Proc. of the 11th International Workshop on Distributed Algorithms Saarbrucken, Germany. September, 1997.6. F.M. Assis Silva, A Transaction Model based on Mobile Agents, PhD Thesis, Technical University Berlin, 1999.7. Jay J. Wylie, et al., Selecting the Right Data Distribution Scheme for a Survivable Storage System, Technical Report, CMU-CS-01-120, Carnegie Mellon University, May2001. 158. “Feuerwhere - tracking firefighters,” 2009. [Online]. Available: 9. A. A. Ahmed, L. A. Latiff, M. Sarijari, and N. Fisal, “Real-time routing in wireless sensor networks,” Distributed Computing Systems Workshops, International Conference on, vol. 0, pp.

10. “The freertos.org project,” 2009. [Online]. Available: 11.P. Levis, S. Madden, J. Polastre, R. Szewczyk, K. Whitehouse, A. Woo, D. Gay, J. Hill, M. Welsh, E. Brewer, and D. Culler, “Tinyos: An operating system for sensor networks.” Ambient Intelligence, 2005, pp. 115–148.12. A. Dunkels, B. Grönvall, and T. Voigt, “Contiki - a lightweight and flexible operating system for tiny networked sensors,” 2004.13. A. Eswaran, A. Rowe, and R. Rajkumar, “Nano-rk: an energyaware resource-centric rtos for sensor networks,” in Real-Time Systems Symposium, 2005. RTSS 2005. 26th IEEE International, 2005, pp. 10 pp.–265.14. S. Bhatti, J. Carlson, H. Dai, J. Deng, J. Rose, A. Sheth, B. Shucker, C. Gruenwald, A. Torgerson, and R. Han, “Mantis os: an embedded multithreaded operating system for wireless micro sensor platforms,” Mob. Netw. Appl., vol. 10, no. 4, pp. 563–579, 2005.

Check your progress answer:

1. Refer 4.32. Refer 4.43. Refer 4.5

BLOCK 3 Introductions to Space Frame

Space Frame is a kind of steel structure, it is widely applicated because of its' beautiful shape, manufacture individually, small fittings, installation easily and conveniently, more safe, more cheap ,and fit for transporation .

The projects we contracted before, after we communicated with them by comparing the advantages of space frame structure and steel structure, all accepted space frame structure finally, while before they planed to build steel structure.

We are professional supplier and manufacturer of steel structure and space frame, and we have rich experience. Usually we help clients to analyze and optimize their project plan to choose the best structure shape.

Unit 1: Space frames

1.1Introduction1.2Applications

1.2.1Construction1.2.2Vehicles1.2.3 Design methods

1.3 Types of space frames1.3.1 Skeleton(braced) frames1.3.2 Necessity of the foundation framework for city underground spatial data1.3.3Value of the city underground spatial data framework

1.4 Stressed skin system1.5 Suspended (cable or membrane) structures1.6 Types of structure with significant tension members

1.6.1 Linear structurers1.6.2 Three-dimensional structures1.6.3 Surface-stressed structures1.6.4 Membrane materials

1.7 Cables1.8 Structural forms1.9 Form-finding1.10 Pretension

1.1 Introduction

A space frame or space structure is a truss-like, lightweight rigid structure constructed from interlocking struts in a geometric pattern. Space frames can be used to span large areas with few interior supports. Like the truss, a space frame is strong because of the inherent rigidity of the triangle; flexing loads (bending moments) are transmitted as tension and compression loads along the length of each strut.

The simplest form of space frame is a horizontal slab of interlocking square pyramids built from aluminum or tubular steel struts. In many ways this looks like the horizontal jib of a tower crane repeated many times to make it wider. A stronger purer form is composed of interlocking tetrahedral pyramids in which all the struts have unit length. More technically this is referred to as an isotropic vector matrix or in a single unit width an octet truss. More complex variations change the lengths of the struts to curve the overall structure or may incorporate other geometrical shapes.

1.2Applications

1.2.1 Construction

Space frames are a common feature in modern construction; they are often found in large roof spans in modernist commercial and industrial buildings.

Notable examples of buildings based on space frames include:

• Stansted airport in London, by Foster and Partners• Bank of China Tower and the Louvre Pyramid, by I. M. Pei• Rogers Centre by Rod Robbie and Michael Allan• McCormick Place East in Chicago• Eden Project in Cornwall, England• Globen, Sweden - Dome with diameter of 110 m, (1989)• Biosphere 2 in Oracle, Arizona

Large portable stages and lighting gantries are also frequently built from space frames and octet trusses.

In February 1986, Paul C. Kranz walked into the U. S. Department of Transportation office in Fort Worth, Texas, with a model of an octet truss. He showed a staff person there how the octet truss was ideal for holding signs over roads. The idea and model was forwarded to the US Department of Transportation in Washington, D. C. Today, the octet truss is the structure of choice for holding signs above roads in the United States.

1.2.2 Vehicles

Space frames are sometimes used in the chassis designs of automobiles and motorcycles. In a space-frame, or tube-frame, chassis, the suspension, engine, and body panels are attached to a skeletal space frame, and the body panels have little or no structural function. By contrast, in a monocoque design, the body serves as part of the structure. Tube-frame chassis are frequently used in certain types of racing cars.

British manufacturers TVR were particularly well known for their tube-frame chassis designs, produced since the 1950s. Other notable examples of tube-frame cars include the Audi A8, Lotus Seven, Ferrari 360, Lamborghini Gallardo, and Mercedes-Benz SLS AMG.

Space frames have also been used in bicycles, such as those designed by Alex Moulton.

1.2.3 Design methods

Space frames are typically designed using a rigidity matrix. The special characteristic of the stiffness matrix in an architectural space frame is the independence of the angular factors. If the joints are sufficiently rigid, the angular deflections can be neglected, simplifying the calculations.

Space frames are essentially three dimensional trusses able to span in two directions. They may be flat for use as roofs, walls or inclined walls, or may be curved to form continuous barrel type roof geometries. Flat frames used as roofs sometimes have slight cambers to direct water to appropriate roof outlets. Space frames allow for easy service distribution within their depth and can provide light elegant structural solutions.

Made of tubular steel frames and structural insulated panels (SIPs), Space-Frames pair naturally energy efficient shapes (hexagons, octagons, dodecagons) with the highly efficient SIP panel system to create limitless usage possibilities. Homes,

HexagonsSizes available:

28' to 60'

OctagonsSizes available:

28' to 60'

cottages, sales offices, restaurants and churches are a few of the intriguing Space-Frames options.

DodecagonsSizes available:

44' to 80'

Clerestory DodecagonsSizes available:

44' to 80'

The possibilities inherent with Space-Frames design continue on the interior of the building. The steel frame is clear spanning and there are no interior columns. The tube steel perimeter tension ring also acts as a continuous header. Windows and doors may be cut anywhere and the tension ring will carry the header load

The floor plans shown on this website are for reference only. They provide inspiration and ideas of how a Space-Frames building might be finished.

1.3 Types of space frames

They are classified broadly in three categories

• Skeleton (braced) frame work e.g. domes, barrel vaults, double and multiplier grids, braced plates. They are more popular. They are innumerable combinations and variation possible and follow regular geometric forms.

• Stressed skin systems e.g. Stressed skin folded plates, stressed skin domes and barrel vaults, pneumatic structures.

• Suspended (cable or membrane) structures

e.g. Cable roofs.

1.3.1 Skeleton (braced) framework:

Definition:

A skeleton built of solid structural components strong enough to resist collapsing.

Digital Earth, Digital City and Digital Ming (Wu etc., 2000) demand for three-dimensional geo-scientific spatial data integration and integral visualization. For the difficulty and high cost to capture the underground spatial data, it is necessary to

integrate all the underground data to comprehensively analysis and describe the characteristic and relationship of the underground spatial objects.

Many times the need for data integration is so demanding that it does not matter if some details are lost, as long as integration achieved (Frederico T., 2001 ， 2000), because “we have a lot of data but we are information poor (Nghi, 2001)”. The spatial data integration needs the foundation framework containing variety kinds data (NSFC, 2001). The general three spatial data framework is the basic for the underground spatial visualization (Simon, 1994). However, the researches on general spatial data foundation framework usually pay attention to the geographical spatial data foundation framework.

It aims to set up a uniform space-time positioning criteria with the characters of three dimension, dynamic, practical and high precision, so as to achieve the seamless integration for the multi-source data (Chen, 2002). The research on the foundation framework for city underground spatial data was neglected. This paper discusses the necessity to establish foundation framework for city underground spatial data as well as its characteristics, main contents and key issues. Besides, the application and value of the foundation framework are discussed.

1.3.2 NECESSITY OF THE FOUNDATION FRAMEWORK FOR CITY UNDERGROUND SPATIAL DATA

The spatial data framework from global, national to the regional scale, prefers to the foundational geographical spatial data. The foundational framework data mainly includes the contents, such as topography, geographical name, administration bourn, road traffic, water system, land cover, cadastre, habitat and remote sensing image et al.. It contains the two or three dimension geometry, attribute and correlativity information on the nature, economy, human culture and environment.

The foundation framework can help the people to integrate, to retrieve and to show the interested information on nature, economy, human culture and environment according to the geographical coordinate and spatial location, and to analyze and to simulate the spatial distribution features, operational conditions and changing tendency (Chen, 2002; Chen, 2001; Chen, 1999). For the spatial data foundation framework to have general sense, it should include the underground spatial data.

According to spatial cognition, each data belongs to certain spatial level, namely over-ground, surface and underground. The traditional foundation framework only includes the data of two spatial level, over-ground and surface. The underground data are missed or neglected. But actually, the three spatial levels are spatially correlated and interacted. If any level of spatial data is missed, the geographical spatial data framework must be imperfect. The reason for the establishment of foundation framework for the underground spatial data includes:

Firstly, the city has accumulated abundant data and information, which provides for the data basic for the framework. Limited to many factors, such as data capturing method, cost and technique, the collection of the underground spatial data is much more difficult. The size of data set is the key to establish the foundation framework of underground spatial data. The data and information include city geology, underground engineering, civil defense engineering etc..

Secondly, the exploitation and development of the city underground space and the precaution of the city geological disaster are the motivation to establish the framework. Because of the complexity of the spatial geometry shape and the relationship between the underground spatial objects, it is difficult for the data captured by the single method to reflect exactly the existence condition and distribution of the underground objects. The key to solve the problem is to integrate all the underground spatial data based on the foundation framework.

Only if the data are integrated, the structure, stratum, mineral distribution, underground water, underground engineering facility and underground construction condition can be understood well. It is important to guarantee and to provide technical support for the exploitation and the development of the city underground space and for the precaution of the city geological disaster. Only in condition that the uniform foundation framework for city spatial data is established, the spatial precision of the underground irregular objects and its attribute accuracy could be reached. It means that all the information items, such as sample value, observation value, body data and variable data, must precisely locate in the orthogonal coordinate (Simon, 1994). Then, it would be possible to establish the spatial datainte grating model to effectively express the geo-characters and geo-process. The data-expression consistency, data-system consistency and content consistency on the same space level (Li etc., 2001) is important during the process of the cognition.

1.3.3 VALUE OF THE CITY UNDERGROUND SPATIAL DATA FRAMEWORK

The foundation framework for city underground spatial data is not only a platform for the uniform coordinate, semantic expression and data integrating, but also a platform for the comprehensive display and analyze on underground data. It provides an effective way to integrate multi-source data to control and to analyze the geological structure, stratum, mine resource and ground water distribution, and helps to decrease the exploration cost, to cutthe blindfold investment and to lower the investment risk.

Besides, the framework can also help to figure out potential city geological disaster, and support to the precaution, prevention and cure of city disaster, especially geo based disaster. In a word, the foundation framework for city underground spatial data not only support the underground mine resource development and groundwater protection, but also set up a basic platform to support the assessment of urban underground space, city planning and engineering design. It can further guide the scientific utilization of

urban underground space and city establishment, and serve for the city sustainable development.

1.4 Stressed skin system:

In mechanical engineering, stressed skin is a type of rigid construction, intermediate between monocoque and a rigid frame with a non-loaded covering:

• Rigid frame: geodesic domes, structures built up of tetrahedrons, early 20th century cars, some 21st century trucks, most chairs, etc. have their structure concentrated in a small part of their surface. These structures may or may not be covered, but the covering contributes little strength to the larger structure.

• Monocoque: small boats, modern racing cars, modern airplanes, and insects use structural elements that are spread, nearly equally, over much of their surfaces.

• A stressed skin structure has its compression-taking elements localized and it tension-taking elements distributed. Typically, the main frame has rectangular structure and is triangulated by the covering.

A stressed-skin panel is an insulated building panel that is comprised of a foam core sandwiched between two “skins.” The core, made from polyurethane or styrene foam, is both durable and light weight. The skins are most often made from oriented strand board (OSB), but other building material such as gypsum wall board, sheetrock, plywood, wafer board, and sheet metal are used as well. The exterior skin must be nail able material since the panels are attached to the building’s exterior enclosing the frame to create a thermal envelop. To finish the installation it is necessary to seal the joints between each panel. Stressed-skin panels are manufactured in factories under controlled conditions to standardize quality. Techniques involve using construction adhesive to bond the skins to the foam core or injecting foam between the two skins.

Stressed-skin panels offer a building material which combines the structural system, wall and roof sheathing, and insulation in a single step. Specific advantages provided:

• High R-Value• Moisture control• Sound barrier• Dimensional stability• Cost reduction• Flexibility of substitute faces• Flexibility of core thickness

1.5 Suspended (cable or membrane) structures

A tensile structure is a construction of elements carrying only tension and no compression or bending. The term tensile should not be confused with temerity, which is a structural form with both tension and compression elements.

Most tensile structures are supported by some form of compression or bending elements, such as masts (as in The O2, formerly the Millennium Dome), compression rings or beams.

Tensile membrane structures are most often used as roofs as they can economically and attractively span large distances.

1.6 Types of structure with significant tension members

1.6.1 Linear structures

• Suspension bridges• Draped cables• Cable-stayed beams or trusses• Cable trusses• Straight tensioned cables

1.6.2 Three-dimensional structures

• Bicycle wheel (can be used as a roof in a horizontal orientation)• 3D cable trusses• Tensegrity structures• Tensairity structures

1.6.3 Surface-stressed structures

• Prestressed membranes• Pneumatically stressed membranes

1.6.4 Membrane materials

Common materials for doubly curved fabric structures are PTFE-coated fibreglass and PVC-coated polyester. These are woven materials with different strengths in different directions. The warp fibres (those fibres which are originally straight—equivalent to the starting fibres on a loom) can carry greater load than the weft or fill fibres, which are woven between the warp fibres.

Other structures make use of ETFE film, either as single layer or in cushion form (which can be inflated, to provide good insulation properties or for aesthetic effect—as on the Allianz Arena in Munich). ETFE cushions can also be etched with patterns in order to let different levels of light through when inflated to different levels. They are most often supported by a structural frame as they cannot derive their strength from double curvature.

1.7 Cables

Cables can be of mild steel, high strength steel (drawn carbon steel), stainless steel, polyester or aramid fibres. Structural cables are made of a series of small strands twisted or bound together to form a much larger cable. Steel cables are either spiral strand, where circular rods are twisted together and "glued" using a polymer, or locked coil strand, where individual interlocking steel strands form the cable (often with a spiral strand core).

Spiral strand is slightly weaker than locked coil strand. Steel spiral strand cables have a Young's modulus, E of 150±10 kN/mm² (or 150±10 GPa) and come in sizes from 3 to 90 mm diameter. Spiral strand suffers from construction stretch, where the strands compact when the cable is loaded. This is normally removed by pre-stretching the cable and cycling the load up and down to 45% of the ultimate tensile load.

Locked coil strand typically has a Young's Modulus of 160±10 kN/mm² and comes in sizes from 20 mm to 160 mm diameter.

The properties of the individuals strands of different materials are shown in the table below, where UTS is ultimate tensile strength, or the breaking load:

1.8 Structural forms

Air-supported structures are a form of tensile structures where the fabric envelope is supported by pressurised air only.

The majority of fabric structures derive their strength from their doubly curved shape. By forcing the fabric to take on double-curvature [1] the fabric gains sufficient stiffness to withstand the loads it is subjected to (for example wind and snow loads). In order to induce an adequately doubly curved form it is most often necessary to pretension or priestess the fabric or its supporting structure.

1.9 Form-finding

The behavior of structures which depend upon prestress to attain their strength is non-linear, so anything other than a very simple cable has, until the 1990s, been very difficult to design. The most common way to design doubly curved fabric structures was to construct scale models of the final buildings in order to understand their behaviour and to conduct form-finding exercises. Such scale models often employed stocking material or tights, or soap film, as they behave in a very similar way to structural fabrics (they cannot carry shear).

Soap films have uniform stress in every direction and require a closed boundary to form. They naturally form a minimal surface—the form with minimal area and embodying minimal energy. They are however very difficult to measure. For large films the self-weight of the film can seriously and adversely affect the form.

For a membrane with curvature in two directions, the basic equation of equilibrium is:

where:

• R1 and R2 are the principal radii of curvature for soap films or the directions of the warp and weft for fabrics

• t1 and t2 are the tensions in the relevant directions• w is the load per square metre

Lines of principal curvature have no twist and intersect other lines of principal curvature at right angles.

A geodesic or geodetic line is usually the shortest line between two points on the surface. These lines are typically used when defining the cutting pattern seam-lines. This is due to their relative straightness after the planar cloths have been generated, resulting in lower cloth wastage and closer alignment with the fabric weave.

In a pre-stressed but unloaded surface w = 0, so .

In a soap film surface tensions are uniform in both directions, so R1 = −R2.

It is now possible to use powerful non-linear numerical analysis programs (or finite element analysis) to formfind and design fabric and cable structures. The programs must allow for large deflections.

The final shape, or form, of a fabric structure depends upon:

• shape, or pattern, of the fabric• the geometry of the supporting structure (such as masts, cables, ringbeams etc.)• the pretension applied to the fabric or its supporting structure

t is important that the final form will not allow ponding of water, as this can deform the membrane and lead to local failure or progressive failure of the entire structure.

Snow loading can be a serious problem for membrane structure, as the snow often will not flow off the structure as water will. For example, this has in the past caused the (temporary) collapse of the Hubert H. Humphrey Metrodome, an air-inflated structure in Minneapolis, Minnesota. Some structures prone to ponding use heating to melt snow which settles on them.

There are many different doubly curved forms, many of which have special mathematical properties. The most basic doubly curved from is the saddle shape, which can be a hyperbolic paraboloid (not all saddle shapes are hyperbolic paraboloids). This is a double ruled surface and is often used in both in lightweight shell structures (see hyperboloid structures). True ruled surfaces are rarely found in tensile structures. Other forms are anticlastic saddles, various radial, conical tent forms and any combination of them.

1.10 Pretension

Pretension is tension artificially induced in the structural elements in addition to any self-weight or imposed loads they may carry. It is used to ensure that the normally very flexible structural elements remain stiff under all possible loads.

A day to day example of pretension is a shelving unit supported by wires running from floor to ceiling. The wires hold the shelves in place because they are tensioned - if the wires were slack the system would not work.

Pretension can be applied to a membrane by stretching it from its edges or by pretensioning cables which support it and hence changing its shape. The level of pretension applied determines the shape of a membrane structure.

The film begins with the cast lined up on a stage singing "Seasons of Love", a song expressing a year in the life of the bohemians. On Christmas Eve, 1989, apartment tenants Mark (Anthony Rapp) and Roger (Adam Pascal) express their anger at being asked to pay rent that was waived by their friend. At the same time, Tom Collins (Jesse L. Martin), a former roommate of Mark's, arrives in town and is attacked in an alley ("Rent"). Benjamin Coffin III (Taye Diggs), also known as Benny, the landlord and former roommate of Mark, Roger, and Collins, plans to evict the homeless living in the lot next to Mark and Roger's building and build a cyber studio in its place. He offers Mark and Roger free rent if they convince Maureen (Idina Menzel) (Mark's ex-girlfriend) to stop her protest against Benny's plans ("You'll See"). A street drummer (and drag queen), Angel (Wilson Jermaine Heredia), finds Collins and gets him cleaned up. Angel mentions that he will be attending a Life Support meeting, telling Collins he has AIDS, to which Collins replies, "Me too."

Mark searches for Collins while Roger sings of his desire to write one final song before dying of AIDS ("One Song Glory"). Flashbacks show that Roger was a drug addict and his girlfriend killed herself after learning that she too had AIDS. A woman who lives downstairs, Mimi (Rosario Dawson), enters and flirts with Roger, asking for a match to light her candle ("Light My Candle"). Mimi is a heroin addict and exotic dancer. She drops her stash of drugs and Roger tries to hide them, but she distracts him and leaves with her stash. The next day, Collins appears at the loft with a bottle of vodka. He has a job at New York University, and Mark guesses that this is how he could afford the vodka. Collins contradicts him, and introduces Angel, who enters the loft wearing a bobbed wig, high-heeled boots, and a Santa dress. She hands Mark and Roger money, and explains

that she was paid by a woman, to push a neighbor's dog off of the twenty-third floor of a building ("Today 4 U"). Maureen calls Mark, asking him to fix her sound equipment. Angel and Collins invite both men to the Life Support meeting. Roger declines but Mark promises to attend. Mark goes to the performance space, finding Maureen's girlfriend, Joanne (Tracie Thoms). Joanne and Mark bond as he works and they discuss Maureen's cheating habits ("Tango: Maureen").

Mark enters the Life Support meeting late. He is obviously uncomfortable surrounded by so many AIDS patients, but relaxes and asks if he can film the meeting. The group sings of their desire to live every day to the fullest ("Life Support"). That night, Mimi is performing at the Cat Scratch club where she works ("Out Tonight"). Later, she sneaks into Mark and Roger's apartment while Roger sits playing his guitar. Roger rebukes her for using heroin and intruding on him, throwing her out ("Another Day"). At another Life Support meeting, those present question how their lives will continue now that they have AIDS ("Will I?"). Roger joins the group, much to Angel's, Collins' and Mark's joy. Walking back to their apartments, they find a homeless woman being abused by a police officer and aid her (on film), only for her to reprimand Mark for making a name for himself using her life. On a subway train, they talk about moving to Santa Fe and opening a restaurant ("Santa Fe"). Mark and Roger go to help Joanne. Collins and Angel express their love for each other and Angel buys Collins a new coat ("I'll Cover You").

Maureen's protest happens later that night ("Over the Moon"). Benny has put the police on standby, and a riot ensues. Later, everyone meets at the Life Cafe. Mark reveals he sold footage of the riot to the news and Buzzline wants to air it. Benny tells everyone he is sorry and that his wife was not there due to a death in the family. It turns out to be his dog – the dog that Angel offed earlier. Benny tells the group that they need to grow up and be responsible and asks whether they really want to continue living as they are, leading to a riot, with the characters shouting out what inspires them, starting with Mark saying a eulogy for 'dead' Bohemia. Maureen and Joanne disgust Benny and the other men ("La Vie Bohème"). Roger's beeper goes off, signaling his next AZT dose and showing Mimi that he has HIV. Mimi tells him that she, too, has HIV. Roger and Mimi express their interest in each other outside the cafe ("I Should Tell You"). They re-enter the cafe celebrating their new relationship ("La Vie Bohème B").

A montage of Mark's footage plays, showing events that have taken place over time ("Seasons of Love B"). On New Year's Eve the group finds that Benny has seized their possessions. To get some money, Mark takes a job at Buzzline. Joanne and Maureen accompany him, and Joanne gets upset when she sees Maureen flirting with a receptionist. After an argument, Maureen proposes to Joanne. At a fancy club where Joanne's parents are hosting an engagement party for them, Joanne gets angry when Maureen flirts with another woman. Maureen wants Joanne to understand that she's only having fun, while Joanne wants Maureen to follow the rules of relationships that Joanne lives by and stop mocking her for her Type-A personality. The two end their relationship ("Take Me or Leave Me"). Benny returns everyone's things and offers to let Mark and Roger live in the apartment for free. Seeing it as a publicity stunt, Mark refuses, while Roger is bothered by the fact that Mimi was the one who convinced Benny. Mimi and

Benny had previously been in a relationship, and despite her protests that it ended years ago, Roger is distrustful. Mimi and Roger struggle with Mimi's withdrawal ("Without You"). Members of Life Support die, and Collins takes Angel to the hospital. Roger finds Mimi with her drug dealer, and they break up. Angel dies in Collins' arms. During Angel's funeral, Mimi, Mark and Maureen reflect on moments they shared with Angel, and Collins sings the song that he and Angel sang together ("I'll Cover You (Reprise)"). After the funeral, Roger and Mimi argue about their relationship, as do Joanne and Maureen. Roger reveals that he sold his guitar, bought a car, and is leaving for Santa Fe ("Goodbye Love").

In Santa Fe, Roger realizes he still loves Mimi and decides to return. Mark decides to finish his film and quits his job at Buzzline ("What You Own"). When Roger arrives he learns that Mimi quit rehab and is missing. On Christmas Eve, the year after everyone met, Collins returns to the apartment. Collins gives them some money and reveals that he rewired an ATM to dispense cash whenever someone inputs 'A-N-G-E-L'. Joanne and Maureen find Mimi and bring her to the apartment. She has been living on the streets and is dying. Mimi and Roger reconcile, and Mimi finally tells Roger that she loves him ("Finale A"). As she lay dying, Roger sings the song he has written over the past year. As he ends the final verse, Mimi appears to die ("Your Eyes"). Mimi regains consciousness, explaining that she saw Angel, who told her "turn around, girlfriend, and listen to that boy's song." The six friends, their faith in life restored, perform the final song ("Finale B") with Angel's voice heard as well. As Mark's documentary is shown for the first time, the friends all reaffirm that there is "no day but today".

Glossary:

Aerial ShotA shot taken from a crane, plane, or helicopter. Not necessarily a moving shot.

BacklightingThe main source of light is behind the subject, silhouetting it, and directed toward the camera.

Bridging ShotA shot used to cover a jump in time or place or other discontinuity. Examples are

• falling calendar pages• railroad wheels• newspaper headlines• seasonal changes

Camera AngleThe angle at which the camera is pointed at the subject:

• Low• High

• Tilt

CutThe splicing of 2 shots together. this cut is made by the film editor at the editing stage of a film. Between sequences the cut marks a rapid transition between one time and space and another, but depending on the nature of the cut it will have different meanings.

Cross-cuttingLiterally, cutting between different sets of action that can be occuring simultaneously or at different times, (this term is used synonomously but somewhat incorrectly with parallel editing.) Cross-cutting is used to build suspense, or to show the relationship between the different sets of action.

Jump cutCut where there is no match between the 2 spliced shots. Within a sequence, or more particularly a scene, jump cuts give the effect of bad editing. The opposite of a match cut, the jump cut is an abrupt cut between 2 shots that calls attention to itself because it does not match the shots seamlessly. It marks a transition in time and space but is called a jump cut because it jars the sensibilities; it makes the spectator jump and wonder where the narrative has got to. Jean-Luc Godard is undoubtedly one of the best exponents of this use of the jump cut.

Continuity cutsThese are cuts that take us seamlessly and logically from one sequence or scene to another. This is an unobtrusive cut that serves to move the narrative along.

Match cutThe exact opposite of a jump cut within a scene. These cuts make sure that there is a spatial-visual logic between the differently positioned shots within a scene. thus, where the camera moves to, and the angle of the camera, makes visual sense to the spectator. Eyeline matching is part of the same visual logic: the first shot shows a character looking at something off-screen, the second shot shows what is being looked at. Match cuts then are also part of the seamlessness, the reality effect, so much favoured by Hollywood.

Deep focusA technique in which objects very near the camera as well as those far away are in focus at the same time.

DiegesisThe denotative material of film narrative, it includes, according to Christian Metz, not only the narration itself, but also the fictional space and time dimension implied by the narrative.

Dissolve/lap-dissolveThese terms are used inter-changably to refer to a transition between 2 sequences or

scenes. generally associated with earlier cinema but still used on occasion. In a dissolve a first image gradually dissolves or fades out and is replaced by another which fades in over it. This type of transition, which is known also as a soft transition (as opposed to the cut), suggests a longer passage of time than a cut.

DollyA set of wheels and a platform upon which the camera can be mounted to give it mobility. Dolly shot is a shot taken from a moving dolly. Almost synonomous in general usage with tracking shot or follow shot

EditingEditing refers literally to how shots are put together to make up a film. Traditionally a film is made up of sequences or in some cases, as with avant-garde or art cinema, or again, of successive shots that are assembled in what is known as collision editing, or montage.

ellipsisA term that refers to periods of time that have been left out of the narrative. The ellipsis is marked by an editing transitions which, while it leaves out a section of the action, none the less signifies that something has been elided. Thus, the fade or dissolve could indicate a passage of time, a wipe, a change of scene and so on. A jump cut transports the spectator from one action and time to another, giving the impression of rapid action or of disorientation if it is not matched.

eyeline matching

A term used to point to the continuity editing practice ensuring the logic of the look or gaze. In other words, eyeline matching is based on the belief in mainstream cinema that when a character looks into off-screen space the spectator expects to see what he or she is looking at. Thus there will be a cut to show what is being looked at:

• object• view• another character

Eyeline then refers to the trajectory of the looking eye.

The eyeline match creates order and meaning in cinematic space. Thus, for example, character A will look off-screen at character B. Cut to character B, who-if she or he is in the same room and engaged in an exchange either of glances or words with character A-will return that look and so 'certify' that character A is indeed in the space from which we first saw her or him look. This "stabilising" is true in the other primary use of the eyeline match which is the shot/reverse angle shot, also known as the reverse angle shot, commonly used in close-up dialogue secenes. The camera adopts the eyeline trajectory of

the interlocutor looking at the other person as she or he speaks, then switches to the other person's position and does the same.

Extreme long shot

A panoramic view of an exterior location photographed from a considerable distance, often as far as a quarter-mile away. May also serve as the establishing shot

Fade in

A punctuation device. The screen is black at the beginning; gradually the image appears, brightening to full strength. The opposite happens in the fade out

Fill light

An auxiliary light, usually from the side of the subject that can soften shadows and illuminate areas not covered by the key light

FlashbackA scene or sequence (sometime an entire film), that is inserted into a scene in "present" time and that deals with the past. The flashback is the past tense of the film.

Flash-forwardOn the model of the flashback, scenes or shots of future time; the future tense of the film.

Focus

The sharpness of th image. A range of distances from the camera will be acceptably sharp. Possible to have deep focus, shallow focus.Focus in, focus out: a punctuation device whereby the image gradually comes into focus or goes out of focus.

Follow shot

A tracking shot or zoom which follows the subject as it moves.

Framing

The way in which subjects and objects are framed within a shot produces specific

readings. Size and volume within the frame speak as much as dialogue. So too do camera angles. Thus, for example, a high-angle extreme long shot of two men walking away in the distance, (as in the end of Jean Renoir's La Grande Illusion, 1937) points to their vulnerablility - they are about to dissapear, possibly die. Low angle shots in medium close-up on a person can point to their power, but it can also point to ridicule because of the distortion factor.

Check your progress:

1. Explain Types of frames2. Explain Stressed skin system3. Explain Types of structure with significant tension members

Reference:

Chen J.,2002. Developing Dynamic and Multi-dimensional Geo-Spatial Data Framework. GEO-INFORMATION SCIENCE.1,pp.7-13Chen J Y.,2001. Digital China-oriented Construction of China's Modern Geodatic Datum. BULLETIN OF SURVEYING AND MAPPING.3, pp.1-3Chen J.,1999. Recent Progress and Future Directions of National Spatial Data Infrastructure in China. JOURNAL OF REMOTE SENSING. 3(2),pp.94-97Nghi D Q, H D Kammeier., 2001. Balancing data integration needs in urban planning: A Model for Ha Noi City, Viet Nam[J], Cities, 18(2).pp.61-75Frederico T. Fonseca., 2001. Ontology-Driven Geographic Information Systems. PhD Thesis. the University of Maine..Frederico Fonseca, Max Egenhofer., 2000. Clodoveu Davis. Ontology-Driven Information Integration[A]. AAAI-2000Workshop on Spatial and Temporal Granularity[C], Austin,TX,August, Li J, Zhuang D F.,2001. Theories and Systems of Geo-spatial Data Integration, PROGRESS INGEOGRAPHY.20(2).pp.137-145Li C l, Zhang K X.,2001.Study on regional multi source geological spatial information system based on techniques of GIS, Earth Science — Journal of China University ofGeosciences.26(5),pp.545-550.Lu F, Li X J, Zhou C H etc., 2001.Feature-Based Temporal- Spatial Data Modeling: State of the Art and Problem Discussion, Journal of Image and Graphics.6(9),pp.830-835

Check your progress answer:

1. Refer 1.32. Refer 1.43. Refer 1.6

Unit 2: Configuration - types of nodes

2.1 Introduction2.2 Basic topology types2.3 Classification of network topologies

2.3.1 Physical topologies2.3.2 Logical topology

2.4 Daisy chains2.5 Centralization2.6 Decentralization2.7 Hybrids

2.1 Introduction

Network topology is the layout pattern of interconnections of the various elements (links, nodes, etc.) of a computer network. Network topologies may be physical or logical. Physical topology means the physical design of a network including the devices, location and cable installation. Logical topology refers to how data is actually transferred in a network as opposed to its physical design. In general physical topology relates to a core network whereas logical topology relates to basic network.

Topology can be considered as a virtual shape or structure of a network. This shape does not correspond to the actual physical design of the devices on the computer

network. The computers on a home network can be arranged in a circle but it does not necessarily mean that it represents a ring topology.

Any particular network topology is determined only by the graphical mapping of the configuration of physical and/or logical connections between nodes. The study of network topology uses graph theory. Distances between nodes, physical interconnections, transmission rates, and/or signal types may differ in two networks and yet their topologies may be identical.

A local area network (LAN) is one example of a network that exhibits both a physical topology and a logical topology. Any given node in the LAN has one or more links to one or more nodes in the network and the mapping of these links and nodes in a graph results in a geometric shape that may be used to describe the physical topology of the network. Likewise, the mapping of the data flow between the nodes in the network determines the logical topology of the network. The physical and logical topologies may or may not be identical in any particular network.

2.2 Basic topology types

The study of network topology recognizes seven basic topologies:

• Point-to-point topology• Bus (point-to-multipoint) topology• Star topology• Ring topology• Tree topology• Mesh topology• Hybrid topology

This classification is based on the interconnection between computers — be it physical or logical. The physical topology of a network is determined by the capabilities of the network access devices and media, the level of control or fault tolerance desired, and the cost associated with cabling or telecommunications circuits. Networks can be classified according to their physical span as follows:

• LANs (Local Area Networks)• WANs (Wide area internetworks)• Building or campus internetworks

2.3 Classification of network topologies

There are also two basic categories of network topologies

• Physical topologies• Logical topologies

The shape of the cabling layout used to link devices is called the physical topology of the network. This refers to how the cables are laid out to connect many computers to one network. The physical topology you choose for your network influences and is influenced by several factors:

• Office Layout• Troubleshooting Techniques• Cost of Installation• Type of cable used

Logical topology describes the way in which a network transmits information from network/computer to another and not the way the network looks or how it is laid out. The logical layout also describes the different speeds of the cables being used from one network to another.

2.3.1 Physical topologies

The mapping of the nodes of a network and the physical connections between them – the layout of wiring, cables, the locations of nodes, and the interconnections between the nodes and the cabling or wiring system.

Classification of physical topologies

Point-to-point

The simplest topology is a permanent link between two endpoints (the line in the illustration at the top of the page). Switched point-to-point topologies are the basic model of conventional telephony. The value of a permanent point-to-point network is the value of guaranteed, or nearly so, communications between the two endpoints. The value of an on-demand point-to-point connection is proportional to the number of potential pairs of subscribers, and has been expressed as Metcalfe's Law.

Permanent (dedicated) Easiest to understand, of the variations of point-to-point topology, is a point-to-point communications channel that appears, to the user, to be permanently associated with the two endpoints. A children's "tin-can telephone" is one example, with a microphone to a single public address speaker is another. These are examples of physical dedicated channels.

Within many switched telecommunications systems, it is possible to establish a permanent circuit. One example might be a telephone in the lobby of a public building, which is programmed to ring only the number of a telephone dispatcher. "Nailing down" a switched connection saves the cost of running a physical circuit between the two points. The resources in such a connection can be released when no longer needed, for example, a television circuit from a parade route back to the studio.Switched:

Using circuit-switching or packet-switching technologies, a point-to-point circuit can be set up dynamically, and dropped when no longer needed. This is the basic mode of conventional telephony.

Bus

Bus network topology In local area networks where bus topology is used, each node is connected to a single cable. Each computer or server is connected to the single bus cable through some kind of connector. A terminator is required at each end of the bus cable to prevent the

signal from bouncing back and forth on the bus cable. A signal from the source travels in both directions to all

machines connected on the bus cable until it finds the MAC address or IP address on the network that is the intended recipient. If the machine address does not match the intended

address for the data, the machine ignores the data. Alternatively, if the data does match the machine address, the data is accepted. Since the bus topology consists of only one wire, it is rather inexpensive to implement when compared to other topologies. However, the low cost of implementing the technology is offset by the high cost of managing the network. Additionally, since only one cable is utilized, it can be the single point of failure. If the network cable breaks, the entire network will be down.

Linear bus

The type of network topology in which all of the nodes of the network are connected to a common transmission medium which has exactly two endpoints (this is the 'bus', which is also commonly referred to as the backbone, or trunk) – all data that is transmitted between nodes in the network is transmitted over this common transmission medium and is able to be received by all nodes in the network virtually simultaneously (disregarding propagation delays) Note: The two endpoints of the common transmission medium are normally terminated with a device called a terminator that exhibits the characteristic impedance of the transmission medium and which dissipates or absorbs the energy that remains in the signal to prevent the signal from being reflected or propagated back onto the transmission medium in the opposite direction, which would cause interference with and degradation of the signals on the transmission medium (See Electrical termination).

Distributed bus

The type of network topology in which all of the nodes of the network are connected to a common transmission medium which has more than two endpoints that are created by adding branches to the main section of the transmission medium – the

physical distributed bus topology functions in exactly the same fashion as the physical linear bus topology (i.e., all nodes share a common transmission medium).

Notes:1.) All of the endpoints of the common transmission medium are normally terminated with a device called a 'terminator' (see the note under linear bus).2.) The physical linear bus topology is sometimes considered to be a special case of the physical distributed bus topology – i.e., a distributed bus with no branching segments.3.) The physical distributed bus topology is sometimes incorrectly referred to as a physical tree topology – however, although the physical distributed bus topology resembles the physical tree topology, it differs from the physical tree topology in that there is no central node to which any other nodes are connected, since this hierarchical functionality is replaced by the common bus.

Star

Star network topology

In local area networks with a star topology, each network host is connected to a central hub. In contrast to the bus topology, the star topology connects each node to the hub with a point-to-point connection. All traffic that traverses the network passes

through the central hub. The hub acts as a signal booster or repeater. The star topology is considered the easiest topology to design and implement. An advantage of the star topology is the

simplicity of adding additional nodes. The primary disadvantage of the star topology is that the hub represents a single point of failure.

Notes

• A point-to-point link (described above) is sometimes categorized as a special instance of the physical star topology – therefore, the simplest type of network that is based upon the physical star topology would consist of one node with a single point-to-point link to a second node, the choice of which node is the 'hub' and which node is the 'spoke' being arbitrary

• After the special case of the point-to-point link, as in note (1) above, the next simplest type of network that is based upon the physical star topology would consist of one central node – the 'hub' – with two separate point-to-point links to two peripheral nodes – the 'spokes'.

• Although most networks that are based upon the physical star topology are commonly implemented using a special device such as a hub or switch as the central node (i.e., the 'hub' of the star), it is also possible

to implement a network that is based upon the physical star topology using a computer or even a simple common connection point as the 'hub' or central node – however, since many illustrations of the physical star network topology depict the central node as one of these special devices, some confusion is possible, since this practice may lead to the misconception that a physical star network requires the central node to be one of these special devices, which is not true because a simple network consisting of three computers connected as in note (2) above also has the topology of the physical star.

• Star networks may also be described as either broadcast multi-access or nonbroadcast multi-access (NBMA), depending on whether the technology of the network either automatically propagates a signal at the hub to all spokes, or only addresses individual spokes with each communication.

Extended star

A type of network topology in which a network that is based upon the physical star topology has one or more repeaters between the central node (the 'hub' of the star) and the peripheral or 'spoke' nodes, the repeaters being used to extend the maximum transmission distance of the point-to-point links between the central node and the peripheral nodes beyond that which is supported by the transmitter power of the central node or beyond that which is supported by the standard upon which the physical layer of the physical star network is based.

If the repeaters in a network that is based upon the physical extended star topology are replaced with hubs or switches, then a hybrid network topology is created that is referred to as a physical hierarchical star topology, although some texts make no distinction between the two topologies.

Distributed Star

A type of network topology that is composed of individual networks that are based upon the physical star topology connected together in a linear fashion – i.e., 'daisy-chained' – with no central or top level connection point (e.g., two or more 'stacked' hubs, along with their associated star connected nodes or 'spokes').

Ring

Ring network topology

A network topology that is set up in a circular fashion in which data travels around the ring in one direction and each device on the right acts as a repeater to keep the signal strong as it travels. Each device incorporates a receiver for the incoming signal and a transmitter to send the data on to the next device in the ring. The network is dependent on the ability of the signal to travel around the ring

Mesh

The value of fully meshed networks is proportional to the exponent of the number of subscribers, assuming that communicating groups of any two endpoints, up to and including all the endpoints, is approximated by Reed's Law

Fully connected mesh topology

The number of connections in a full mesh = n(n - 1) / 2

Fully connected

Note: The physical fully connected mesh topology is generally too costly and complex for practical networks, although the topology is used when there are only a small number of nodes to be interconnected.

Partially connected mesh topology

Partially connected

The type of network topology in which some of the nodes of the network are connected to more than one other node in the network with a point-to-point link – this makes it possible to take advantage of some of the redundancy that is provided by a physical fully connected mesh topology without the expense and complexity required for a connection between every node in the network.

Note: In most practical networks that are based upon the physical partially connected mesh topology, all of the data that is transmitted between nodes in the network takes the shortest path (or an approximation of the shortest path) between nodes, except in the case of a failure or break in one of the links, in which case the data takes an alternative path to the destination. This requires that the nodes of the network possess some type of logical 'routing' algorithm to determine the correct path to use at any particular time.

Tree

Tree network topology

Also known as a hierarchy network.

The type of network topology in which a central 'root' node (the top level of the hierarchy) is

connected to one or more other nodes that are one level lower in the hierarchy (i.e., the second level) with a point-to-point link between each of the second level nodes and the top level central 'root' node, while each of the second level nodes that are connected to the top level central 'root' node will also have one or more other nodes that are one level lower in the hierarchy (i.e., the third level) connected to it, also with a point-to-point link, the top level central 'root' node being the only node that has no other node above it in the hierarchy (The hierarchy of the tree is symmetrical.) Each node in the network having a specific fixed number, of nodes connected to it at the next lower level in the hierarchy, the number, being referred to as the 'branching factor' of the hierarchical tree.This tree has individual peripheral nodes.

1.) A network that is based upon the physical hierarchical topology must have at least three levels in the hierarchy of the tree, since a network with a central 'root' node and only one hierarchical level below it would exhibit the physical topology of a star.2.) A network that is based upon the physical hierarchical topology and with a branching factor of 1 would be classified as a physical linear topology.3.) The branching factor, f, is independent of the total number of nodes in the network and, therefore, if the nodes in the network require ports for connection to other nodes the total number of ports per node may be kept low even though the

total number of nodes is large – this makes the effect of the cost of adding ports to each node totally dependent upon the branching factor and may therefore be kept as low as required without any effect upon the total number of nodes that are possible.4.) The total number of point-to-point links in a network that is based upon the physical hierarchical topology will be one less than the total number of nodes in the network.5.) If the nodes in a network that is based upon the physical hierarchical topology are required to perform any processing upon the data that is transmitted between nodes in the network, the nodes that are at higher levels in the hierarchy will be required to perform more processing operations on behalf of other nodes than the nodes that are lower in the hierarchy. Such a type of network topology is very useful and highly recommended.

2.3.2 Logical topology

The logical topology, in contrast to the "physical", is the way that the signals act on the network media, or the way that the data passes through the network from one device to the next without regard to the physical interconnection of the devices. A network's logical topology is not necessarily the same as its physical topology. For example, twisted pair Ethernet is a logical bus topology in a physical star topology layout. While IBM's Token Ring is a logical ring topology, it is physically set up in a star topology.

The logical classification of network topologies generally follows the same classifications as those in the physical classifications of network topologies but describes the path that the data takes between nodes being used as opposed to the actual physical connections between nodes.

Notes:

1. Logical topologies are often closely associated with Media Access Control methods and protocols.

2. The logical topologies are generally determined by network protocols as opposed to being determined by the physical layout of cables, wires, and network devices or by the flow of the electrical signals, although in many cases the paths that the electrical signals take between nodes may closely match the logical flow of data, hence the convention of using the terms logical topology and signal topology interchangeably.

3. Logical topologies are able to be dynamically reconfigured by special types of equipment such as routers and switches.

2.4 Daisy chains

Except for star-based networks, the easiest way to add more computers into a network is by daisy-chaining, or connecting each computer in series to the next. If a message is intended for a computer partway down the line, each system bounces it along in sequence

until it reaches the destination. A daisy-chained network can take two basic forms: linear and ring.

• A linear topology puts a two-way link between one computer and the next. However, this was expensive in the early days of computing, since each computer (except for the ones at each end) required two receivers and two transmitters.

• By connecting the computers at each end, a ring topology can be formed. An advantage of the ring is that the number of transmitters and receivers can be cut in half, since a message will eventually loop all of the way around. When a node sends a message, the message is processed by each computer in the ring. If a computer is not the destination node, it will pass the message to the next node, until the message arrives at its destination. If the message is not accepted by any node on the network, it will travel around the entire ring and return to the sender. This potentially results in a doubling of travel time for data.

2.5 Centralization

The star topology reduces the probability of a network failure by connecting all of the peripheral nodes (computers, etc.) to a central node. When the physical star topology is applied to a logical bus network such as Ethernet, this central node (traditionally a hub) rebroadcasts all transmissions received from any peripheral node to all peripheral nodes on the network, sometimes including the originating node. All peripheral nodes may thus communicate with all others by transmitting to, and receiving from, the central node only. The failure of a transmission line linking any peripheral node to the central node will result in the isolation of that peripheral node from all others, but the remaining peripheral nodes will be unaffected. However, the disadvantage is that the failure of the central node will cause the failure of all of the peripheral nodes also,

If the central node is passive, the originating node must be able to tolerate the reception of an echo of its own transmission, delayed by the two-way round trip transmission time (i.e. to and from the central node) plus any delay generated in the central node. An active star network has an active central node that usually has the means to prevent echo-related problems.

A tree topology (a.k.a. hierarchical topology) can be viewed as a collection of star networks arranged in a hierarchy. This tree has individual peripheral nodes (e.g. leaves) which are required to transmit to and receive from one other node only and are not required to act as repeaters or regenerators. Unlike the star network, the functionality of the central node may be distributed.

As in the conventional star network, individual nodes may thus still be isolated from the network by a single-point failure of a transmission path to the node. If a link connecting a leaf fails, that leaf is isolated; if a connection to a non-leaf node fails, an entire section of the network becomes isolated from the rest.

In order to alleviate the amount of network traffic that comes from broadcasting all signals to all nodes, more advanced central nodes were developed that are able to keep track of the identities of the nodes that are connected to the network. These network switches will "learn" the layout of the network by "listening" on each port during normal data transmission, examining the data packets and recording the address/identifier of each connected node and which port it's connected to in a lookup table held in memory. This lookup table then allows future transmissions to be forwarded to the intended destination only.

2.6 Decentralization

In a mesh topology (i.e., a partially connected mesh topology), there are at least two nodes with two or more paths between them to provide redundant paths to be used in case the link providing one of the paths fails. This decentralization is often used to advantage to compensate for the single-point-failure disadvantage that is present when using a single device as a central node (e.g., in star and tree networks). A special kind of mesh, limiting the number of hops between two nodes, is a hypercube. The number of arbitrary forks in mesh networks makes them more difficult to design and implement, but their decentralized nature makes them very useful. This is similar in some ways to a grid network, where a linear or ring topology is used to connect systems in multiple directions. A multi-dimensional ring has a toroidal topology, for instance.

A fully connected network, complete topology or full mesh topology is a network topology in which there is a direct link between all pairs of nodes. In a fully connected network with n nodes, there are n(n-1)/2 direct links. Networks designed with this topology are usually very expensive to set up, but provide a high degree of reliability due to the multiple paths for data that are provided by the large number of redundant links between nodes. This topology is mostly seen in military applications. However, it can also be seen in the file sharing protocol BitTorrent in which users connect to other users in the "swarm" by allowing each user sharing the file to connect to other users also involved. Often in actual usage of BitTorrent any given individual node is rarely connected to every single other node as in a true fully connected network but the protocol does allow for the possibility for any one node to connect to any other node when sharing files.

2.7 Hybrids

Hybrid networks use a combination of any two or more topologies in such a way that the resulting network does not exhibit one of the standard topologies (e.g., bus, star, ring, etc.). For example, a tree network connected to a tree network is still a tree network topology. A hybrid topology is always produced when two different basic network topologies are connected. Two common examples for Hybrid network are: star ring network and star bus network

• A Star ring network consists of two or more star topologies connected using a multistation access unit (MAU) as a centralized hub.

• A Star Bus network consists of two or more star topologies connected using a bus trunk (the bus trunk serves as the network's backbone).

While grid networks have found popularity in high-performance computing applications, some systems have used genetic algorithms to design custom networks that have the fewest possible hops in between different nodes. Some of the resulting layouts are nearly incomprehensible, although they function quite well.

A Snowflake topology is really a "Star of Stars" network, so it exhibits characteristics of a hybrid network topology but is not composed of two different basic network topologies being connected together.

Glossary:

Administrator

One of two types of administrators in Oracle Content Services: system administrators, or application administrators.

Administration Mode

Provides access to Oracle Content Services application administration functions such as allocating quota and assigning roles.

Advanced Queuing (AQ)

Provides an infrastructure for distributed applications to communicate asynchronously using messages. Advanced Queuing is built into the Oracle database and supports sophisticated queuing features, including subscriptions, inter-queue message propagation, message latency, message expiration, structured payloads, and exception queues. Full name: Oracle Streams Advanced Queueing.

Agents

Processes that perform operations periodically (time-based) or in response to events generated by other Oracle Content Services servers or processes (event-based). An agent is a type of Oracle Content Services server.

Application administrators

Administrators who are responsible for tasks related to a particular Site, such as managing users, quotas, categories, and content. There are a variety of application administration roles, including User Administrator, Category Administrator, Container Administrator, Content Administrator, and Quota Administrator. See Oracle Content Services Application Administrator's Guide for more information about application administration roles and tasks.

Applications tier

The tier of Oracle Collaboration Suite that runs the server applications that provide specific functionality to end users. The term "Applications tier" replaces the term "middle tier" that was used in previous releases. Each Applications tier corresponds to an instance of Oracle Application Server. See also Oracle Collaboration Suite Applications.

Archive

Location where items are stored that have been deleted from user or Library trash. Each Site contains an Archive folder. Depending on how the Site has been configured, items in the Archive may be automatically deleted after a specified period of time. Files and folders in the Archive can be restored by the Site's Content Administrator.

BFILE

A read-only Oracle data type consisting of a directory object and a filename. Oracle Content Services provides transparent access to content stored as either a BLOB (online storage) or a BFILE (near-line storage). If BFILEs are enabled for your Oracle Content Services domain, you can configure content archiving or content aging.

BLOB

A type of Large Object (LOB) provided by the database. All documents in Oracle Content Services are stored as BLOBs. Full name: Binary Large Object.

BPEL

An XML-based markup language for composing a set of discrete Web services into an end-to-end process flow. Full name: Business Process Execution Language. See also Oracle BPEL Process Manager.

Client tier

The tier of Oracle Collaboration Suite that consists of the end-user applications that reside on client devices, such as desktops, laptops, wireless phones, and PDAs. See also Oracle Collaboration Suite Applications.

Committed Data Cache

Provides caching of the attribute values of frequently used objects without a database request, greatly improving performance and scalability.

Custom workflow

A customized workflow process created in the BPEL Designer (a component of Oracle BPEL Process Manager. Custom workflows must be registered with Oracle Content Services before they can be used.

Domain

A logical grouping of Oracle Content Services nodes, and an Oracle Database instance (called the Oracle Collaboration Suite Database) that contains the Oracle Content Services data.

Domain properties

Settings that apply to the entire Oracle Content Services domain. For example, the domain property IFS.DOMAIN.SEARCH.AttemptContextSearchRewrite determines whether or not Oracle Content Services should attempt to generate fast-response SQL for text searches.

EMC Centera

A partner solution that provides retention hardware support. You can integrate Oracle Content Services with EMC Centera to provide retention storage for Oracle Records Management.

Formats

Attributes that indicate document file type (for example, .doc or .zip). The format of a document determines how its content is indexed. Also known as MIME types.

FTP

One of three protocols supported by Oracle Content Services, used for file transfers across Wide Area Networks such as the Internet. FTPS is also supported. Full name: File Transfer Protocol.

FTPS

FTP over SSL. FTPS defines a mechanism to implement the FTP Security Extensions based on the TLS protocol. There are two types of FTPS are supported by Oracle Content Services:

• Implicit FTPS secures the channel on connection.• Explicit FTPS secures the connection when the client issues an AUTH command.

An Explicit FTPS connection starts out as a regular FTP connection; the connection becomes secure only after the client issues an AUTH command.

FTPS should not be confused with SFTP, a service of the Secure Shell that is not related to FTP.

Group tool

One of the Oracle Content Services command-line tools. Allows you to create and update groups.

HTTP

One of three protocols supported by Oracle Content Services, used for Web browser-based access. HTTP has been extended with WebDAV, a protocol designed for Wide Area Networks such as the Internet. Full name: Hypertext Transfer Protocol.

HTTP nodes

One of two types of Oracle Content Services nodes. The Oracle Content Services HTTP node runs as part of an OC4J process called OC4J_Content. The Oracle Records Management HTTP node runs as part of an OC4J process called OC4J_RM. Through servlets that are configured to work with OC4J, the HTTP nodes provide the following support:

• The Oracle Content Services HTTP node supports the Oracle Content Services application, portlet, and WebDAV.

• The Oracle Records Management HTTP node supports the Oracle Records Management application and WebDAV.

Identity management

The process by which various components in an identity management system manage the security life cycle for network entities in an organization. Most commonly refers to the management of an organization's application users. See also Oracle Identity Management.

Infrastructure tier

The tier of Oracle Collaboration Suite that consists of the components that provide services, such as identity management and metadata storage, for the Applications tier. Components of the Infrastructure tier include Oracle Collaboration Suite Database and Oracle Identity Management. See also Oracle Collaboration Suite Infrastructure.

Libraries

Configurable folders for storing and sharing content with an allocated quota. Libraries were known as Workspaces in previous releases.

Library tool

One of the Oracle Content Services command-line tools. Allows you to create or update Libraries.

LDAP

An Internet protocol that applications use to look up contact information from a server, such as a central directory. LDAP servers index all the data in their entries, and "filters" may be used to select just the person or group you want, and return just the information you want. Full name: Lightweight Directory Access Protocol.

LOB

The majority of data stored in Oracle Content Services is stored as LOBs in database tablespaces. Full name: Large Object.

Loggers

Functional areas with configurable logging levels for each node. For example, you can specify a more detailed level of logging for a particular protocol server or agent logger in which you are interested.

Network Appliance SnapLock

A partner solution that provides retention hardware support. You can integrate Oracle Content Services with Network Appliance SnapLock to provide retention storage for Oracle Records Management.

Nodes

The application software that comprises the product, along with the underlying Java Virtual Machine (JVM) required to support the software at runtime. There are two types of nodes: regular nodes, and HTTP nodes. Each node is based on a particular node configuration.

Node configuration

A configuration object that specifies the runtime behavior of a particular node. Each node has its own corresponding node configuration. If you want to make permanent changes to a node, such as changing server or services, modify the node configuration for the node. If you want to make temporary (runtime) changes to a node, modify the node itself. Changes made at runtime are lost when the node is restarted. You cannot create a node directly; instead, you must first create an active node configuration, and then a corresponding node will be created automatically.

Node manager

The actual process that gets started when a node is started. It is responsible for starting the default service and servers for this node. It also provides an administrative API for the node that lets you to find out information about node log levels, locale information, available free memory, and the node's Oracle home.

OC4J

A complete set of J2EE containers written entirely in Java that execute on the Java Virtual Machine (JVM) of the standard Java Development Kit (JDK). OC4J supplies the following J2EE containers: a servlet container that complies with the servlet 2.3 specification, and a JSP container that complies with the Sun JSP 1.2 specification. Full name: Oracle Application Server Containers for J2EE.

OmniPortlet

A declarative portlet-building tool that enables you to build portlets against a variety of data sources, including XML files, comma-delimited value files (for example, spreadsheets), Web Services, databases, Web pages, and SAP data sources. OmniPortlet users can also choose a pre-built layout for the data. Pre-built layouts include tabular, news, bullet, form, or chart. You can use the OmniPortlet to build a custom Oracle Content Services portlet. Full name: OracleAS Portal OmniPortlet.

Check your progress

1. Explain Classification of network topology2. Explain Physical topology3. Explain Decentralization

Reference:

1. Groth, David; Toby Skandier (2005). Network+ Study Guide, Fourth Edition'. Sybex, Inc.. ISBN 0-7821-4406-3.

2. ^ ATIS committee PRQC. "network topology". ATIS Telecom Glossary 2007. Alliance for Telecommunications Industry Solutions. Retrieved 2008-10-10.

3. Bicsi, B., (2002). Network Design Basics for Cabling Professionals. City: McGraw-Hill Professional

4. Inc, S., (2002). Networking Complete. Third Edition. San Francisco: Sybex

5. Tendaishe Sigauke, (2007: 46) Explaining networking terms6. Harris, C. M., Shock and vibration handbook, Mc Graw Hill, New York,

3rd ed., 1988.

7. Sewall, J.L.; Naumann, E.C., An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners, Washington, D.C, NASA (NASA TN D-4705), 1968.

8. Alzahabi, B.; Natarajan, L. K., Non-Uniqueness in Cylindrical Shells Optimization, International Conference on Computer Aided Optimum Design of Structures, OPTI 2003, Detroit, 2003.

9. Alzahabi, B.; Natarajan, L. K., Frequency Response Optimization of Cylindrical Shells using MSC.NASTRAN, The 1st International Conference on Finite Element Process, Luxembourg City, LUXFEM, Luxembourg, 2003. Unit 5

Check your progress answers

1. Refer 2.32. Refer 2.3.13. Refer 2.6

Unit 3: General principles of design Philosophy

3.1 Introduction3.2 Design as a process3.3 The rational model3.4 Criticism of the rational model

3.4.1The Action-centric model3.4.2 Descriptions of design activities3.4.3 Criticism of the Action-centric perspective

3.5 Philosophies and studies of design3.5.1 Philosophies for guiding design

3.5.2 Approaches to design3.5.3 Methods of designing3.5.4 Philosophies for the purpose of designs

3.6 Terminology3.6.1 Design and art3.6.2 Design and engineering3.6.3 Design and Production3.6.4 Process design

3.1 Introduction

Design as a noun informally refers to a plan for the construction of an object or a system (as in architectural blueprints, engineering drawing, business process, circuit diagrams and sewing patterns) while “to design” (verb) refers to making this plan. No generally-accepted definition of “design” exists, and the term has different connotations in different fields (see design disciplines below). However, one can also design by directly constructing an object (as in pottery, engineering, management, cowboy coding and graphic design).

More formally, design has been defined as follows.

(noun) a specification of an object, manifested by an agent, intended to accomplish goals, in a particular environment, using a set of primitive components, satisfying a set of requirements, subject to constraints;(verb, transitive) to create a design, in an environment (where the designer operates)

Here, a "specification" can be manifested as either a plan or a finished product and "primitives" are the elements from which the design object is composed.

With such a broad denotation, there is no universal language or unifying institution for designers of all disciplines. This allows for many differing philosophies and approaches toward the subject (see Philosophies and studies of design, below).

The person designing is called a designer, which is also a term used for people who work professionally in one of the various design areas, usually also specifying which area is being dealt with (such as a fashion designer, concept designer or web designer). A designer’s sequence of activities is called a design process. The scientific study of design is called design science.

Designing often necessitates considering the aesthetic, functional, economic and sociopolitical dimensions of both the design object and design process. It may involve considerable research, thought, modeling, interactive adjustment, and re-design.

Meanwhile, diverse kinds of objects may be designed, including clothing, graphical user interfaces, skyscrapers, corporate identities, business processes and even methods of designing.

3.2 Design as a process

Substantial disagreement exists concerning how a designer in many fields, whether amateur or professional, alone or in teams, produce designs. Dorst and Dijkhuis argued that “there are many ways of describing design processes” and discussed “two basic and fundamentally different ways”, both of which have several names. The prevailing view has been called “The Rational Model”, “Technical Problem Solving” and “The Reason-Centric Perspective”. The alternative view has been called “Reflection-in-Action”, “co-evolution” and “The Action-Centric Perspective”.

3.3 The Rational Model

The Rational Model was independently developed by Simon and Pahl and Beitz. It posits that:

1. designers attempt to optimize a design candidate for known constraints and objectives,

2. the design process is plan-driven,3. the design process is understood in terms of a discrete sequence of stages.

The Rational Model is based on a rationalist philosophy and underlies the Waterfall Model, Systems Development Life Cycle and much of the engineering design literature.

Example sequence of stages

Typical stages consistent with The Rational Model include the following.

• Pre-production design o Design brief or Parti – an early (often the beginning) statement of design

goalso Analysis – analysis of current design goalso Research – investigating similar design solutions in the field or related

topicso Specification – specifying requirements of a design solution for a product

(product design specification) or service.o Problem solving – conceptualizing and documenting design solutionso Presentation – presenting design solutions

• Design during production o Development – continuation and improvement of a designed solutiono Testing – in situ testing a designed solution

• Post-production design feedback for future designs o Implementation – introducing the designed solution into the environment

o Evaluation and conclusion – summary of process and results, including constructive criticism and suggestions for future improvements

• Redesign – any or all stages in the design process repeated (with corrections made) at any time before, during, or after production.

Each stage has many associated best practices.

3.4Criticism of the Rational Model

The Rational Model has been widely criticized on two primary grounds

1. Designers do not work this way – extensive empirical evidence has demonstrated that designers do not act as the rational model suggests.

2. Unrealistic assumptions – goals are often unknown when a design project begins, and the requirements and constraints continue to change

3.4.1The Action-Centric Model

The Action-Centric Perspective is a label given to a collection of interrelated concepts, which are antithetical to The Rational Model. It posits that:

1. designers use creativity and emotion to generate design candidates,2. the design process is improvised,3. no universal sequence of stages is apparent – analysis, design and implementation

are contemporary and inextricably linked

The Action-Centric Perspective is a based on an empiricist philosophy and broadly consistent with the Agile approach and amethodical development. Substantial empirical evidence supports the veracity of this perspective in describing the actions of real designers.

3.4.2 Descriptions of design activities

At least two views of design activity are consistent with the Action-Centric Perspective. Both involve three basic activities.

In the Reflection-in-Action paradigm, designers alternate between “framing,” “making moves,” and “evaluate moves”. “Framing” refers to conceptualizing the problem, i.e., defining goals and objectives. A “move” is a (tentative) design decision.

In the Sensemaking-Coevolution-Implementation Framework, designers alternate between its three titular activities. Sensemaking includes both framing and evaluating moves. Implementation is the process of constructing the design object. Coevolution is “the process where the design agent simultaneously refines its mental picture of the design object based on its mental picture of the context, and vice versa”.

3.4.3 Criticism of the Action-Centric Perspective

As this perspective is relatively new, it has not yet encountered much criticism. One possible criticism is that it is less intuitive than The Rational Model.

3.5Philosophies and studies of design

There are countless philosophies for guiding design as the design values and its accompanying aspects within modern design vary, both between different schools of thought and among practicing designers. Design philosophies are usually for determining design goals. A design goal may range from solving the least significant individual problem of the smallest element, to the most holistic influential utopian goals. Design goals are usually for guiding design. However, conflicts over immediate and minor goals may lead to questioning the purpose of design, perhaps to set better long term or ultimate goals.

3.5.1 Philosophies for guiding design

Design philosophies are fundamental guiding principles that dictate how a designer approaches his/her practice. Reflections on material culture and environmental concerns (Sustainable design) can guide a design philosophy.

One example is the First Things First manifesto which was launched within the graphic design community and states "We propose a reversal of priorities in favor of more useful, lasting and democratic forms of communication - a mindshift away from product marketing and toward the exploration and production of a new kind of meaning. The scope of debate is shrinking; it must expand. Consumerism is running uncontested; it must be challenged by other perspectives expressed, in part, through the visual languages and resources of design."

In The Sciences of the Artificial by polymath Herbert Simon the author asserts design to be a meta-discipline of all professions. "Engineers are not the only professional designers. Everyone designs who devises courses of action aimed at changing existing situations into preferred ones. The intellectual activity that produces material artifacts is no different fundamentally from the one that prescribes remedies for a sick patient or the one that devises a new sales plan for a company or a social welfare policy for a state. Design, so construed, is the core of all professional training; it is the principal mark that distinguishes the professions from the sciences. Schools of engineering, as well as schools of architecture, business, education, law, and medicine, are all centrally concerned with the process of design."

3.5.2Approaches to design

A design approach is a general philosophy that may or may not include a guide for specific methods. Some are to guide the overall goal of the design. Other approaches are

to guide the tendencies of the designer. A combination of approaches may be used if they don't conflict.

Some popular approaches include:

• KISS principle, (Keep it Simple Stupid, etc.), which strives to eliminate unnecessary complications.

• There is more than one way to do it (TIMTOWTDI), a philosophy to allow multiple methods of doing the same thing.

• Use-centered design, which focuses on the goals and tasks associated with the use of the artifact, rather than focusing on the end user.

• User-centered design, which focuses on the needs, wants, and limitations of the end user of the designed artifact.

• Critical design uses designed artifacts as an embodied critique or commentary on existing values, mores, and practices in a culture.

3.5.3Methods of designing

Design Methods is a broad area that focuses on:

• Exploring possibilities and constraints by focusing critical thinking skills to research and define problem spaces for existing products or services—or the creation of new categories; (see also Brainstorming)

• Redefining the specifications of design solutions which can lead to better guidelines for traditional design activities (graphic, industrial, architectural, etc.);

• Managing the process of exploring, defining, creating artifacts continually over time

• Prototyping possible scenarios, or solutions that incrementally or significantly improve the inherited situation

• Trendspotting; understanding the trend process.

3.5.4Philosophies for the purpose of designs

In philosophy, the abstract noun "design" refers to a pattern with a purpose. Design is thus contrasted with purposelessness, randomness, or lack of complexity.

To study the purpose of designs, beyond individual goals (e.g. marketing, technology, education, entertainment, hobbies), is to question the controversial politics, morals, ethics and needs such as Maslow's hierarchy of needs. "Purpose" may also lead to existential questions such as religious morals and teleology. These philosophies for the "purpose of" designs are in contrast to philosophies for guiding design or methodology.

Often a designer (especially in commercial situations) is not in a position to define purpose. Whether a designer is, is not, or should be concerned with purpose or intended use beyond what they are expressly hired to influence, is debatable, depending on the situation. In society, not understanding or disinterest in the wider role of design might

also be attributed to the commissioning agent or client, rather than the designer. Some newer fields of design have built-in purposes and values, such as user-centered design, slow design, and sustainable design.

In structuration theory, achieving consensus and fulfillment of purpose is as continuous as society. Raised levels of achievement often lead to raised expectations. Design is both medium and outcome, generating a Janus-like face, with every ending marking a new beginning.

3.6Terminology

The word "design" is often considered ambiguous, as it is applied differently in a varying contexts.

3.6.1 Design and art

Today the term design is widely associated with the Applied arts as initiated by Raymond Loewy and teachings at the Bauhaus and Ulm School of Design (HfG Ulm) in Germany during the 20th Century.

The boundaries between art and design are blurred, largely due to a range of applications both for the term 'art' and the term 'design'. Applied arts has been used as an umbrella term to define fields of industrial design, graphic design, fashion design, etc. The term 'decorative arts' is a traditional term used in historical discourses to describe craft objects, and also sits within the umbrella of Applied arts. In graphic arts (2D image making that ranges from photography to illustration) the distinction is often made between fine art and commercial art, based on the context within which the work is produced and how it is traded.

To a degree, some methods for creating work, such as employing intuition, are shared across the disciplines within the Applied arts and Fine art. Mark Getlein suggests the principles of design are "almost instinctive", "built-in", "natural", and part of "our sense of 'rightness'." However, the intended application and context of the resulting works will vary greatly.

3.6.2 Design and engineering

In engineering, design is a component of the engineering process. Many overlapping methods and processes can be seen when comparing Product design, Industrial design and Engineering. The American Heritage Dictionary defines design as: "To conceive or fashion in the mind; invent," and "To formulate a plan", and defines engineering as: "The application of scientific and mathematical principles to practical ends such as the design, manufacture, and operation of efficient and economical structures, machines, processes, and systems.". Both are forms of problem-solving with a defined distinction being the application of "scientific and mathematical principles". The increasingly scientific focus of engineering in practice, however, has raised the importance of new

more "human-centered" fields of design.[31] How much science is applied in a design is a question of what is considered "science". Along with the question of what is considered science, there is social science versus natural science. Scientists at Xerox PARC made the distinction of design versus engineering at "moving minds" versus "moving atoms".

3.6.3 Design and production

The relationship between design and production is one of planning and executing. In theory, the plan should anticipate and compensate for potential problems in the execution process. Design involves problem-solving and creativity. In contrast, production involves a routine or pre-planned process. A design may also be a mere plan that does not include a production or engineering process, although a working knowledge of such processes is usually expected of designers. In some cases, it may be unnecessary and/or impractical to expect a designer with a broad multidisciplinary knowledge required for such designs to also have a detailed specialized knowledge of how to produce the product.

Design and production are intertwined in many creative professional careers, meaning problem-solving is part of execution and the reverse. As the cost of rearrangement increases, the need for separating design from production increases as well. For example, a high-budget project, such as a skyscraper, requires separating (design) architecture from (production) construction. A Low-budget project, such as a locally printed office party invitation flyer, can be rearranged and printed dozens of times at the low cost of a few sheets of paper, a few drops of ink, and less than one hour's pay of a desktop publisher.

This is not to say that production never involves problem-solving or creativity, nor that design always involves creativity. Designs are rarely perfect and are sometimes repetitive. The imperfection of a design may task a production position (e.g. production artist, construction worker) with utilizing creativity or problem-solving skills to compensate for what was overlooked in the design process. Likewise, a design may be a simple repetition (copy) of a known preexisting solution, requiring minimal, if any, creativity or problem-solving skills from the designer.

3.6.4 Process design

"Process design" (in contrast to "design process" mentioned above) refers to the planning of routine steps of a process aside from the expected result. Processes (in general) are treated as a product of design, not the method of design. The term originated with the industrial designing of chemical processes. With the increasing complexities of the information age, consultants and executives have found the term useful to describe the design of business processes as well as manufacturing processes.

Glossary:

Alley: the space between columns within a page. Not to be confused with the gutter, which is the combination of the inside margins of two facing pages.

Ascender: in typography, the parts of lowercase letters that rise above the x-height of the font, e.g. b, d, f, h, k, I, and t.

Banner: the title of a periodical, which appears on the cover of the magazine and on the first page of the newsletter. It contains the name of the publication and serial information -- date, volume, number.

Baseline: in typography, the imaginary horizontal line upon which the main body of the letters sits. Rounded letters actually dip slightly below the baseline to give optical balance.

Bit-mapped (mode): the Paint graphics mode describes an image made of pixels where the pixel is either on (black) or off (white).

Black (font): a font that has more weight than the bold version of a typeface.

Bleed: an element that extends to the edge of the page. To print a bleed, the publication is printed on oversized paper which is trimmed.

Block quote: a long quotation -- four or more lines -- within body text, that is set apart in order to clearly distinguish the author's words from the words that the author is quoting.

Callout: an explanatory label for an illustration, often drawn with a leader line pointing to a part of the illustration.

Camera-ready copy: final publication material that is ready to be made into a negative for a printing plate. May be a computer file or actual print and images on a board.

Cap height: in typography, the distance from the baseline to the top of the capital letters.

Caption: an identification (title) for an illustration, usually a brief phrase. The caption should also support the other content.

Character: any letter, figure, punctuation, symbol or space

Clip art: ready-made artwork sold or distributed for clipping and pasting into publications. Available in hard-copy books, and in electronic form, as files on disk.

Color separation: the process of creating separate negatives and plates for each color of ink (cyan, magenta, yellow, and black) that will be used in the publication.

Color spacing: the addition of spaces to congested areas of words or word spacing to achieve a more pleasing appearance after the line has been set normally.

Column gutter: the space between columns of type.Comprehensive layout (comp): a blueprint of the publication, showing exactly how the type will be set and positioned, and the treatment, sizing, and placement of illustrations on the page.

Condensed font: a font in which the set-widths of the characters is narrower than in the standard typeface. (Note: not the inter-character space -- that is accomplished through tracking).

Continuous tone: artwork that contains gradations of gray, as opposed to black-and-white line art. Photographs and some drawings, like charcoal or watercolor, require treatment as continuous-tone art.

Copy: generally refers to text -- typewritten pages, word-processing files, typeset galleys or pages -- although sometimes refers to all source materials (text and graphics) used in a publication.

Copyfitting: the fitting of a variable amount of copy within a specific and fixed amount of space.

Counter: in typography, an enclosed area within a letter, in uppercase, lowercase, and numeric letterforms.

Crop marks: on a mechanical, horizontal and vertical lines that indicate the edge of the printed piece.

Cropping: for artwork, cutting out the extraneous parts of an image, usually a photograph.

Cutlines: explanatory text, usually full sentences, that provides information about illustrations. Cutlines are sometimes called captions or legends; not to be confused with title-captions, which are headings for the illustration, or key-legends, which are part of the artwork.

Descender: in typography, the part of the letterform that dips below the baseline; usually refers to lowercase letters and some punctuation, but some typefaces have uppercase letters with descenders.

Dingbat typeface: a typeface made up of nonalphabetic marker characters, such as arrows, asterisks, encircled numbers.

Discretionary hyphen: a hyphen that will occur only if the word appears at the end of a line, not if the word appears in the middle of a line.

Display type: large and/or decorative type used for headlines and as graphic elements in display pieces. Common sizes are 14, 18, 24, 30, 36, 48, 60, and 72 point.

Dither: for digital halftones, the creation of a flat bitmap by simply rutning dots off or on. All dots are the same size there are simply more of them in dark areas and fewer of them in light areas -- as opposed to deep bitmaps used in gray-scale images.

DPI (dots per inch): the unit of measurement used to describe the resolution of printed output. The most common desktop laser printers output a 300 dpi. Medium-resolution printers output at 600 dpi. Image setters output at 1270-2540 dpi.

Duotone: a halftone image printed with two colors, one dark and the other light. The same photograph is halftoned twice, using the same screen at two different angles; combining the two improves the detail and contrast.

Egyptian type: originally, from 1815 on, bold face with heavy slabs or square serifs.

Em space: a space as wide as the point size of the types. This measurement is relative; in 12-point type an em space is 12 points wide, but in 24-point type an em space is 24 points wide.

En space: a space half as wide as the type is high (half an em space.

Expanded (font): a font in which the set widths of the characters are wider than in the standard typeface. (Note: not the intercharacter space -- that is accomplished through letterspacing -- but the characters themselves).

Extended type: typefaces that are wide horizontally -- Hellenic, Latin Wide, Egyptian Expanded, Microgramma Extended, etc.

Facing pages: in a double-sided document, the two pages that appear as a spread when the publication is opened.

Feather: to insert small amounts of additional leading between lines, paragraphs, and before and after headings in order to equalize the baselines of columns on a page.

Folio: a page number, often set with running headers or footers.

Font: a set of characters in a specific typeface, at a specific point size, and in a specific style. "12-point Times Bold" is a font -- the typeface Times, at 12-point size, in the bold style. Hence "12-point Times Italic" and "10-point Times Bold" are separate fonts.

Galleys: in traditional publishing, the type set in long columns, not laid out on a page. In desktop publishing, galleys can be printed out using a page-assembly program, for proofreading and copyfitting purposes.

Greeked text: in page-assembly programs, text that appears as gray bars approximating the lines of type rather than actual characters. This speeds up the amount of time it takes to draw images on the screen.Gray-scale image: a "deep" bitmap that records with each dot its gray-scale level. The impression of greenness is a function of the size of the dot; a group of large dots looks dark and a group of small dots looks light.

Gutter: In double-sided documents, the combination of the inside margins of facing pages; the gutter should be wide enough to accommodate binding.

Check your progress:

1. Explain Criticism of the rational model2. Explain Philosophies and studies of design3. Explain Terminology

Reference:

Beck, K., Beedle, M., van Bennekum, A., Cockburn, A., Cunningham, W., Fowler, M., Grenning, J., Highsmith, J., Hunt, A., Jeffries, R., Kern, J., Marick, B., Martin, R.C., Mellor, S., Schwaber, K., Sutherland, J., and Thomas, D. "Manifesto for agile software development," 2001. Available Accessed: June 22, 2010

Bourque, P., and Dupuis, R. (eds.) Guide to the software engineering body of knowledge (SWEBOK). IEEE Computer Society Press, 2004.

Brooks, F.P. The design of design: Essays from a computer scientist, Addison-Wesley Professional, 2010, 448 pages.

Cross, N., Dorst, K., and Roozenburg, N. Research in design thinking, Delft University Press, Delft, 1992.

Dorst, K., and Cross, N. "Creativity in the design process: Co-evolution of problem-solution," Design Studies (22), September 2001, pp 425–437.

Dorst, K., and Dijkhuis, J. "Comparing paradigms for describing design activity," Design Studies (16:2) 1995, pp 261–274.

Faste, R., "The Human Challenge in Engineering Design," International Journal of Engineering Education, Vol. 17, 2001

McCracken, D.D., and Jackson, M.A. "Life cycle concept considered harmful," SIGSOFT Software Engineering Notes (7:2) 1982, pp 29–32.

Newell, A., and Simon, H. Human problem solving, Prentice-Hall, Inc., 1972, 920 pages.

Pahl, G., and Beitz, W. Engineering design: A systematic approach, Springer-Verlag, London, 1996.

Pahl, G., Beitz, W., Feldhusen, J., and Grote, K.-H. Engineering design: A systematic approach, (3rd ed.), Springer-Verlag, 2007.

Ralph, P. "Comparing two software design process theories," International Conference on Design Science Research in Information Systems and Technology (DESRIST 2010), Springer, St. Gallen, Switzerland, 2010, pp. 139–153.

Royce, W.W. "Managing the development of large software systems: Concepts and techniques," Proceedings of Wescon, 1970.

Check your progress answer:

1. Refer 3.42. Refer 3.53. Refer 3.6

Unit 4: Behaviour of Space Frames

4.1 Introduction4.2 Characteristics of trusses

4.2.1 Planar truss4.2.2 Space frame truss

4.3 Truss types4.3.1 Pratt truss4.3.2 Bowstring truss4.3.3 King post truss4.3.4 Lenticular truss4.3.5 Vierendeel truss

4.4 Static of truss

4.1 Introduction

In architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in forces in the members which are either tensile or compressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes.

A planar truss is one where all the members and nodes lie within a two dimensional plane, while a space truss has members and nodes extending into three dimensions.

4.2 Characteristics of trusses

A truss consists of straight members connected at joints. Trusses are composed of triangles because of the structural stability of that shape and design. A triangle is the simplest geometric figure that will not change shape when the lengths of the sides are fixed. In comparison, both the angles and the lengths of a four-sided figure must be fixed for it to retain its shape.

4.2.1 Planar truss

Planar roof trusses

The simplest form of a truss is one single triangle. This type of truss is seen in a framed roof consisting of rafters and a ceiling joist.and in other mechanical structures such as bicycles.

Because of the stability of this shape and the methods of analysis used to calculate the forces within it, a truss composed entirely of triangles is known as a simple truss.The traditional diamond-shape bicycle frame, which utilizes two conjoined triangles, is an example of a simple truss.

A planar truss lies in a single plane. Planar trusses are typically used in parallel to form roofs and bridges.

The depth of a truss, or the height between the upper and lower chords, is what makes it an efficient structural form. A solid girder or beam of equal strength would have substantial weight and material cost as compared to a truss. For a given span length, a deeper truss will require less material in the chords and greater material in the verticals and diagonals. An optimum depth of the truss will maximize the efficiency.

4.2.2 Space frame truss

A space frame truss is a three-dimensional framework of members pinned at their ends. A tetrahedron shape is the simplest space truss, consisting of six members which meet at four joints. Large planar structures may be composed from tetrahedrons with common edges and they are also employed in the base structures of large free-standing power line pylons

4.3 Truss types

There are two basic types of truss:

• The pitched truss, or common truss, is characterized by its triangular shape. It is most often used for roof construction. Some common trusses are named according to their web configuration. The chord size and web configuration are determined by span, load and spacing.

• The parallel chord truss, or flat truss, gets its name from its parallel top and bottom chords. It is often used for floor construction.

A combination of the two is a truncated truss, used in hip roof construction. A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with metal connector plates.

4.3.1 Pratt truss

The Pratt truss was patented in 1844 by two Boston railway engineers, Caleb Pratt and his son Thomas Willis Pratt. The design uses vertical members for compression and horizontal members to respond to tension. What is remarkable about this style is that it remained popular even as wood gave way to iron, and even still as iron gave way to steel. The continued popularity of the Pratt truss is probably due to the fact that the configuration of the members means that longer diagonal members are only in tension for gravity load effects. This allows these members to be used more efficiently, as slenderness effects related to buckling under compression loads (which are compounded by the length of the member) will typically not control the design. Therefore, for given planar truss with a fixed depth, the Pratt configuration is usually the most efficient under static, vertical loading.

The Southern Pacific Railroad bridge in Tempe, Arizona is a 393 meter (1,291 foot) long truss bridge built in 1912. The structure is composed of nine Pratt truss spans of varying lengths. The bridge is still in use today.

The Wright Flyer used a Pratt truss in its wing construction, as the minimization of compression member lengths allowed for lower aerodynamic drag.

4.3.2 Bowstring truss

Named for their shape, bowstring trusses were first used for arched truss bridges, known as tied-arch bridges.

Thousands of bowstring trusses were used during World War II for holding up the curved roofs of aircraft hangars and other military buildings. Many variations exist in the arrangements of the members connecting the nodes of the upper arc with those of the lower, straight sequence of members, from nearly isosceles triangles to a variant of the Platt truss.

4.3.3 King post truss

One of the simplest truss styles to implement, the king post consists of two angled supports leaning into a common vertical support.

The queen post truss, sometimes queenpost or queenspost, is similar to a king post truss in that the outer supports are angled towards the center of the structure. The primary difference is the horizontal extension at the centre which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans.

4.3.4 Lenticular truss

American architect Ithiel Town designed Town's Lattice Truss as an alternative to heavy-timber bridges. His design, patented in 1820 and 1835, uses easy-to-handle planks arranged diagonally with short spaces in between them.

4.3.5 Vierendeel truss

The Vierendeel truss is a truss where the members are not triangulated but form rectangular openings, and is a frame with fixed joints that are capable of transferring and resisting bending moments. Regular trusses comprise members that are commonly assumed to have pinned joints, with the implication that no moments exist at the jointed ends. This style of truss was named after the Belgian engineer Arthur Vierendeel, who developed the design in 1896. Its use for bridges is rare due to higher costs compared to a triangulated truss.

The utility of this type of truss in buildings is that a large amount of the exterior envelope remains unobstructed and can be used for fenestration and door openings. This is preferable to a braced-frame system, which would leave some areas obstructed by the diagonal braces.

4.4 Statics of trusses

A truss that is assumed to comprise members that are connected by means of pin joints, and which is supported at both ends by means of hinged joints or rollers, is described as being statically determinate. Newton's Laws apply to the structure as a whole, as well as to each node or joint. In order for any node that may be subject to an external load or force to remain static in space, the following conditions must hold: the sums of all (horizontal and vertical) forces, as well as all moments acting about the node equal zero. Analysis of these conditions at each node yields the magnitude of the forces in each member of the truss. These may be compression or tension forces.

Trusses that are supported at more than two positions are said to be statically indeterminate, and the application of Newton's Laws alone is not sufficient to determine the member forces.

In order for a truss with pin-connected members to be stable, it must be entirely composed of triangles. In mathematical terms, we have the following necessary condition for stability:

where m is the total number of truss members, j is the total number of joints and r is the number of reactions (equal to 3 generally) in a 2-dimensional structure.

When m = 2j − 3, the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2j equilibrium equations, once we know the external loads and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any member is taken out (or fails), then the truss as a whole fails. While the relation (a) is necessary, it is not sufficient for stability, which also depends on the truss geometry, support conditions and the load carrying capacity of the members.

Some structures are built with more than this minimum number of truss members. Those structures may survive even when some of the members fail. Their member forces depend on the relative stiffness of the members, in addition to the equilibrium condition described.

Glossary:

· atom – a Lisp entity that is not a cons. This includes symbols and strings.· alist – a list whose elements are conses.

· bookmark – just what it sounds like: a saved location in a file or buffer· bound variable – a variable that has a symbol value· buffer – editing happens in buffers (workspaces)· car – see cons· cdr – see cons· character property – a text property or an overlay property· chord – a key sequence with keys pressed simultaneously· command – an InteractiveFunction· completion – completing input in the minibuffer or text in another buffer· cons (aka cons cell) – A Lisp object that is composed of a pair of Lisp objects of any kind. The first is called the car; the second is called the cdr. See also atom.· cursor (text cursor) – how it differs from the pointer (mouse pointer); its relation with point· custom file – file, other than your init file (~/.emacs), where customizations from Customize are saved. It is the value of variable ‘custom-file’.· Customize – Emacs user interface for changing and saving preferences (settings)· default directory – directory assumed for the current buffer; it is the value of variable ‘default-directory’

· [[device?]] – Under XEmacs, frames are shown on devices (TTY, X, MS Windows, GTK)· [[display?]] – Under GNU Emacs, frames are shown on displays (TTY, X)· doc string – self-documentation for functions and variables· DWIM – DoWhatIMean: sophisticated user-interface design that sometimes doesn’t do what you intend or expect ;-)· dynamic scoping – variable binding (value) behavior that means the last binding of a given variable wins – lexical context does not govern binding· echo area – Occupies the same frame space as the minibuffer. Used to display messages.· Electricity – extra or sophisticated behavior (see also DWIM)· Emacsen – different Emacs implementations· Emacs Lisp – the Lisp dialect that Emacs uses. Much of Emacs is written in Emacs Lisp, and you can use Emacs Lisp to customize or extend Emacs.· extensible – the ‘E’ in “Emacs”· face – Is it a [[font?]]? Is it a color? No, it is a face!· [[font?]] – ???????? FIXME· frame – Emacs windows are shown in frames (called “windows” outside of Emacs)· fringe – thin strips at the left and right edges of a window, with glyphs that indicate various things· function cell – the function associated with a symbol; aka symbol function· GPL – GNU General Public License: publishing license used for free software· header line – at the top of a window, used by some modes· Info – Emacs’s on-board help system: hypertext manuals (see InfoMode)· init file – your personal startup file, loaded when Emacs starts up: ~/.emacs or ~/_emacs

· InteractiveFunction – command· key binding – a mapping (relation) between an Emacs command and a key sequence. A key binding can be a global key binding, a local key binding (enabled only for a

given major mode), or a minor-mode key binding (enabled only for a given minor mode)· keyboard macro – a recording of key sequences that you can replay· keymap – a collection of key bindings, that is, a mapping (relation) between Emacs commands and key sequences. A keymap can be a global keymap, a local keymap (applicable only to a given major mode), or a minor-mode keymap (applicable only to a given minor mode)· key sequence – a key sequence can be bound to a command, to execute it· kill – cut, that is, delete and copy to the kill ring· kill ring – ring of previously killed (cut) or copied text snippets; the value of variable ‘kill-ring’

· lambda expression – a function representation that is a sexp that evaluates to a cons whose car is the symbol ‘lambda’. (See WikiPedia : Lambda calculus .)· line – a line of text. See also line ending.· line ending – one or more characters at the end of a line· line wrap – how lines that are wider than a window are displayed (unless they are truncated at the right edge)· minibuffer – special buffer at the bottom of a frame, which you use to enter commands· minor mode – several minor modes can be active at the same time· mode line – at the bottom of a window, it describes the current buffer status· modifier key – (1) a keyboard key that, when pressed, modifies the behavior of another keyboard key pressed at the same time (e.g. Control, Shift, Alt); (2) a soft key that does the same thing (e.g. Control, Shift, Meta, Hyper, Super)· mule – multilingual environment· narrowing – limiting buffer scope temporarily· obarray – a symbol table implemented as a special kind of vector. Think of it as a hash table for looking up symbols. The value of variable ‘obarray’ is the obarray used by default by ‘intern’ and ‘read’. See Manual : Creating Symbols .

Check your progress

1. Explain Characteistics of truss2. Explain Truss types3. Explain Static of truss

Reference:

1. ^ Ricker, Nathan Clifford (1912) [1912]. A Treat on Design and Construction of Roofs. New York: J. Wiley & Sons. pp. 12. Retrieved 2008-08-15.2. ^ Maginnis, Owen Bernard (1903). Roof Framing Made Easy (2nd edition ed.). New York: The Industrial Publication Company. pp. 9. Retrieved 2008-08-16.3. ^ a b c Hibbeler, Russell Charles (1983) [1974]. Engineering Mechanics-Statics (3rd edition ed.). New York: Macmillan Publishing Co., Inc.. pp. 199–224. ISBN 0-02-354310-8.

4. ^ Wingerter, R., and Lebossiere, P., ME 354, Mechanics of Materials Laboratory: Structures, University of Washington (February 2004), p.15. ^ Merriman, Mansfield (1912) [192]. American Civil Engineers' Pocket Book. New York: J. Wiley & Sons. pp. 785. Retrieved 2008-08-16. "The Economic Depth of a Truss is that which makes the material in a bridge a minimum."6. ^ Bethanga Bridge at the NSW Heritage Office; retrieved 2008-Feb-067. ^ A Brief History of Covered Bridges in Tennessee at the Tennessee Department of Transportation; retrieved 2008-Feb-068. ^ The Pratt Truss courtesy of the Maryland Department of Transportation; retrieved 2008-Feb-69. ^ Tempe Historic Property Survey at the Tempe Historical Museum; retrieved 2008-Feb-0610. ^ http://www.arct.cam.ac.uk/personal-page/james/ichs/Vol%202%201221-1232%20Gasparini.pdf11. ^ Covered Bridge's Truss Types12. ^ Vierendeel bruggen

Check your progress answers

1. Refer 4.22. Refer 4.33. Refer 4.4

BLOCK 4 Analysis and Design

Object-oriented analysis and design (OOAD) is a software engineering approach that models a system as a group of interacting objects. Each object represents some entity of interest in the system being modeled, and is characterised by its class, its state (data elements), and its behavior. Various models can be created to show the static structure, dynamic behavior, and run-time deployment of these collaborating objects. There are a number of different notations for representing these models, such as the Unified Modeling Language (UML).

Object-oriented analysis (OOA) applies object-modelling techniques to analyze the functional requirements for a system. Object-oriented design (OOD) elaborates the analysis models to produce implementation specifications. OOA focuses on what the system does, OOD on how the system does it.

Object-oriented systems

An object-oriented system is composed of objects. The behavior of the system results from the collaboration of those objects. Collaboration between objects involves them sending messages to each other. Sending a message differs from calling a function in that when a target object receives a message, it itself decides what function to carry out to service that message. The same message may be implemented by many different functions, the one selected depending on the state of the target object.

The implementation of "message sending" varies depending on the architecture of the system being modeled, and the location of the objects being communicated with.

Object-oriented analysis

Object-oriented analysis (OOA) looks at the problem domain, with the aim of producing a conceptual model of the information that exists in the area being analyzed. Analysis models do not consider any implementation constraints that might exist, such as concurrency, distribution, persistence, or how the system is to be built. Implementation constraints are dealt during object-oriented design (OOD). Analysis is done before the Design

The sources for the analysis can be a written requirements statement, a formal vision document, and interviews with stakeholders or other interested parties. A system may be divided into multiple domains, representing different business, technological, or other areas of interest, each of which are analyzed separately.

The result of object-oriented analysis is a description of what the system is functionally required to do, in the form of a conceptual model. That will typically be presented as a set of use cases, one or more UML class diagrams, and a number of interaction diagrams. It may also include some kind of user interface mock-up. The purpose of object oriented analysis is to develop a model that describes computer software as it works to satisfy a set of customer defined requirements.

Object-oriented design

Object-oriented design (OOD) transforms the conceptual model produced in object-oriented analysis to take account of the constraints imposed by the chosen architecture and any non-functional – technological or environmental – constraints, such as transaction throughput, response time, run-time platform, development environment, or programming language.

The concepts in the analysis model are mapped onto implementation classes and interfaces. The result is a model of the solution domain, a detailed description of how the system is to be built.

Unit 1: Analysis of space frames

1.1Introduction1.2Relation of basis1.3Types of frames

1.3.1Tight frames1.3.2Uniform frames1.3.3The dual frame

1.4Position vs displacement1.5Siano’s extension: orientational analysis1.6Dimensionless concepts

1.6.1Constants1.6.2Formalisms

1.1 Introduction

In linear algebra, a frame of a vector space V with an inner product can be seen as a generalization of the idea of a basis to sets which may be linearly dependent. The key issue related to the construction of a frame appears when we have a sequence of vectors

, with each and we want to express an arbitrary element as a linear

combination of the vectors : and want to determine the coefficients ck. If the set does not span V, then these coefficients cannot be determined for all such . If spans V and also is linearly independent, this set forms a basis of V, and the coefficients ck are uniquely determined by : they are the coordinates of relative to this basis. If, however, spans V but is not linearly independent, the question of how to determine the coefficients becomes less apparent, in particular if V is of infinite dimension.

Given that spans V and is linearly dependent, it may appear obvious that we should remove vectors from the set until it becomes linearly independent and forms a basis. There are some problems with this strategy:

1. By removing vectors randomly from the set, it may lose its possibility to span V before it becomes linearly independent.

2. Even if it is possible to devise a specific way to remove vectors from the set until it becomes a basis, this approach may become infeasible in practice if the set is large or infinite.

3. In some applications, it may be an advantage to use more vectors than necessary to represent . This means that we want to find the coefficients ck without

removing elements in .

In 1952, Duffin and Schaeffer gave a solution to this problem, by describing a condition on the set that makes it possible to compute the coefficients ck in a simple way.

More precisely, a frame is a set of elements of V which satisfy the so-called frame condition:

There exist two real numbers, A and B such that and

.This means that the constants A and B can be chosen independently of v: they only

depend on the set .

The numbers A and B are called lower and upper frame bounds.

It can be shown that the frame condition is both necessary and sufficient to form a frame a set of dual frame vectors with the following property:

for any . This implies that a frame together with its dual frame has the same properties as a basis and its dual basis in terms of reconstructing a vector from scalar products.

1.2 Relation to bases

If the set is a frame of V, it spans V. Otherwise there would exist at least one non-zero which would be orthogonal to all . If we insert into the frame condition, we obtain

therefore , which is a violation of the initial assumptions on the lower frame bound.

If a set of vectors spans V, this is not a sufficient condition for calling the set a frame. As

an example, consider and the infinite set given by

This set spans V but since we

cannot choose . Consequently, the set is not a frame.

1.3 Types of frames

1.3.1 Tight frames

A frame is tight if the frame bounds A and B are equal. This means that the frame obeys a generalized Parseval's identity. If A = B = 1, then a frame is either called normalized or

Parseval. However, some of the literature refers to a frame for which where c is a constant independent of k (see uniform below) as a normalized frame.

1.3.2 Uniform frames

A frame is uniform if each element has the same norm: where c is a constant independent of k. A uniform normalized tight frame with c = 1 is an orthonormal basis.

1.3.3The dual frame

The frame condition is both sufficient and necessary for allowing the construction

of a dual or conjugate frame, , relative the original frame, . The duality of this frame implies that

is satisfied for all . In order to construct the dual frame, we first need the linear mapping: defined as

From this definition of and linearity in the first argument of the inner product, it now follows that

which can be inserted into the frame condition to get

The properties of can be summarised as follows:

1. is self-adjoint, positive definite, and has positive upper and lower bounds. This leads to

2. the inverse of exists and it, too, is self-adjoint, positive definite, and has positive upper and lower bounds.

The dual frame is defined by mapping each element of the frame with :

To see that this make sense, let be arbitrary and set

It is then the case that

which proves that

Alternatively, we can set

By inserting the above definition of and applying known properties of and its inverse, we get

which shows that

This derivation of the dual frame is a summary of section 3 in the article by Duffin and Schaeffer. They use the term conjugate frame for what here is called dual frame.

In physics and science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions (usually mass, length, time, electric charge, and temperature) which describe it; for example, speed has the dimension length per unit time, and may be measured in meters per second, miles per hour, or other units. Dimensional analysis is based on the fact that a physical law must be independent of the units used to measure the physical variables. A straightforward practical consequence is that any meaningful equation (and any inequality and inequation) must have the same dimensions in the left and right sides. Checking this is the basic way of performing dimensional analysis.

Dimensional analysis is routinely used to check the plausibility of derived equations and computations. It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena, and to categorize types of physical quantities and units based on their relations to or dependence on other units, or their dimensions if any.

The basic principle of dimensional analysis was known to Isaac Newton (1686) who referred to it as the "Great Principle of Similitude".[1] James Clerk Maxwell played a major role in establishing modern use of dimensional analysis by distinguishing mass, length, and time as fundamental units, while referring to other units as derived.[2] The 19th-century French mathematician Joseph Fourier made important contributions[3] based on the idea that physical laws like F = ma should be independent of the units employed to measure the physical variables. This led to the conclusion that meaningful laws must be homogeneous equations in their various units of measurement, a result which was eventually formalized in the Buckingham π theorem. This theorem describes how every physically meaningful equation involving n variables can be equivalently rewritten as an equation of n − m dimensionless parameters, where m is the number of fundamental dimensions used. Furthermore, and most importantly, it provides a method for computing these dimensionless parameters from the given variables.

A dimensional equation can have the dimensions reduced or eliminated through nondimensionalization, which begins with dimensional analysis, and involves scaling quantities by characteristic units of a system or natural units of nature. This gives insight into the fundamental properties of the system, as illustrated in the examples below.

1.4 Position vs displacement

Some discussions of dimensional analysis implicitly describes all quantities are mathematical vectors. (In mathematics scalars are considered a special case of vectors; the emphasis here is that vectors are closed under addition, subtraction, and scalar multiplication, and permit scalar division.). This assumes an implicit point of reference—an origin. While this is useful and often perfectly adequate, allowing many important errors to be caught, it can fail to model certain aspects of physics. A more rigorous approach requires distinguishing between position and displacement (or moment in time versus duration, or absolute temperature versus temperature change).

Consider points on a line, each with a position with respect to a given origin, and distances among them. Positions and displacements all have units of length, but their meaning is not interchangeable:

• adding two displacements should yield a new displacement (walking ten paces then twenty paces gets you thirty paces forward),

• adding a displacement to a position should yield a new position (walking one block down the street from an intersection gets you to the next intersection),

• subtracting two positions should yield a displacement,• but one may not add two positions.

This illustrates the subtle distinction between affine quantities (ones modeled by an affine space, such as position) and vector quantities (ones modeled by a vector space, such as displacement).

• Vector quantities may be added to each other, yielding a new vector quantity, and a vector quantity may be added to a suitable affine quantity (a vector space acts on an affine space), yielding a new affine quantity.

• Affine quantities cannot be added, but may be subtracted, yielding relative quantities which are vectors, and these relative differences may then be added to each other or to an affine quantity.

Properly then, positions have dimension of affine length, while displacements have dimension of vector length. To assign a number to an affine unit, one must not only choose a unit of measurement, but also a point of reference, while to assign a number to a vector unit only requires a unit of measurement.

Thus some physical quantities are better modeled by vectorial quantities while others tend to require affine representation, and the distinction is reflected in their dimensional analysis.

This distinction is particularly important in the case of temperature for which there is an absolute zero that is different in different measuring systems. That is, for absolute temperatures

0 K = −273.15 °C = −459.67 °F = 0 °R,

but for relative temperatures,

1 K = 1 °C ≠ 1 °F = 1 °R

Unit conversion for relative temperatures, where no temperature difference is zero in all units, is simply a matter of multiplying by, e.g., 1 °F / 1 K. But because these systems for absolute temperatures have different origins, conversion from one absolute temperature requires accounting for that. As a result, simple dimensional analysis can still lead to errors if it becomes ambiguous if 1 K equals −272.15 °C or 1 °C.

1.5 Siano's extension: orientational analysis

Huntley's extension has some serious drawbacks:

• It does not deal well with vector equations involving the cross product,• nor does it handle well the use of angles as physical variables.

It also is often quite difficult to assign the L, Lx, Ly, Lz, symbols to the physical variables involved in the problem of interest. He invokes a procedure that involves the "symmetry" of the physical problem. This is often very difficult to apply reliably: It is unclear as to what parts of the problem that the notion of "symmetry" is being invoked. Is it the symmetry of the physical body that forces are acting upon, or to the points, lines or areas at which forces are being applied? What if more than one body is involved with different symmetries? Consider the spherical bubble attached to a cylindrical tube, where one wants the flow rate of air as a function of the pressure difference in the two parts. What are the Huntley extended dimensions of the viscosity of the air contained in the connected parts? What are the extended dimensions of the pressure of the two parts? Are they the same or different? These difficulties are responsible for the limited application of Huntley's addition to real problems.

Angles are, by convention, considered to be dimensionless variables, and so the use of angles as physical variables in dimensional analysis can give less meaningful results. As an example, consider the projectile problem mentioned above. Suppose that, instead of the x- and y-components of the initial velocity, we had chosen the magnitude of the velocity v and the angle θ at which the projectile was fired. The angle is, by convention, considered to be dimensionless, and the magnitude of a vector has no directional quality, so that no dimensionless variable can be composed of the four variables g, v, R, and θ. Conventional analysis will correctly give the powers of g and v, but will give no information concerning the dimensionless angle θ.

Siano (Siano, 1985-I, 1985-II) has suggested that the directed dimensions of Huntley be replaced by using orientational symbols 1x 1y 1z to denote vector directions, and an orientationless symbol 10. Thus, Huntley's 1x becomes L 1x with L specifying the dimension of length, and 1x specifying the orientation. Siano further shows that the orientational symbols have an algebra of their own. Along with the requirement that 1i

−1 = 1i, the following multiplication table for the orientation symbols results:

Note that the orientational symbols form a group (the Klein four-group or "Viergruppe"). In this system, scalars always have the same orientation as the identity element,

independent of the "symmetry of the problem." Physical quantities that are vectors have the orientation expected: a force or a velocity in the z-direction has the orientation of 1z. For angles, consider an angle θ that lies in the z-plane. Form a right triangle in the z plane with θ being one of the acute angles. The side of the right triangle adjacent to the angle then has an orientation 1x and the side opposite has an orientation 1y. Then, since tan(θ) = 1y/1x = θ + ... we conclude that an angle in the xy plane must have an orientation 1y/1x = 1z, which is not unreasonable. Analogous reasoning forces the conclusion that sin(θ) has orientation 1z while cos(θ) has orientation 10. These are different, so one concludes (correctly), for example, that there are no solutions of physical equations that are of the form a cos(θ)+b sin(θ) , where a and b are real scalars. Note that an expression such as sin(θ + π / 2) = cos(θ) is not dimensionally inconsistent since it is a special case of the sum of angles formula and should properly be written:

which for a = θ and b = π / 2 yields . Physical quantities may be expressed as complex numbers (e.g. eiθ) which imply that the complex quantity i has an orientation equal to that of the angle it is associated with (1z in the above example).

The assignment of orientational symbols to physical quantities and the requirement that physical equations be orientationally homogeneous can actually be used in a way that is similar to dimensional analysis to derive a little more information about acceptable solutions of physical problems. In this approach one sets up the dimensional equation and solves it as far as one can. If the lowest power of a physical variable is fractional, both sides of the solution is raised to a power such that all powers are integral. This puts it into "normal form". The orientational equation is then solved to give a more restrictive condition on the unknown powers of the orientational symbols, arriving at a solution that is more complete than the one that dimensional analysis alone gives. Often the added information is that one of the powers of a certain variable is even or odd.

As an example, for the projectile problem, using orientational symbols, θ, being in the xy-plane will thus have dimension 1z and the range of the projectile R will be of the form:

Dimensional homogeneity will now correctly yield a = −1 and b = 2, and orientational homogeneity requires that c be an odd integer. In fact the required function of theta will be sin(θ)cos(θ) which is a series of odd powers of θ.

It is seen that the Taylor series of sin(θ) and cos(θ) are orientationally homogeneous using the above multiplication table, while expressions like cos(θ) + sin(θ) and exp(θ) are not, and are (correctly) deemed unphysical.

It should be clear that the multiplication rule used for the orientational symbols is not the same as that for the cross product of two vectors. The cross product of two identical vectors is zero, while the product of two identical orientational symbols is the identity element.

1.6 Dimensionless concepts

1.6.1 Constants

The dimensionless constants that arise in the results obtained, such as the C in the Poiseuille's Law problem and the κ in the spring problems discussed above come from a more detailed analysis of the underlying physics, and often arises from integrating some differential equation. Dimensional analysis itself has little to say about these constants, but it is useful to know that they very often have a magnitude of order unity. This observation can allow one to sometimes make "back of the envelope" calculations about the phenomenon of interest, and therefore be able to more efficiently design experiments to measure it, or to judge whether it is important, etc.

1.6.2 Formalisms

Paradoxically, dimensional analysis can be a useful tool even if all the parameters in the underlying theory are dimensionless, e.g., lattice models such as the Ising model can be used to study phase transitions and critical phenomena. Such models can be formulated in a purely dimensionless way. As we approach the critical point closer and closer, the distance over which the variables in the lattice model are correlated (the so-called correlation length, ξ ) becomes larger and larger. Now, the correlation length is the relevant length scale related to critical phenomena, so one can, e.g., surmize on "dimensional grounds" that the non-analytical part of the free energy per lattice site should be ˜1 / ξd where d is the dimension of the lattice.

It has been argued by some physicists, e.g., Michael Duff that the laws of physics are inherently dimensionless. The fact that we have assigned incompatible dimensions to Length, Time and Mass is, according to this point of view, just a matter of convention, borne out of the fact that before the advent of modern physics, there was no way to relate mass, length, and time to each other. The three independent dimensionful constants: c, , and G, in the fundamental equations of physics must then be seen as mere conversion factors to convert Mass, Time and Length into each other.

Just as in the case of critical properties of lattice models, one can recover the results of dimensional analysis in the appropriate scaling limit; e.g., dimensional analysis in mechanics can be derived by reinserting the constants , c, and G (but we can now consider them to be dimensionless) and demanding that a nonsingular relation between quantities exists in the limit , and . In problems involving a gravitational field the latter limit should be taken such that the field stays finite.

Glossary:

AbstractA summary of a magazine or journal article, written by someone other than the original author.

Abstract wordsWords that refer to ideas or concepts.

Acceptance speechA speech that gives thanks for a gift, an award, or some other form of public recognition.

AcronymA word composed of the initial letters or parts of a series of words.

Active listeningGiving undivided attention to a speaker in a genuine effort to understand the speaker's point of view.

Ad hominem fallacyAn attempt to discredit a position by attacking the people who favor it.

AdrenalineA hormone released into the bloodstream in response to physical or mental stress.

After-dinner speechA brief, often humorous, ceremonial speech, presented after a meal, that offers a message without asking for radical changes in attitude or action.

Agenda-setting functionThe work of informative speaking in raising topics to attention and creating a sense of their importance.

AgreementThe third stage in the persuasive process requires that listeners not only accept the speaker’s recommendations but remember their reasons for doing so.

AlliterationRepetition of the initial consonant sound of close or adjoining words.

AmplificationThe art of developing ideas by finding ways to restate them in a speech.

Analogical persuasionCreating a strategic perspective on a subject by relating it to something about which the audience has strong positive or negative feelings.

Analogical reasoningReasoning in which a speaker compares two similar cases and infers that what is true for the first case is also true for the second.

Analogous color schemeColors adjacent on the color wheel; used in a presentation aid to suggest both differences and close relationships among the components represented.

AnalogyA connection established between two otherwise dissimilar ideas or things.

AnimationThe way objects enter and/or exit a PowerPoint slide.

AntithesisA language technique that combines opposing elements in the same sentence or adjoining sentences.

Appreciative listeningListening for pleasure or enjoyment.

Appreciative phasePhase of listening in which we enjoy the beauty of messages, responding to such factors as the simplicity, balance, and proportion of speeches and the eloquence of their language.

ArgumentsArrangements of proofs designed to answer key questions that arise in persuasive designs.

ArticulationThe physical production of particular speech sounds.

AssimilationThe tendency of listeners to interpret the positions of a speaker with whom they agree as closer to their own views than they actually are.

AtlasA book of maps.

AttitudeA frame of mind in favor of or opposed to a person, policy, belief, institution, topic, etc.

Audience-centerednessKeeping the audience foremost in mind at every step of speech preparation and presentation.

Audience demographicsObservable characteristics of listeners, including age, gender, educational level, group affiliations, and sociocultural backgrounds, that the speaker considers when adapting to an audience.

Audience dynamicsThe motivations, attitudes, beliefs, and values that influence the behavior of listeners.

Autocratic leaderA leader who makes decisions without consultation, issues orders or gives direction, and controls the members of the group through the use of rewards or punishments.

Award presentationA speech of tribute that recognizes achievements of the award recipient, explains the nature of the award, and describes why the recipient qualifies for the award.

AwarenessThis first stage in the persuasive process includes knowing about a problem, paying attention to it, and understanding how it affects our lives.

BalanceAchieving a balance among the major parts of a presentation.

Bandwagon

A fallacy which assumes that because something is popular, it is therefore good, correct, or desirable.

Bar graphA graph that uses vertical or horizontal bars to show comparisons among two or more items.

Begging the questionAssuming that an argument has been proved without actually presenting the evidence.

BeliefsIdeas we express about subjects that may explain our attitudes towards them.

BibliographyA list of all the sources used in preparing a speech.

Bill of RightsThe first ten amendments to the United States Constitution.

Biographical aidA reference work that provides information about people.

BodyThe middle part of a speech, used to develop the main ideas.

Body languageCommunication achieved using facial expressions, eye contact, movements, and gestures.

BookmarkA feature in a Web browser that stores links to Web sites so they can be easily revisited.

Boomerang effectAn audience’s hostile reaction to a speech advocating too much or too radical change.

BrainstormingA method of generating ideas by free association of words and thoughts.

Brief exampleA specific instance illustrating a more general idea.

BriefingA short, informative presentation given in an organizational setting.

Bulleted listA presentation aid that highlights themes by presenting them in a list of brief statements.

Burden of proofThe obligation facing a persuasive speaker to prove that a change from current policy is necessary.

Call numberA number used in libraries to classify books and periodicals and to indicate where they can be found on the shelves.

Call the questionA motion that proposes to end the discussion on a motion and to bring it to a vote.

CatalogueA listing of all the books, periodicals, and other resources owned by a library.

Categorical designThe use of natural or traditional divisions within a subject as a way of structuring an informative speech.

Causal orderA method of speech organization in which the main points show a cause-effect relationship.

Causal reasoningReasoning that seeks to establish the relationship between causes and effects.

Causation designA pattern for an informative speech that shows how one condition generates, or is generated by, another.

Central ideaA one-sentence statement that sums up or encapsulates the major ideas of a speech.

Check your progress:

1. Explain Types of frames2. Explain position vs displacement3. Explain Dimensionless concepts

Reference:

• Barenblatt, G. I. (1996), Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge, UK: Cambridge University Press, ISBN 0-521-43522-6

• Barnett (2007), "Dimensions and Economics: Some Problems", Quarterly Journal of Austrian Economics 7 (1)

• Buckingham, Edgar (1914), "On Physically Similar Systems: Illustrations of the Use of Dimensional Analysis", Phys. Rev. 4: 345, Bibcode 1914PhRv....4..345B, doi:10.1103/PhysRev.4.345

• Gibbings, J.C. (2011), Dimensional Analysis, Springer, ISBN 1849963169• Hart, George W. (March 1 1995), Multidimensional Analysis: Algebras and

Systems for Science and Engineering, Springer-Verlag, ISBN 0-387-94417-6• Huntley, H. E. (1967), Dimensional Analysis, Dover, LOC 67-17978• Perry, J. H.; et al. (1944), "Standard System of Nomenclature for Chemical

Engineering Unit Operations", Trans. Am. Inst. Chem. Engrs. 40 (251)• Pesic, Peter (2005), Sky in a Bottle, Cambridge, Mass: MIT Press, pp. 227–8,

ISBN 0-262-16234-2• Petty, G. W. (2001), "Automated computation and consistency checking of

physical dimensions and units in scientific programs.", Software — Practice and Experience 31: 1067–76, doi:10.1002/spe.401

• Porter, Alfred W. (1933), The Method of Dimensions, Methuen• Lord Rayleigh (1915), "The Principle of Similitude", Nature 95 (2368): 66–8,

Bibcode 1915Natur..95...66R, doi:10.1038/095066c0• Van Driest, E. R. (March 1946), "On Dimensional Analysis and the Presentation

of Data in Fluid Flow Problems", J. App. Mech 68 (A-34)

• Whitney, H. (1968), "The Mathematics of Physical Quantities, Parts I and II", Am. Math. Mo. (Mathematical Association of America) 75 (2): 115–138, 227–256, doi:10.2307/2315883

• GA Vignaux (1992), Erickson, Gary J.; Neudorfer, Paul O., ed., Dimensional Analysis in Data Modelling, Kluwer Academic, ISBN 0-7923-2031-X

• Wacław Kasprzak, Bertold Lysik, Marek Rybaczuk (1990), Dimensional Analysis in the Identification of Mathematical Models, World Scientific, ISBN 9789810203047

• PF Mendez, F Ordóñez (September 2005), "Scaling Laws From Statistical Data and Dimensional Analysis", Journal of Applied Mechanics 72 (5): 648–657, Bibcode 2005JAM....72..648M, doi:10.1115/1.1943434

• G Hart (1994), The theory of dimensioned matrices

• S. Drobo (1954), "On the foundations of dimensional analysis", Studia Mathematica

Check your progress answers

1. Refer 1.32. Refer 1.43. Refer 1.6

Unit 2: Detailed design of Space frames

2.1 Introduction2.2 Different aspects of frame of reference2.3 Observational frames of reference

2.3.1 Measurement apparatus2.3.2 Non-inertial frames2.3.3 Walls2.3.4 Platform framing

2.4 Roofs

2.1 Introduction

Audi AG (Xetra: NSU) is a German manufacturer of a range of automobiles, from supermini to crossover SUVs in various body styles and price ranges that are marketed

under the Audi brand (German pronunciation: [ aˈ ʊdi]), positioned as the premium brand within the Volkswagen Group.

The company is headquartered in Ingolstadt, Germany, and has been a wholly owned (99.55%) subsidiary of Volkswagen AG since 1966, following a phased purchase of its predecessor, Auto Union, from its former owner, Daimler-Benz. Volkswagen relaunched the Audi brand with the 1965 introduction of the Audi F103 series.

The company name is based on the surname of the founder August Horch, his surname meaning listen in German—which, when translated into Latin, becomes Audi.

A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer. It may also refer to both an observational reference frame and an attached coordinate system, as a unit.

2.2Different aspects of "frame of reference"

The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference. Sometimes the state of motion is emphasized, as in rotating frame of reference. Sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference

In this article the term observational frame of reference is used when emphasis is upon the state of motion rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a coordinate system may be employed for many purposes where the state of motion is not the primary concern. For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, of course, the formulation of many problems in physics employs generalized coordinates, normal modes or eigenvectors, which are only indirectly related to space and time. It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below:

• An observational frame (such as an inertial frame or non-inertial frame of reference) is a physical concept related to state of motion.

• A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations.[2] Consequently, an observer in an

observational frame of reference can choose to employ any coordinate system (Cartesian, polar, curvilinear, generalized, …) to describe observations made from that frame of reference. A change in the choice of this coordinate system does not change an observer's state of motion, and so does not entail a change in the observer's observational frame of reference. This viewpoint can be found elsewhere as well. Which is not to dispute that some coordinate systems may be a better choice for some observations than are others.

• Choice of what to measure and with what observational apparatus is a matter separate from the observer's state of motion and choice of coordinate system.

2.3 Observational frames of reference

An observational frame of reference, often referred to as a physical frame of reference, a frame of reference, or simply a frame, is a physical concept related to an observer and the observer's state of motion. Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized only by its state of motion. However, there is lack of unanimity on this point. In special relativity, the distinction is sometimes made between an observer and a frame. According to this view, a frame is an observer plus a coordinate lattice constructed to be an orthonormal right-handed set of spacelike vectors perpendicular to a timelike vector. See Doran. This restricted view is not used here, and is not universally adopted even in discussions of relativity. In general relativity the use of general coordinate systems is common (see, for example, the Schwarzschild solution for the gravitational field outside an isolated sphere).

There are two types of observational reference frame: inertial and non-inertial.

An inertial frame of reference is defined as one in which all laws of physics take on their simplest form. In special relativity these frames are related by Lorentz transformations. In Newtonian mechanics, a more restricted definition requires only that Newton's first law holds true; that is, a Newtonian inertial frame is one in which a free particle travels in a straight line at constant speed, or is at rest. These frames are related by Galilean transformations. These relativistic and Newtonian transformations are expressed in spaces of general dimension in terms of representations of the Poincaré group and of the Galilean group.

In contrast to the inertial frame, a non-inertial frame of reference is one in which fictitious forces must be invoked to explain observations. An example is an observational frame of reference centered at a point on the Earth's surface. This frame of reference orbits around the center of the Earth, which introduces a fictitious force known as the Coriolis force (among others).

2.3.1 Measurement apparatus

A further aspect of a frame of reference is the role of the measurement apparatus (for example, clocks and rods) attached to the frame (see Norton quote above). This question is not addressed in this article, and is of particular interest in quantum mechanics, where the relation between observer and measurement is still under discussion (see measurement problem).

In physics experiments, the frame of reference in which the laboratory measurement devices are at rest is usually referred to as the laboratory frame or simply "lab frame." An example would be the frame in which the detectors for a particle accelerator are at rest. The lab frame in some experiments is an inertial frame, but it is not required to be (for example the laboratory in the surface of the Earth in many physics experiments is not inertial). In particle physics experiments, it is often useful to transform energies and momenta of particles from the lab frame where they are measured, to the center of momentum frame "COM frame" in which calculations are sometimes simplified, since potentially all kinetic energy still present in the COM frame may be used for making new particles.

In this connection it may be noted that the clocks and rods often used to describe observers' measurement equipment in thought, in practice are replaced by a much more complicated and indirect metrology that is connected to the nature of the vacuum, and uses atomic clocks that operate according to the standard model and that must be corrected for gravitational time dilation.[30] (See second, meter and kilogram).

In fact, Einstein felt that clocks and rods were merely expedient measuring devices and they should be replaced by more fundamental entities based upon, for example, atoms and molecules.[31]

2.3.2 Non-inertial frames

Main articles: Fictitious force, Non-inertial frame, and Rotating frame of reference

Here we consider the relation between inertial and non-inertial observational frames of reference. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below.

An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g. x' , y' , a' .

The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as R. Given a point of interest that exists in both frames, the vector from the inertial origin to the point is called r, and the vector from the accelerated origin to the point is called r'. From the geometry of the situation, we get

Taking the first and second derivatives of this, we obtain

where V and A are the velocity and acceleration of the accelerated system with respect to the inertial system and v and a are the velocity and acceleration of the point of interest with respect to the inertial frame.

These equations allow transformations between the two coordinate systems; for example, we can now write Newton's second law as

When there is accelerated motion due to a force being exerted there is manifestation of inertia. If an electric car designed to recharge its battery system when decelerating is switched to braking, the batteries are recharged, illustrating the physical strength of manifestation of inertia. However, the manifestation of inertia does not prevent acceleration (or deceleration), for manifestation of inertia occurs in response to change in velocity due to a force. Seen from the perspective of a rotating frame of reference the manifestation of inertia appears to exert a force (either in centrifugal direction, or in a direction orthogonal to an object's motion, the Coriolis effect).

A common sort of accelerated reference frame is a frame that is both rotating and translating (an example is a frame of reference attached to a CD which is playing while the player is carried). This arrangement leads to the equation (see Fictitious force for a derivation):

or, to solve for the acceleration in the accelerated frame,

Multiplying through by the mass m gives

where

(Euler force)

(Coriolis force)

(centrifugal force)

Framing, in construction known as light-frame construction, is a building technique based around structural members, usually called studs, which provide a stable frame to which interior and exterior wall coverings are attached, and covered by a roof comprising horizontal ceiling joists and sloping rafters (together forming a truss structure) or manufactured pre-fabricated roof trusses—all of which are covered by various sheathing materials to give weather resistance.

Modern light-frame structures usually gain strength from rigid panels (plywood and other plywood-like composites such as oriented strand board (OSB) used to form all or part of wall sections, but until recently carpenters employed various forms of diagonal bracing (called wind braces) to stabilize walls. Diagonal bracing remains a vital interior part of many roof systems, and in-wall wind braces are required by building codes in many municipalities or by individual state laws in the United States.

Light frame construction using standardized dimensional lumber has become the dominant construction method in North America and Australia because of its economy. Use of minimal structural materials allows builders to enclose a large area with minimal cost, while achieving a wide variety of architectural styles. The ubiquitous platform framing and the older balloon framing are the two different light frame construction systems used in North America.

2.3.3 Walls

Wall framing in house construction includes the vertical and horizontal members of exterior walls and interior partitions, both of bearing walls and non-bearing walls. These stick members, referred to as studs, wall plates and lintels (headers), serve as a nailing base for all covering material and support the upper floor platforms, which provide the lateral strength along a wall. The platforms may be the boxed structure of a ceiling and roof, or the ceiling and floor joists of the story above.[1] The technique is variously referred to colloquially in the building trades as stick and frame, stick and platform, or stick and box as the sticks (studs) give the structure its vertical support, and the box shaped floor sections with joists contained within length-long post and lintels (more commonly called headers), supports the weight of whatever is above, including the next wall up and the roof above the top story. The platform, also provides the lateral support against wind and holds the stick walls true and square. Any lower platform supports the weight of the platforms and walls above the level of its component headers and joists.

Framing lumber should be grade-stamped, and have a moisture content not exceeding 19%.[2]

There are three historically common methods of framing a house.

• Post and Beam, which is now used predominately in barn construction.

• Balloon framing using a technique suspending floors from the walls was common until the late 1940s, but since that time, platform framing has become the predominant form of house construction.[3]

• Platform framing often forms wall sections horizontally on the sub-floor prior to erection, easing positioning of studs and increasing accuracy while cutting the necessary manpower. The top and bottom plates are end-nailed to each stud with two nails at least 3.25 in (83 mm) in length (16d or 16 penny nails). Studs are at least doubled (creating posts) at openings, the jack stud being cut to receive the lintels(headers) that are placed and end-nailed through the outer studs.[3]

Wall sheathing, usually a plywood or other laminate, is usually applied to the framing prior to erection, thus eliminating the need to scaffold, and again increasing speed and cutting manpower needs and expenses. Some types of exterior sheathing, such as asphalt-impregnated fibreboard, plywood, oriented strand board and waferboard, will provide adequate bracing to resist lateral loads and keep the wall square, but construction codes in most jurisdictions will require a stiff plywood sheathing. Others, such as rigid glass-fibre, asphalt-coated fibreboard, polystyrene or polyurethane board, will not.[1] In this latter case, the wall should be reinforced with a diagonal wood or metal bracing inset into the studs.[4] In jurisdictions subject to strong wind storms (hurricane countries, tornado alleys) local codes or state law will generally require both the diagonal wind braces and the stiff exterior sheathing regardless of the type and kind of outer weather resistant coverings.

2.3.4 Platform framing

In Canada and the United States, the most common method of light-frame construction for houses and small apartment buildings as well as some small commercial buildings is platform framing.

The framed structure sits atop a concrete (most common) or treated wood foundation. A sill plate is anchored, usually with 'J' bolts to the foundation wall. Generally these plates must be pressure treated to keep from rotting. The bottom of the sill plate is raised a minimum 6 inches (150 mm) above the finished grade by the foundation. This again is to prevent the sill-plate from rotting as well as providing a termite barrier.

The floors, walls and roof of a framed structure are created by assembling (using nails) consistently sized framing elements of dimensional lumber (2×4, 2×6, etc.) at regular spacings (12 in, 16 in, and 24 in on center. Sometimes the lesser known -19.2" on center- method is used), forming stud-bays (wall) or joist-bays (floor). The floors, walls and roof are typically made torsionally stable with the installation of a plywood or composite wood skin referred to as sheathing. Sheathing has very specific nailing requirements (such as size and spacing); these measures allow a known amount of shear force to be resisted by the element. Spacing the framing members properly allows them to align with the edges of standard sheathing. In the past, tongue and groove planks installed diagonally were used as sheathing. Occasionally, wooden or galvanized steel braces are

used instead of sheathing. There are also engineered wood panels made for shear and bracing.

The floor, or the platform of the name, is made up of joists (usually 2x6, 2×8, 2×10 or 2×12, depending on the span) that sit on supporting walls, beams or girders. The floor joists are spaced at (12 in, 16 in, and 24 in on center) and covered with a plywood subfloor. In the past, 1x planks set at 45-degrees to the joists were used for the subfloor.

Where the design calls for a framed floor, the resulting platform is where the framer will construct and stand that floor's walls (interior and exterior load bearing walls and space-dividing, non-load bearing partitions). Additional framed floors and their walls may then be erected to a general maximum of four in wood framed construction. There will be no framed floor in the case of a single-level structure with a concrete floor known as a slab on grade.

Stairs between floors are framed by installing stepped stringers and then placing the horizontal treads and vertical risers.

A framed roof is an assembly of rafters and wall-ties supported by the top story's walls. Prefabricated and site-built trussed rafters are also used along with the more common stick framing method. Trusses are engineered to redistribute tension away from wall-tie members and the ceiling members. The roof members are covered with sheathing or strapping to form the roof deck for the finish roofing material.

Floor joists can be engineered lumber (trussed, I-joist, etc.), conserving resources with increased rigidity and value. They allow access for runs of plumbing, HVAC, etc. and some forms are pre-manufactured.

Double framing is a style of framing used to reduce heat loss and air infiltration. Two walls are built around the perimeter of the building with a small gap in between. The inner wall carries the structural load of the building and is constructed as described above. The exterior wall is not load bearing and can be constructed using lighter materials. Insulation is installed in the entire space between the outside edge of the exterior wall and the inside edge of the interior wall. The size of the gap depends upon how much insulation is desired. The vapour barrier is installed on the outside of the inner wall, rather than between the studs and drywall of a standard framed structure. This increases its effectiveness as it is not perforated by electrical and plumbing connections.

2.4 Roofs

Roofs are usually built to provide a sloping surface intended to shed rain or snow, with slopes ranging from 1 cm of rise per 15 cm (less than an inch per linear foot) of rafter length, to steep slopes of more than 2 cm per cm (two feet per foot) of rafter length. A light-frame structure built mostly inside sloping walls comprising a roof is called an A-frame.

Roofs are most often covered with shingles made of asphalt, fiberglass and small gravel coating, but a wide range of materials are used. Molten tar is often used to waterproof flatter roofs, but newer materials include rubber and synthetic materials. Steel panels are popular roof coverings in some areas, preferred for their durability. Slate or tile roofs offer more historic coverings for light-frame roofs.

Light-frame methods allow easy construction of unique roof designs. Hip roofs, which slope toward walls on all sides and are joined at hip rafters that span from corners to a ridge. Valleys are formed when two sloping roof sections drain toward each other. Dormers are small areas in which vertical walls interrupt a roof line, and which are topped off by slopes at usually right angles to a main roof section. Gables are formed when a length-wise section of sloping roof ends to form a triangular wall section. Clerestories are formed by an interruption along the slope of a roof where a short vertical wall connects it to another roof section. Flat roofs, which usually include at least a nominal slope to shed water, are often surrounded by parapet walls with openings (called scuppers) to allow water to drain out. Sloping crickets are built into roofs to direct water away from areas of poor drainage, such as behind a chimney at the bottom of a sloping section.

Glossary:· ring – a data structure that acts as if it is circular (no end)· scroll bar – just what you think, controlled by command and variable ‘scroll-bar-mode’

· search ring – ring of previously used search strings; the value of variable ‘search-ring’ (see also regexp search ring)· secondary selection – like an additional region, but less ephemeral· sexp – a symbolic expression in Lisp· special display buffer (aka special buffer) – a buffer that is always displayed in its own, dedicated frame· symbol (aka variable) – a Lisp object that has a name, a value cell, a function cell, and a plist (property list)· tag – a name indexed in a tags file so you can quickly look up its definition· text property – a property attached to a character that affects its display or behavior· TtyFrames – Teletype (TTY), or terminal, screens· universal argument – the command bound to ‘C-u’· user option (aka user variable, aka option) – a variable that can be customized using Customize or set using ‘M-x set-variable’· value cell – the value of a symbol (variable); aka symbol value· variable – a symbol, whether bound or not· window – a frame pane; it shows a buffer· yank – paste

EgocentrismHolding the view that one’s own experiences and thoughts are the norm.

Either-or

A fallacy that forces listeners to choose between two alternatives when more than two alternatives exist.

Electronic brainstormingA group technique in which participants generate ideas in computer chat groups or by email.

Emergent leaderA group member who emerges as a leader during the group's deliberations.

Empathic phasePhase of listening in which we suspend judgment, allow speakers to be heard, and try to see things from their points of view.

Emphatic listeningListening to provide emotional support for a speaker.

EmpiricalA form of thinking that emphasizes the close inspection of reality.

EnactmentThe fourth stage of the persuasive process in which listeners take appropriate action as the result of their agreement.

Encoding processThe process by which the speaker combines words, tones, and gestures to convey thought and feelings to the audience.

Enduring metaphorsMetaphors of unusual power and popularity that are based on experience that lasts across time and that crosses many cultural boundaries.

EnunciationThe manner in which individual words are articulated and pronounced in context.

Ethical decisionsSound ethical decisions involve weighing a potential course of action against a set of ethical standards or guidelines.

EthicsThe branch of philosophy that deals with issues of right and wrong in human affairs.

EthnocentrismThe belief that one's own group or culture is superior to all other groups or cultures.

EthosThe name used by Aristotle for what modern students of communication refer to as credibility.

EulogyA speech of tribute presented upon a person’s death.

EventAnything that happens or is regarded as happening.

EvidenceSupporting materials used to prove or disprove something.

ExampleA specific case used to illustrate or to represent a group of people, ideas, conditions, experiences, or the like.

Expanded conversational styleA presentational quality that, while more formal than everyday conversation, preserves its directness and spontaneity.

Expert testimonyTestimony from people who are recognized experts in their fields.

ExplanationsA combination of facts and statistics to clarify a topic or process mentioned in a speech.

Extemporaneous speechA carefully prepared and rehearsed speech that is presented from a brief set of notes.

Extemporaneous presentation(extemporaneous speaking) A form of presentation in which a speech, although carefully prepared and practiced, is not written out or memorized.

Extended exampleA story, narrative, or anecdote developed at some length to illustrate a point.

Eye contactDirect visual contact with the eyes of another person.

Facts and statisticsItems of information that can be used to illustrate and prove points made by the speaker. When expressed numerically, such information appears in statistics.

Factual exampleAn illustration based on something that actually happened or that really exists.

Fair useA provision of copyright law that permits students and teachers to use portions of copyrighted materials for educational purposes.

FallacyAn error in reasoning.

False causeAn error in causal reasoning in which a speaker mistakenly assumes that because one event follows another, the first event is the cause of the second. This error is often known by its Latin name, post hoc, ergo propter hoc, meaning 'after this, therefore because of this.'

Faulty analogyA comparison drawn between things that are dissimilar in some important way.

FeedbackThe audience’s immediate response to a speaker.

Figurative analogyA comparison made between things that belong to different fields.

Figurative languageThe use of words in certain surprising and unusual ways in order to magnify the power of their meaning.

FilteringListening to only part of a message, the part the listener wants to hear.

Fixed-alternative questionsQuestions that offer a fixed choice between two or more alternatives.

Flawed statistical comparisonsStatistical reasoning that offers fallacious conclusions by comparing unequal and unlike situations.

Flow chartA visual method of representing power and responsibility relationships.

FontA complete set of type of the same design.

Formal outlineThe final outline in a process leading from the first rough ideas for a speech to the finished product.

Frame of referenceThe sum of a person's knowledge, experience, goals, values, and attitudes. No two people can have exactly the same frame of reference.

Free-rein leaderA leader who leaves members free to decide what, how, and when to act, offering no guidance.

GazetteerA geographical dictionary.

Gender stereotypingGeneralizations based on oversimplified or outmoded assumptions about gender and gender roles.

General encyclopediaA comprehensive reference work that provides information about all branches of human knowledge.

General purposeThe broad goal of a speech.

Check your progress:1. Explain Different aspects of frame of reference2. Explain observational frames of reference3. Explain Roofs

Reference:

1. ^ The distinction between macroscopic and microscopic frames shows up, for example, in electromagnetism where constitutive relations of various time and length scales are used to determine the current and charge densities entering Maxwell's equations. See, for example, Kurt Edmund Oughstun (2006). Electromagnetic and Optical Pulse Propagation 1: Spectral Representations in Temporally Dispersive Media. Springer. p. 165. ISBN 038734599X.. These distinctions also appear in thermodynamics. See Paul McEvoy (2002). Classical Theory. MicroAnalytix. p. 205. ISBN 1930832028..

2. ^ In very general terms, a coordinate system is a set of arcs xi = xi (t) in a complex Lie group; see Lev Semenovich Pontri ͡agin. L.S. Pontryagin: Selected Works Vol. 2: Topological Groups (3rd Edition ed.). Gordon and Breach. p. 429. ISBN 2881241336.. Less abstractly, a coordinate system in a space of n-dimensions is defined in terms of a basis set of vectors {e1, e2,… en}; see Edoardo

Sernesi, J. Montaldi (1993). Linear Algebra: A Geometric Approach. CRC Press. p. 95. ISBN 0412406802. As such, the coordinate system is a mathematical construct, a language, that may be related to motion, but has no necessary connection to motion.

3. ^ J X Zheng-Johansson and Per-Ivar Johansson (2006). Unification of Classical, Quantum and Relativistic Mechanics and of the Four Forces. Nova Publishers. p. 13. ISBN 1594542600.

4. ^ Jean Salençon, Stephen Lyle (2001). Handbook of Continuum Mechanics: General Concepts, Thermoelasticity. Springer. p. 9. ISBN 3540414436.

5. ^ Katherine Brading & Elena Castellani (2003). Symmetries in Physics: Philosophical Reflections. Cambridge University Press. p. 417. ISBN 0521821371.

6. ^ Oliver Davis Johns (2005). Analytical Mechanics for Relativity and Quantum Mechanics. Oxford University Press. Chapter 16. ISBN 019856726X.

7. ^ Donald T Greenwood (1997). Classical dynamics (Reprint of 1977 edition by Prentice-Hall ed.). Courier Dover Publications. p. 313. ISBN 0486696901.

8. ^ Matthew A. Trump & W. C. Schieve (1999). Classical Relativistic Many-Body Dynamics. Springer. p. 99. ISBN 079235737X.

9. ^ A S Kompaneyets (2003). Theoretical Physics (Reprint of the 1962 2nd Edition ed.). Courier Dover Publications. p. 118. ISBN 0486495329.

10. ^ M Srednicki (2007). Quantum Field Theory. Cambridge University Press. Chapter 4. ISBN 978-0-521-86449-7.

Check your progress answers

1. Refer 2.2 2. Refer 2.33. Refer 2.4

Unit 3: Introduction to Computer Aided Design and Software Packages

3.1 Introduction3.2 Computer aided design3.3 uses3.4 Types3.5 Technology

3.1 Introduction

Computer-aided design (CAD), also known as computer-aided design and drafting (CADD), is the utilization of computer technology for that process of design and design-documentation. Computer Aided Drafting describes the entire process of drafting with a computer. CADD software, or environments, provides the user with input-tools for the purpose of streamlining design processes; drafting, documentation, and manufacturing processes. CADD output is usually in the form of electronic files for print or machining operations. The development of CADD-based software programs are in direct correlation with the processes it seeks to economize; industry-based software (construction, manufacturing, etc.) typically uses vector-based (linear) environments whereas graphic-based software utilizes raster-based (pixelated) environments.

CADD environments often involve not only shapes. As in the manual drafting of technical and engineering drawings, the output of CAD must convey information, for example materials, processes, dimensions, and tolerances, according to application-specific conventions.

CAD may be used to design curves and figures in two-dimensional (2D) space; or curves, surfaces, and solids in three-dimensional (3D) objects.

CAD is an important industrial art extensively utilized in many applications, including automotive, shipbuilding, and aerospace industries, industrial and architectural design, prosthetics, and much more. CAD can also be widely used to produce computer animation for special effects in movies, advertising and technical manuals. The modern ubiquity and power of computers implies that even perfume bottles and shampoo dispensers are designed using techniques uncommon by engineers from the 1960s. Due to the enormous economic importance, CAD is a major power for research in computational geometry, computer graphics (both hardware and software), and discrete differential geometry.

The look of geometric models for object shapes, in particular, is occasionally called computer-aided geometric design (CAGD).

A software package refers to computer software packaged in an archive format to be installed by a package management system or a self-sufficient installer.

Linux based operating systems are normally segmented into packages. Each package contains a specific application or service. Examples of packages include a library for handling the PNG image format, a collection of fonts, or a web browser.

The package is typically provided as compiled code, with installation and removal of packages handled by a package management system (PMS) rather than a simple file archiver. Each package intended for such a PMS contains meta-information such as a package description, version, and "dependencies". The package management system can evaluate this meta-information to allow package searches, to perform an automatic upgrade to a newer version, to check that all dependencies of a package are fulfilled and/or to fulfill them automatically.

3.2 Computer aided design

HRV System Design

Using the latest Computer Aided Design package we offer a complete design service to ensure that our services are completely integrated into your building.

As with all of our installations we follow all of the relevant guidelines & regulations.

Equipment Sales

Our "Plug and Play" approach to Heat Recovery Ventilation ensures that our ventilation systems can be installed from start to finish by any competent person.

Duct Installation

Our installation teams are available to carry out 1st fix duct installations nationwide. We are C2 Registered and Fully Insured and we offer a professional and efficient service.

HRV Unit Installation & System Commissioning

Our technicians are trained in-house to the highest standards & will explain the day-to-day operation of the Quality HRV System.

HRV System Maintenance

Quality HRV systems have been designed so the homeowner can carry out the following maintenance:

• Quarterly • Annual • Bi-Annual• Contract option available for all installations.

Indoor Air Quality Consultation Services

We can provide monitoring equipment with data logging to report on indoor air quality.

Computer-aided design (CAD), also known as computer-aided design and drafting (CADD) , is the use of computer technology for the process of design and design-documentation. Computer Aided Drafting describes the process of drafting with a computer. CADD software, or environments, provides the user with input-tools for the purpose of streamlining design processes; drafting, documentation, and manufacturing processes. CADD output is often in the form of electronic files for print or machining operations. The development of CADD-based software is in direct correlation with the processes it seeks to economize; industry-based software (construction, manufacturing, etc.) typically uses vector-based (linear) environments whereas graphic-based software utilizes raster-based (pixelated) environments.

CADD environments often involve more than just shapes. As in the manual drafting of technical and engineering drawings, the output of CAD must convey information, such as materials, processes, dimensions, and tolerances, according to application-specific conventions.

CAD may be used to design curves and figures in two-dimensional (2D) space; or curves, surfaces, and solids in three-dimensional (3D) objects.

CAD is an important industrial art extensively used in many applications, including automotive, shipbuilding, and aerospace industries, industrial and architectural design, prosthetics, and many more. CAD is also widely used to produce computer animation for special effects in movies, advertising and technical manuals. The modern ubiquity and power of computers means that even perfume bottles and shampoo dispensers are designed using techniques unheard of by engineers of the 1960s. Because of its enormous economic importance, CAD has been a major driving force for research in computational geometry, computer graphics (both hardware and software), and discrete differential geometry

The design of geometric models for object shapes, in particular, is occasionally called computer-aided geometric design (CAGD)

Beginning in the 1980s Computer-Aided Design programs reduced the need of draftsmen significantly, especially in small to mid-sized companies. Their affordability and ability to run on personal computers also allowed engineers to do their own drafting work, eliminating the need for entire departments. In today's world most, if not all, students in universities do not learn drafting techniques because they are not required to do so. The days of hand drawing for final drawings are almost obsolete. Universities no longer require the use of protractors and compasses to create drawings, instead there are several classes that focus on the use of CAD software such as Pro Engineer or IEAS-MS.

Current computer-aided design software packages range from 2D vector-based drafting systems to 3D solid and surface modellers. Modern CAD packages can also frequently allow rotations in three dimensions, allowing viewing of a designed object from any desired angle, even from the inside looking out. Some CAD software is capable of dynamic mathematic modeling, in which case it may be marketed as CADD — computer-aided design and drafting.

CAD is used in the design of tools and machinery and in the drafting and design of all types of buildings, from small residential types (houses) to the largest commercial and industrial structures (hospitals and factories).

CAD is mainly used for detailed engineering of 3D models and/or 2D drawings of physical components, but it is also used throughout the engineering process from conceptual design and layout of products, through strength and dynamic analysis of assemblies to definition of manufacturing methods of components. It can also be used to design objects.

CAD has become an especially important technology within the scope of computer-aided technologies, with benefits such as lower product development costs and a greatly shortened design cycle. CAD enables designers to lay out and develop work on screen, print it out and save it for future editing, saving time on their drawings.

3.3Uses

CAD is one part of the whole Digital Product Development (DPD) activity within the Product Lifecycle Management (PLM) process, and as such is used together with other tools, which are either integrated modules or stand-alone products, such as:

• Computer-aided engineering (CAE) and Finite element analysis (FEA)• Computer-aided manufacturing (CAM) including instructions to Computer

Numerical Control (CNC) machines• Photo realistic rendering

• Document management and revision control using Product Data Management (PDM).

CAD is also used for the accurate creation of photo simulations that are often required in the preparation of Environmental Impact Reports, in which computer-aided designs of intended buildings are superimposed into photographs of existing environments to represent what that locale will be like were the proposed facilities allowed to be built. Potential blockage of view corridors and shadow studies are also frequently analyzed through the use of CAD..

CAD has also has been proven to be usefull to engineers as well. Using four properties which are history, features, parameterization, and high level constraints (Zhang). The construction history can be used to look back into the model's personal features and work on the single area rather than the whole model (zhang). Parameters and constraints can be used to determine the size, shape, and the different modeling elements. The features in the CAD system can be used for the variety of tools for measurement such as tensile strength, yeild strength, also its stress and strain and how the element gets affected in certain temperatures.

CAD is used to design and develop products, such as buildings, bridges, highways and interstates, aircraft, ships, automobiles, digital cameras, mobile phones, TVs, clothes, shoes, and computers, just to name a few. In addition, CAD is used throughout the engineering process from theoretical design and layout, detailed engineering and examination of components to definition of manufacturing methods in the following fields: Architecture, Industrial Design, Engineering, Garden design, and Construction Building engineering, Mechanical (Mechanical Computer Aided Design), Automotive Aerospace, Consumer Goods, Machinery, Ship Building, Electronic and Electrical (Electronic Computer-Aided Design), Manufacturing process planning, Digital circuit design, Software applications, Apparel and Textile CAD.

In the field of architecture, the software package may create results in numerous formats, however, they generally provide a graphically based result that can be used to produce concept sketches used for assessments and approvals, and finally working drawings.

Computer-aided drafting often refers to the actual technical drawing element of the project, which uses a computer instead of the traditional drawing board of years gone by. The input of the design process may derive from specialized calculation packages, pre-existing component drawings, graphical images such as maps, photos and other media, or simply from hand-drawn sketches created by the designer. It is the operator's job to use the CAD software in order to mend all the components together to produce drawings and specifications that can later be used to estimate the amounts of materials needed to construct the product as well as the estimated cost of the project, and ultimately provide the detailed drawings necessary to actually produce the product.

Computer-aided drafting software is also used in Civil Engineering for site design, roads, grading and drainage, mapping and cartography. It is also used in the production

surveyor's plans and legal descriptions of land, and as the input format to geographic and facilities information systems. In addition, many landscape architecture and interior designers are also using CAD software so that they can present a detailed visual design to their customers of precisely what the project will look like upon completion. This can include such items as dcor, paint color, furniture, as well as 3D images of the landscape and surrounding buildings.

3.4 Types

There are several different types of CAD . Each of these different types of CAD systems require the operator to think differently about how he or she will use them and he or she must design their virtual components in a different manner for each.

There are many producers of the lower-end 2D systems, including a number of free and open source programs. These provide an approach to the drawing process without all the fuss over scale and placement on the drawing sheet that accompanied hand drafting, since these can be adjusted as required during the creation of the final draft.

3D wireframe is basically an extension of 2D drafting (not often used today). Each line has to be manually inserted into the drawing. The final product has no mass properties associated with it and cannot have features directly added to it, such as holes. The operator approaches these in a similar fashion to the 2D systems, although many 3D systems allow using the wireframe model to make the final engineering drawing views.

3D "dumb" solids are created in a way analogous to manipulations of real world objects (not often used today). Basic three-dimensional geometric forms (prisms, cylinders, spheres, and so on) have solid volumes added or subtracted from them, as if assembling or cutting real-world objects. Two-dimensional projected views can easily be generated from the models. Basic 3D solids don't usually include tools to easily allow motion of components, set limits to their motion, or identify interference between components.

3D parametric solid modeling require the operator to use what is referred to as "design intent". The objects and features created are adjustable. Any future modifications will be simple, difficult, or nearly impossible, depending on how the original part was created. One must think of this as being a "perfect world" representation of the component. If a feature was intended to be located from the center of the part, the operator needs to locate it from the center of the model, not, perhaps, from a more convenient edge or an arbitrary point, as he could when using "dumb" solids. Parametric solids require the operator to consider the consequences of his actions carefully.

Some software packages provide the ability to edit parametric and non-parametric geometry without the need to understand or undo the design intent history of the geometry by use of direct modeling functionality. This ability may also include the additional ability to infer the correct relationships between selected geometry (e.g., tangency, concentricity) which makes the editing process less time and labor intensive

while still freeing the engineer from the burden of understanding the model’s. These kind of non history based systems are called Explicit Modellers or Direct CAD Modelers.

Top end systems offer the capabilities to incorporate more organic, aesthetics and ergonomic features into designs. Freeform surface modelling is often combined with solids to allow the designer to create products that fit the human form and visual requirements as well as they interface with the machine.

Technical drawing, also known as drafting or draughting, is the act and discipline of composing plans that visually communicate how something functions or is to be constructed.

A drafter, draftsperson, or draughtsman is a person who makes a drawing (technical or otherwise). A professional drafter who makes technical drawings is sometimes called a drafting technician.

People who communicate with technical drawings may use technical standards that define practical symbols, perspectives, units of measurement, notation systems, visual styles, or layout conventions. These enable a drafter to communicate more concisely by using a commonly-understood convention. Together, such conventions constitute a visual language, and help to ensure that the drawing is unambiguous and relatively easy to understand.

This need for unambiguous communication in the preparation of a functional document distinguishes technical drawing from the expressive drawing of the visual arts. Artistic drawings are subjectively interpreted; their meanings are multiply determined. Technical drawings are understood to have one intended meaning.

The basic drafting procedure is to place a piece of paper (or other material) on a smooth surface with right-angle corners and straight sides—typically a drawing board. A sliding straightedge known as a T-square is then placed on one of the sides, allowing it to be slid across the side of the table, and over the surface of the paper.

"Parallel lines" can be drawn simply by moving the T-square and running a pencil or technical pen along the T-square's edge, but more typically the T-square is used as a tool to hold other devices such as set squares or triangles. In this case the drafter places one or more triangles of known angles on the T-square—which is itself at right angles to the edge of the table—and can then draw lines at any chosen angle to others on the page. Modern drafting tables (which have by now largely been replaced by CAD workstations) come equipped with a drafting machine that is supported on both sides of the table to slide over a large piece of paper. Because it is secured on both sides, lines drawn along the edge are guaranteed to be parallel.

In addition, the drafter uses several tools to draw curves and circles. Primary among these are the compasses, used for drawing simple arcs and circles, and the French curve,

typically a piece of plastic with complex curves on it. A spline is a rubber coated articulated metal that can be manually bent to most curves.

Drafting templates assist the drafter with creating recurring objects in a drawing without having to reproduce the object from scratch every time. This is especially useful when using common symbols; i.e. in the context of stagecraft, a lighting designer will typically draw from the USITT standard library of lighting fixture symbols to indicate the position of a common fixture across multiple positions. Templates are sold commercially by a number of vendors, usually customized to a specific task, but it is also not uncommon for a drafter to create their own templates.

This basic drafting system requires an accurate table and constant attention to the positioning of the tools. A common error is to allow the triangles to push the top of the T-square down slightly, thereby throwing off all angles. Even tasks as simple as drawing two angled lines meeting at a point require a number of moves of the T-square and triangles, and in general drafting can be a time consuming process.

A solution to these problems was the introduction of the mechanical "drafting machine", an application of the pantograph (sometimes referred to incorrectly as a "pentagraph" in these situations) which allowed the drafter to have an accurate right angle at any point on the page quite quickly. These machines often included the ability to change the angle, thereby removing the need for the triangles as well.

In addition to the mastery of the mechanics of drawing lines, arcs and circles (and text) onto a piece of paper—with respect to the detailing of physical objects—the drafting effort requires a thorough understanding of geometry, trigonometry and spatial comprehension, and in all cases demands precision and accuracy, and attention to detail of high order.

Although drafting is sometimes accomplished by a project engineer, architect—or even by shop personnel such as a machinist—skilled drafters (and/or designers) usually accomplish the task and are always in demand to some level.

3.5 Technology

Originally software for Computer-Aided Design systems was developed with computer languages such as Fortran, but with the advancement of object-oriented programming methods this has radically changed. Typical modern parametric feature based modeler and freeform surface systems are built around a number of key C modules with their own APIs. A CAD system can be seen as built up from the interaction of a graphical user interface (GUI) with NURBS geometry and/or boundary representation (B-rep) data via a geometric modeling kernel. A geometry constraint engine may also be employed to manage the associative relationships between geometry, such as wireframe geometry in a sketch or components in an assembly.

Unexpected capabilities of these associative relationships have led to a new form of prototyping called digital prototyping. In contrast to physical prototypes, which entail manufacturing time in the design.

Today, CAD systems exist for all the major platforms (Windows, Linux, UNIX and Mac OS X); some packages even support multiple platforms.

Right now, no special hardware is required for most CAD software. However, some CAD systems can do graphically and computationally expensive tasks, so a good graphics card, high speed (and possibly multiple) CPUs and large amounts of RAM are recommended.

The human-machine interface is generally via a computer mouse but can also be via a pen and digitizing graphics tablet. Manipulation of the view of the model on the screen is also sometimes done with the use of a Spacemouse/SpaceBall. Some systems also support stereoscopic glasses for viewing the 3D model.

Designers have long used computers for their calculations. Initial developments were carried out in the 1960s within the aircraft and automotive industries in the area of 3D surface construction and NC programming, most of it independent of one another and often not publicly published until much later. Some of the mathematical description work on curves was developed in the early 1940s by Robert Issac Newton from Pawtucket, Rhode Island. Robert A. Heinlein in his 1957 novel The Door into Summer suggested the possibility of a robotic Drafting Dan. However, probably the most important work on polynomial curves and sculptured surface was done by Pierre Bezier (Renault), Paul de Casteljau (Citroen), Steven Anson Coons (MIT, Ford), James Ferguson (Boeing), Carl de Boor (GM), Birkhoff (GM) and Garibedian (GM) in the 1960s and W. Gordon (GM) and R. Riesenfeld in the 1970s.

It is argued that a turning point was the development of the SKETCHPAD system at MIT in 1963 by Ivan Sutherland (who later created a graphics technology company with Dr. David Evans). The distinctive feature of SKETCHPAD was that it allowed the designer to interact with his computer graphically: the design can be fed into the computer by drawing on a CRT monitor with a light pen. Effectively, it was a prototype of graphical user interface, an indispensable feature of modern CAD.

The first commercial applications of CAD were in large companies in the automotive and aerospace industries, as well as in electronics. Only large corporations could afford the computers capable of performing the calculations. Notable company projects were at GM (Dr. Patrick J.Hanratty) with DAC-1 (Design Augmented by Computer) 1964; Lockheed projects; Bell GRAPHIC 1 and at Renault (Bezier) – UNISURF 1971 car body design and tooling.

One of the most influential events in the development of CAD was the founding of MCS (Manufacturing and Consulting Services Inc.) in 1971 by Dr. P. J. Hanratty,[11] who wrote the system ADAM (Automated Drafting And Machining) but more importantly supplied

code to companies such as McDonnell Douglas (Unigraphics), Computervision (CADDS), Calma, Gerber, Autotrol and Control Data.

As computers became more affordable, the application areas have gradually expanded. The development of CAD software for personal desktop computers was the impetus for almost universal application in all areas of construction.

Other key points in the 1960s and 1970s would be the foundation of CAD systems United Computing, Intergraph, IBM, Intergraph IGDS in 1974 (which led to Bentley Systems MicroStation in 1984)

CAD implementations have evolved dramatically since then. Initially, with 3D in the 1970s, it was typically limited to producing drawings similar to hand-drafted drawings. Advances in programming and computer hardware, notably solid modeling in the 1980s, have allowed more versatile applications of computers in design activities.

Key products for 1981 were the solid modelling packages -Romulus (ShapeData) and Uni-Solid (Unigraphics) based on PADL-2 and the release of the surface modeler CATIA (Dassault Systemes). Autodesk was founded 1982 by John Walker, which led to the 2D system AutoCAD. The next milestone was the release of Pro/ENGINEER in 1988, which heralded greater usage of feature-based modeling methods and parametric linking of the parameters of features. Also of importance to the development of CAD was the development of the B-rep solid modeling kernels (engines for manipulating geometrically and topologically consistent 3D objects) Parasolid (ShapeData) and ACIS (Spatial Technology Inc.) at the end of the 1980s and beginning of the 1990s, both inspired by the work of Ian Braid. This led to the release of mid-range packages such as SolidWorks in 1995, Solid Edge (then Intergraph) in 1996 and Autodesk Inventor in 1999.

Technology CAD (or Technology Computer Aided Design, or TCAD) is a branch of electronic design automation that models semiconductor fabrication and semiconductor device operation. The modeling of the fabrication is termed Process TCAD, while the modeling of the device operation is termed Device TCAD. Included are the modelling of process steps (such as diffusion and ion implantation), and modelling of the behavior of the electrical devices based on fundamental physics, such as the doping profiles of the devices. TCAD may also include the creation of compact models (such as the well known SPICE transistor models), which try to capture the electrical behavior of such devices but do not generally derive them from the underlying physics. (However, the SPICE simulator itself is usually considered as part of ECAD rather than TCAD.)

From the diagram on the right:

• See SPICE for an example of a circuit simulator• See semiconductor device modeling for a description of modeling devices from

dopant profiles.• See semiconductor process simulation for the generation of these profiles• See BACPAC for an analysis tool that tries to take all of these into account to

estimate system performance

Glossary:

AOMArchive Object Management - involves organizing large data troves

AECO PLMArchitecture, Engineering, Construction, Operations, Plant Lifecycle Management

BOMBill Of Materials - This software stores the bill of materials of a product type as well as that of a specific instance of a product type. It can also store and manage configuration information giving, for example, all of the possible and/or permissible combinations of parts that could go to make up a specific product. The border between PDM and BOM is not entirely clear, but BOMs generally do not have design data beyond permissible configuration data, and PDMs generally do not hold the parts list for a specific instance of a product.

BPMBusiness Process Management

CAD

Computer-Aided Design - Interactive computer graphics applications that enable users to create geometry accurately both as to-scale 2D illustrations and 3D digital models

CAEComputer-Aided Engineering (Digital Product Simulation) - This acronym has traditionally been associated with software that does engineering calculations including simulations of the performance of parts, machines and systems according to the physics and/or chemistry of what they do and their environment.

CAMComputer-Aided Manufacturing - This acronym has traditionally been associated with NC (or numerical control) and refers to systems that create machining codes that cause NC machine tools to create a part from a digital model of its geometry

CFDComputational Fluid Dynamics

DMPMDigital Manufacturing Process Management describes software that simulates and/or optimizes the manufacturing process, including robot programming, process planning, and assembly line balancing.

DMSDocument Management Solutions (or DM, Document Management)

DMUDigital Mock Up

DPSDigital Prototyping and Simulation

ECMEnterprise Content Management

EDMEnterprise Data Management

EPCEngineering, Procurement, Construction

ERPEnterprise Resource Planning, (or supply chain software)

ESMEngineering Simulation Management is software that manages all the product and component simulation information on an enterprise-wide basis.

GISGeographic Information Systems

ILMInformation Lifecycle Management

ITInformation Technology

MPMManufacturing Process Management

M&OMaintenance and Operations

MVP

digital Mock-up, Visualization and 3D PublishingNVH

Noise, Vibration and HarshnessOO

Owner/OperatorP&ID

Process and Instrumentation DiagramsPDM

Product Data Management is data management software specifically designed to store and manage product design and manufacturing information including product configuration information.

PIMProduct information management

PLMProduct Lifecycle Management is a vision and philosophy that seeks to transform the way discrete and process manufacturers do business. PLM promises many benefits including faster time to market, better quality products, and lower manufacturing costs. For their part, PLM suppliers offer powerful, feature-rich software packages designed to achieve these benefits. This software includes CAD, CAM, CAE, DMPM, PDM, ESM, and BOM. Indeed the software solutions offered to facilitate PLM are continuing to multiply and evolve. The principal method whereby PLM achieves its benefits is by catalyzing better collaboration between all disciplines, departments, divisions, and the supply chain of a manufacturing enterprise by capturing information at the point of creation and distributing it to all that can benefit from it in a form they can understand and at a time when most needed.

ROIReturn On Investment

SBDSimulation-Based Design

VPDVirtual Product Development

Check your progress:1. Explain Computer aided design2. Explain Uses of CAD3. Explain Types of CAD

Reference:

1. ^ Carlo Rovelli (2004). Quantum Gravity. Cambridge University Press. p. 98 ff. ISBN 0521837332.

2. ^ William Barker & Roger Howe (2008). Continuous symmetry: from Euclid to Klein. American Mathematical Society. p. 18 ff. ISBN 0821839004.

3. ^ Arlan Ramsay & Robert D. Richtmyer (1995). Introduction to Hyperbolic Geometry. Springer. p. 11. ISBN 0387943390.

4. ^ According to Hawking and Ellis: "A manifold is a space locally similar to Euclidean space in that it can be covered by coordinate patches. This structure allows differentiation to be defined, but does not distinguish between different coordinate systems. Thus, the only concepts defined by the manifold structure are those that are independent of the choice of a coordinate system." Stephen W. Hawking & George Francis Rayner Ellis (1973). The Large Scale Structure of Space-Time. Cambridge University Press. p. 11. ISBN 0521099064. A mathematical definition is: A connected Hausdorff space M is called an n-dimensional manifold if each point of M is contained in an open set that is homeomorphic to an open set in Euclidean n-dimensional space.

5. ^ Shigeyuki Morita, Teruko Nagase, Katsumi Nomizu (2001). Geometry of Differential Forms. American Mathematical Society Bookstore. p. 12. ISBN 0821810456.

6. ^ Granino Arthur Korn, Theresa M. Korn (2000). Mathematical handbook for scientists and engineers : definitions, theorems, and formulas for reference and review. Courier Dover Publications. p. 169. ISBN 0486411478.

7. ^ See Encarta definition. Archived 2009-10-31.8. ^ Katsu Yamane (2004). Simulating and Generating Motions of Human Figures.

Springer. pp. 12–13. ISBN 3540203176.9. ^ Achilleus Papapetrou (1974). Lectures on General Relativity. Springer. p. 5.

ISBN 9027705402.10. ^ Wilford Zdunkowski & Andreas Bott (2003). Dynamics of the Atmosphere.

Cambridge University Press. p. 84. ISBN 052100666X.11. ^ A. I. Borisenko, I. E. Tarapov, Richard A. Silverman (1979). Vector and Tensor

Analysis with Applications. Courier Dover Publications. p. 86. ISBN 0486638332.12. ^ See Arvind Kumar & Shrish Barve (2003). How and Why in Basic Mechanics.

Orient Longman. p. 115. ISBN 8173714207.13. ^ Chris Doran & Anthony Lasenby (2003). Geometric Algebra for Physicists.

Cambridge University Press. p. §5.2.2, p. 133. ISBN 978-0-521-71595-9..14. ^ For example, Møller states: "Instead of Cartesian coordinates we can obviously

just as well employ general curvilinear coordinates for the fixation of points in physical space.…we shall now introduce general "curvilinear" coordinates xi in four-space…." C. Møller (1952). The Theory of Relativity. Oxford University Press. p. 222 and p. 233.

Check your progress answers

1. Refer 3.22. Refer 3.33. Refer 3.4

Unit 4: Applications of Space Frames

4.1 Introduction4.2 Objectives4.3 Methodology4.4 Confidentially4.5 Advantages of space frame structures4.6 Description of space frame systems4.7 Design4.8 Vertical loads4.9 Applications4.10 Design methods

4.1 Introduction

This report examines vehicle body construction in the automotive industry. It focuses on the emergence of spaceframes and the potential impact on vehicle manufacture and customer order fulfilment. Body construction today requires a high strength-to-weight ratio and rigidity, combined with cost effectiveness and ease of production. The welded steel monocoque has provided such a combination for volume production since the 1950’s. However, voluntary agreement with the EU on fuel efficiency savings which require lighter weight vehicles, increasingly competitive markets and rising environmental concern has forced vehicle manufacturers (VM’s) to reconsider current strategy. The questioning of mass production in favour of the adoption of JIT and Flexible Manufacturing Systems1 has been followed recently by significant levels of investment in alternative methods of alloy and composite body construction technology. This has resulted in a barrage of complex and confusing terminology, often used to describe similar design principles. This report aims to define the current state of body structure, and identify the implications for 3DayCar.

One of his newest projects is a residential skyscraper named 80 South Street after its own address, composed of 10 townhouses in the shape of cubes stacked on top of one another. The townhouses move up a main beam and follow a ladder-like pattern, providing each townhouse with its own roof. The "townhouse in the sky" design has attracted a high profile clientele, willing to pay the hefty US$30 million for each cube. It is planned to be built in New York City's financial district facing the East River. As of 2008 this project had been canceled; the Manhattan real estate market had gone soft, and none of the ten multi-million dollar townhouses had been sold.

He designed the approved (now cancelled) skyscraper, the Chicago Spire, in Chicago. Originally commissioned by Chicagoan Christopher Carley, Irish developer Garrett Kelleher purchased the building site for the project in July 2006 when Carley's financing plans fell through. Construction of the building began in August 2007 for completion in

2011. The Chicago Spire would have been the tallest building in North America. The project was later cancelled in early 2010.[2]

His work includes three bridges that will eventually span the Trinity River in Dallas. Construction of the first bridge (Margaret Hunt Hill Bridge), named after donor Margaret Hunt Hill, has been repeatedly delayed due to high costs, a fact that has sparked much controversy and criticism. If they are completed, Dallas will join the Dutch county of Haarlemmermeer in having three Calatrava bridges.

Calatrava's design for the Peace Bridge, a 130m pedestrian bridge to span the Bow River in downtown Calgary, Alberta, Canada, will cost approximately $24.5 million. The project was approved by city council in early January 2009 and is scheduled for completion in fall 2010. Public disclosure of Peace Bridge was made on 28 July 2009 to the public and praised as a sleek, elegant contribution to downtown Calgary. The design showed a sleek, tubular, single span red and white trestle, offering separate pathways for cyclists and pedestrians. The bridge is expected to serve 5,000 pedestrians and cyclists daily.

On 16 June 2009, it was announced that Calatrava would be designing the first building of the new University of South Florida Polytechnic campus in Lakeland Florida. This will be his first work in the southeastern United States.

4.2 Objectives

The following represent the prime objectives of this report:• To define the current state of spaceframe development in the context of European

and Global automotive manufacture.• To identify the key drivers of change in terms of automotive body construction

today and in relation to 3DayCar.• To compare the potential benefits to 3DayCar of the spaceframe over the welded

steel monocoque in terms of production flexibility and reducing customer order lead-time.

• To examine what impact the introduction of spaceframes might have in relation to current & future platform strategy and the implications for 3DayCar.

Space frame systems are three-dimensional structures which are constructed by connecting straight tubular struts to each others with the use of solid spherical hubs. Theese systems carry loads by axial forces. The conic parts are welded to the strut edges and the struts connecting by spherical hubs. .

Some of the advantages of space frames are described below:

• Because of the space frame systems are three-dimensional structures which work in two direction, for a large spans it provides economical solutions.

• İt is possible to cover spans until 100 m. without column by using space frame systems.

• They provide a great flexibility in the selection of support locations and allows to apply for different geometrical shapes / areas.

• The design / manufacture / installation process is completed in a very short interval due to the use of prefabricated components. İt gives a big opportunity to the customer to start his production

• Transporting to far distances is provided easily due to the use of prefabricated components.

• Space frame systems are lighter than traditional steel and reinforced concrete structures. Therefore, it provides significant economy in foundation costs.

• Space frame systems are the most useful structures for the earth-quake areas due to their light unit weight.

• İt is not nacessary to cover by hung ceilings because of its aesthetic appearance. • Additional structures to support the heating, ventilating, electrical and other

systems are not required for space frame structures. • Because of the aesthetic attribute, space frames are very suitable for glass or

policarbonate skylights. • İt provides various alternative solutions in architectural areas for complex

geometrical shapes (pyramid, triangle, dome, barrel vault e.t.c.)

4.3 Methodology

This report has been compiled from a combination of numerous e-mail exchanges, 10 telephone interviews, 4 site tours and an on-going review of current literature. A questionnaire was used initially to structure a number of interviews, but it was soon found that the limited number of respondents with direct experience of spaceframes favoured a broader approach to the study. The author is indebted to all those who provided much needed information on the subject and who freely offered their opinion. Industry publications such as Automotive News2 has filled a number of gaps and provided a sound background to the study. Where specific information was required, the author has endeavoured to approach the individual concerned. However, in an industry where technology is inherently aligned to competitive advantage, it was found that product development data, particularly costs, was very difficult to attain.

4.4Confidentiality

Whilst some of this report was produced using information freely available in journals and on the Internet, as a whole its contents should be considered confidential to 3DayCar. The author has been provided with specific details of VM product range and platform strategy and some discretion has been applied in deciding what should be included. Personal opinion from individuals, where appropriate and if permission has been granted, is recorded as such in the text; otherwise the outcome of any interview is generally reflected in the body of the report. The usual restrictions apply regarding access by companies or individuals outside the 3DayCar programme

4.5 ADVANTAGES OF SPACE FRAME STRUCTURES

• Structural solution that provides complete freedom in large span areas while providing strong resistance and economic efficiency.

• Demountable steel elements are light and easy to handle, and their assembly is safe and time saver.

• Providing column-free space, aesthetic appearances and spectacular qualities while offering flexibility and adaptability.

• Created a wide array of ultra-modern , functional and innovative designs while blending professional engineering experience with state of the art computer technology.

• Satisfying the needs of an extremely diverse range of clients demands from municipalities to aviation, from sport halls to shopping centers for their own specific project needs.

• Best fit to any structures with their outstanding and elegant designings while perfectly interfacing with any structures whether new or renovation works.

• Manufactured in sophistication and elegance with the specialy prepared corrosion resistant round tubes and spherical nodes that are available in spans up to 100 meters.

• Uses exclusive assembly methods and organized according to structural rules depending on deadline and the requests of the work owner.

• Ensuring the rigidity of materials, make up of elements able to transmit compression or tention forces and utilising advantage of 3-D structural behavior.

• Offers are prepared in detail and complete turnkey service from feasibility studies to preliminary/final/shop drawings and from simulation to installations.

4.6 DESCRIPTION OF SPACE FRAME SYSTEMS

Since its basic structure property comes from its rigid modularity; The type of the modules can also be in square, rectangular, triangular or hexagonal forms depending on the decision made during design stage in consideration of requirement of project along with its effectiveness in manufacturing , handling , and cost benefits together with its aesthetics.

Define Elements of Square Module:

a: Module Length in x-axis

b: Module Length in y-axis

h: Module depth / Ø : Module angles

4.7 DESIGN

POLARKON always takes into account in all aspects of architectural and structural properties of substructure where the space frame system with its superstructure and claddings are seated on. For this purpose; POLARKON aims to provide necessary cooperation with other design groups, in order to assure the best design parameters at the earlier design stage. To reach the architectural and functional requirements of the structure the best suitable modul type and size are closely analysed in finding new design alternatives.

When it is necessary, POLARKON also provides pre-structural analysis before design stage, and all reactions and displacements are reported to client for structural control of the substructure. The technical drawings showing dimensional properties of main supports , purlins, water drainage system, gutters, and claddings e.t.c. are also provided to the client depending on contract conditions.

The structural computer modelling can also be constituted after determination of all necessary data in respect of main geometrical form, modulation sizes,support points, and types including with horizontal and vertical for specified earthquake, and wind loads together with thermal loads.

Unless otherwise required by the client; POLARKON obeys the following criterias during the determination of load parameters.

4.8 Vertical Loads :

• Dead Loads : Space Frame own weight.• Snow Load : The values tabulated in TS-EN 498 are accepted as base standart

loading values. However POLARKON always accepts the values at least 50 pct more than standart values and stays in plus "safe side" in consideration of unusual conditions, like excessive snow, icy conditions, rain after snow and gusty conditions e.t.c..

• Purlins and Beams : Determined by POLARKON in according structural necessities.

• Cladding Material : In according to clients preferences.• Service Loads : Cat walks, any necessary installation for cabling , Air

conditioning, cooling, Heating, Ventilating,etc..

Horizontal Loads :

• Wind Load : Minimum loads specified in TS-EN 498 are taken as for standart application parameters.

• Earthquake : When the structural modelling is completed, geometry of the model is cross checked with the architectural drawings which are followed by structural analysis by using special methods particularly generated for space frame systems. The parameters are subject to structural analysis , calculations and assumptions conform with both national and international standart requirements in according to latest earthquake specifications.

Principles:

Space Structures are economical and aesthically pleasing in appearance. They provide a unique solution for covering large column free areas. This book gives a state of the art presentation of the analysis, design and construction of space structures. The author synthesizes data currently available with his original and exhaustive research to produce the definitive book on space structures.

Principal features and topics of the book include:

• Analysis, design and construction of various types of space structures• Nodes and jointing systems• Approximate methods of analysis• Concepts are explained through over 400 figures, 90 photographs and 35 tables• An extensive bibliography, over 1000 references in total

This book is appropriate for university level architecture / building science / civil engineering departmental libraries. Post graduate students and academics, as well as practising architects and engineers will find much of value in this comprehensive work.

4.9 Applications

Construction

Space frames are a common feature in modern construction; they are often found in large roof spans in modernist commercial and industrial buildings.

Notable examples of buildings based on space frames include:

• Stansted airport in London, by Foster and Partners• Bank of China Tower and the Louvre Pyramid, by I. M. Pei• Rogers Centre by Rod Robbie and Michael Allan• McCormick Place East in Chicago• Eden Project in Cornwall, England• Globen, Sweden - Dome with diameter of 110 m, (1989)

• Biosphere 2 in Oracle, Arizona

Large portable stages and lighting gantries are also frequently built from space frames and octet trusses.

In February 1986, Paul C. Kranz walked into the U. S. Department of Transportation office in Fort Worth, Texas, with a model of an octet truss. He showed a staff person there how the octet truss was ideal for holding signs over roads. The idea and model was forwarded to the US Department of Transportation in Washington, D. C. Today, the octet truss is the structure of choice for holding signs above roads in the United States.

Vehicles

Space frames are sometimes used in the chassis designs of automobiles and motorcycles. In a space-frame, or tube-frame, chassis, the suspension, engine, and body panels are attached to a skeletal space frame, and the body panels have little or no structural function. By contrast, in a monocoque design, the body serves as part of the structure. Tube-frame chassis are frequently used in certain types of racing cars.

British manufacturers TVR were particularly well known for their tube-frame chassis designs, produced since the 1950s. Other notable examples of tube-frame cars include the Audi A8, Lotus Seven, Ferrari 360, Lamborghini Gallardo, and Mercedes-Benz SLS AMG.

Space frames have also been used in bicycles, such as those designed by Alex Moulton.

4.10 Design methods

Space frames are typically designed using a rigidity matrix. The special characteristic of the stiffness matrix in an architectural space frame is the independence of the angular factors. If the joints are sufficiently rigid, the angular deflections can be neglected, simplifying the calculations.

Glossary:

command frame (CFRAME): A special DirectPlay 8 control frame that does not carry application payload data. For more information, see the DirectPlay 8 Protocol: Reliable Specification ([MC-DPL8R] section 2.2.1). See Also, data frame.

CRC-16-IBM algorithm: The CRC-16-IBM algorithm polynomial is x^16 + x^15 + x^2 + 1. Normal and reversed representations are "0x8005" or "0xA001".

data frame (DFRAME): A DirectPlay 8 frame that exists in the standard connection sequence space and typically carries application payload data. The total size of the

DFRAME header and payload should be less than the Maximum Transmission Unit (MTU) of the underlying protocols and network. For more information, see the DirectPlay 8 Protocol: Reliable Specification ([MC-DPL8R] section 2.2.2). See Also, command frame.

DXDiag application: See DirectX Diagnostic (DXDiag).

game session: The metadata associated with the collection of computers participating in a single instance of a computer game.

group: A collection of players within a game session. Typically, players are placed in a group when they serve a common purpose.

Note Groups are not supported by the DirectPlay DXDiag Usage Protocol.

instance: A specific occurrence of a game running in a game session. A game application process or module may be created more than one time on a single computer system, or on separate computer systems. Each time a game application process or module is created, the occurrence is considered to be a separate instance.

modem link (or modem transport): Running the DXDiag application over a modem-to-modem link. See Also, serial link.

name table entry: The DN_NAMETABLE_MEMBERSHIP_INFO structure along with associated strings and data buffers for an individual participant in the DXDiag session. These could be considered players.

next receive: The next 8-bit packet sequence ID expected to be received, indicating acknowledgment of all packets up to this ID. This is typically represented as a field named bNRcv in packet structures. See Also, next send.

next send: The next 8-bit packet sequence ID that will be sent. This is represented as bNSeq in the selective acknowledgment packet structure, which does not have a sequence ID of its own. DirectPlay 8 protocol implementations also keep an internal counter so that IDs can be assigned in order. See Also, Next Receive.

payload: The data that is transported to and from the application that is using either the DirectPlay 4 protocol or DirectPlay 8 protocol.

poll packet (POLL): A packet in which the sender has set the PACKET_COMMAND_POLL bit in the packet header. POLL indicates that the receiver must immediately acknowledge receipt of the packet when it arrives.

selective acknowledgment (SACK): A cumulative mechanism that indicates successful receipt of packets beyond the next receive indicator. Next receive reports all packets prior to when its sequence ID has been received, but subsequent packets may have

arrived out of order or with gaps in the sequence. SACK masks enable the receiver to acknowledge these packets so that they do not have to be retried, in addition to the packets that were truly lost. See Also, acknowledgment (ACK), next receive, and next send.

Check your progress:

1. Explain Objectives2. Explain Advantages of space frame structures3. Explain Application of frames

Reference:

1. ^ Vijay Duggal. "CADD Primer". Mailmax Publishing.2. ^ Farin, G.: A History of Curves and Surfaces in CAGD, Handbook of Computer Aided Geometric Design3. ^ H. Pottmann, S. Brell-Cokcan, and J. Wallner:Discrete surfaces for architectural design4. ^ Gerald Farin :Curves and Surfaces for CAGD: A Practical Guide5. ^ Jennifer Herron (2010). "3D Model-Based Design: Setting the Definitions Straight". MCADCafe.6. ^ "engineershandbook - Types of CAD".7. ^ "History of CAD/CAM". CADAZZ. 2004.8. ^ Pillers, Michelle (1998.03). "MCAD Renaissance of the 90's". Cadence Magazine.9. ^ Bozdoc, Martian. "The History of CAD". iMB.10. ^ Carlson, Wayne (2003). "A Critical History of Computer Graphics and Animation". Ohio State University.11. ^ "MCS Founder".

Check your progress answers

1. Refer 4.22. Refer 4.53. Refer 4.9

BLOCK 5 Special Methods

Special education is the education of students with special needs in a way that addresses the students' individual differences and needs. Ideally, this process involves the individually planned and systematically monitored arrangement of teaching procedures, adapted equipment and materials, accessible settings, and other interventions designed to help learners with special needs achieve a higher level of personal self-sufficiency and success in school and community than would be available if the student were only given access to a typical classroom education.

Common special needs include challenges with learning, communication challenges, emotional and behavioral disorders, physical disabilities, and developmental disorders.[1]

Students with these kinds of special needs are likely to benefit from additional educational services such as different approaches to teaching, use of technology, a specifically adapted teaching area, or resource room.

Intellectual giftedness is a difference in learning and can also benefit from specialized teaching techniques or different educational programs, but the term "special education" is generally used to specifically indicate instruction of students whose special needs reduce their ability to learn independently or in an ordinary classroom, and gifted education is handled separately.

In most developed countries, educators are modifying teaching methods and environments so that the maximum number of students are served in general education environments. Special education in developed countries is often regarded less as a "place" and more as "a range of services, available in every school."[2][3][4][5][6] Integration can reduce social stigmas and improve academic achievement for many students.[7]

The opposite of special education is general education. General education is the standard curriculum presented with standard teaching methods and without additional supports.

Unit 1: Introduction to Formex Algebra

1.1 Introduction1.2 Pricing models in search engine marketing

1.1 Introduction

The analysis of spaceframe structures has been greatly enhanced by the advent of the computer, whereby, the member forces and deflected shapes of structures consisting of perhaps several thousand members could be easily attempted. However, the ability to deal with large and complex structures has created a new problem. Namely, that of data generation. There are, of course, many analysis packages which have been evolved during the recent years to deal with the data generation problems. These packages do not, in general, provide a completely satisfactory answer. The concepts of formex algebra, on the other hand, may indeed provide a complete and universal solution for the problem.

The objectives of this paper are to outline the principles of formex algebra and its associated programming language, known as FORMIAN, and demonstrate the application of these in relation to the analysis of a number of spaceframe structures. Of necessity, the introduction to formex algebra has to be brief and a knowledge of the subject in the actual formulation of the problems, especially in the latter part of the paper is presumed.

Space Structures are economical and aesthetically pleasing in appearance. They provide a unique solution for covering large column free areas. This book gives a state of the art presentation of the analysis, design and construction of space structures. The author synthesizes data currently available with his original and exhaustive research to produce the definitive book on space structures.

Principal features and topics of the book include:

- Analysis, design and construction of various types of space structures - Nodes and jointing systems - Approximate methods of analysis - Concepts are explained through over 400 figures, 90 photographs and 35 tables - An extensive bibliography, over 1000 references in total

Identifying students with special needs

Some children are easily identified as candidates for special needs from their medical history. They may have been diagnosed with a genetic condition that is associated with

mental retardation, may have various forms of brain damage, may have a developmental disorder, may have visual or hearing disabilities, or other disabilities.

Among students whose identification is less obvious, such as students with learning difficulties, two primary methods have been used for identifying them: the discrepancy model and the response to intervention model. The discrepancy model depends on the teacher noticing that the students' achievements are noticeably below what is expected. The response to intervention model advocates earlier intervention.

In the discrepancy model, a student receives special educational services for a specific learning difficulty (SLD) if and only if the student has at least normal intelligence and the student's academic achievement is below what is expected of a student with his or her IQ. Although the discrepancy model has dominated the school system for many years, there has been substantial criticism of this approach (e.g., Aaron, 1995, Flanagan and Mascolo, 2005) among researchers. One reason for criticism is that diagnosing SLDs on the basis of the discrepancy between achievement and IQ does not predict the effectiveness of treatment. Low academic achievers who also have low IQ appear to benefit from treatment just as much as low academic achievers who have normal or high intelligence.

The alternative approach, response to intervention, identifies children who are having difficulties in school in their first or second year after starting school. They then receive additional assistance such as participating in a reading remediation program. The response of the children to this intervention then determines whether they are designated as having a learning disability. Those few who still have trouble may then receive designation and further assistance. Sternberg (1999) has argued that early remediation can greatly reduce the number of children meeting diagnostic criteria for learning disabilities. He has also suggested that the focus on learning disabilities and the provision of accommodations in school fails to acknowledge that people have a range of strengths and weaknesses and places undue emphasis on academics by insisting that people should be propped up in this arena and not in music or sports.

Individual needs

A special education program should be customized to address each individual student's unique needs. Special educators provide a continuum of services, in which students with special needs receive services in varying degrees based on their individual needs. Special education programs need to be individualized so that they address the unique combination of needs in a given student.

In the United States, Canada, and the UK, educational professionals used the initialism IEP when referring to a student’s individualized education plan.

Students with special needs are assessed to determine their specific strengths and weaknesses. Placement, resources, and goals are determined on the basis of the student's needs. Accommodations and Modifications to the regular program may include changes in curriculum, supplementary aides or equipment, and the provision of specialized

physical adaptations that allow students to participate in the educational environment to the fullest extent possible.[9] Students may need this help to access subject matter, to physically gain access to the school, or to meet their emotional needs. For example, if the assessment determines that the student cannot write by hand because of a physical disability, then the school might provide a computer for typing assignments, or allow the student to answer questions orally instead. If the school determines that the student is severely distracted by the normal activities in a large, busy classroom, then the student might be placed in a smaller classroom such as a resource room.

Methods of provision

Schools use different approaches to providing special education services to identified students. These can be broadly grouped into four categories, according to whether and how much contact the student with special needs has with non-disabled students (using North American terminology):

• Inclusion: In this approach, students with special educational needs spend all, or at least more than half, of the school day with students who do not have special educational needs. Because inclusion can require substantial modification of the general curriculum, most schools use it only for selected students with mild to moderate special needs, for which is accepted as a best practice.[10][11] Specialized services may be provided inside or outside the regular classroom, depending on the type of service. Students may occasionally leave the regular classroom to attend smaller, more intensive instructional sessions in a resource room, or to receive other related services that might require specialized equipment or might be disruptive to the rest of the class, such as speech and language therapy, occupational therapy, physical therapy, or might require greater privacy, such as counseling sessions with a social worker.[12]

• Mainstreaming refers to the practice of educating students with special needs in classes with non-disabled students during specific time periods based on their skills. Students with special needs are segregated in separate classes exclusively for students with special needs for the rest of the school day.[13]

• Segregation in a self-contained classroom or special school: In this model, students with special needs spend no time in classes with non-disabled students. Segregated students may attend the same school where regular classes are provided, but spend their time exclusively in a separate classroom for students with special needs. If their special class is located in an ordinary school, they may be provided opportunities for social integration outside the classroom, e.g., by eating meals with non-disabled students.[14] Alternatively, these students may attend a special school.[13]

• Exclusion: A student who does not receive instruction in any school is excluded from school. Historically, most students with special needs have been excluded from school,[15] and such exclusion may still occur where there is no legal mandate for special education services, such as in developing countries. It may also occur when a student is in hospital,[13] housebound,[13] or detained by the criminal justice system.[citation needed] These students may receive one-on-one

instruction or group instruction. Students who have been suspended or expelled are not considered excluded in this sense.

Instructional strategies

Different instructional techniques are used for some students with special educational needs. Instructional strategies are classified as being either accommodations or modifications.

An accommodation is a reasonable adjustment to teaching practices so that the student learns the same material, but in a format that is accessible to the student. Accommodations may be classified by whether they change the presentation, response, setting, or scheduling.[16] For example, the school may accommodate a student with visual impairments by providing a large-print textbook; this is a presentation accommodation.

A modification changes or adapts the material to make it simpler.[17] Modifications may change what is learned, how difficult the material is, what level of mastery the student is expected to achieve, whether and how the student is assessed, or any another aspect of the curriculum. For example, the school may modify a reading assignment for a student with reading difficulties by substituting a shorter, easier book. A student may receive both accommodations and modifications.

Issues

At-risk students (those with educational needs that are not associated with a disability) are often placed in classes with students who have disabilities. Critics assert that placing at-risk students in the same classes as students with disabilities may impede the educational progress of people with disabilities.[22] Some special education classes have been criticized for a watered-down curriculum.[23]

The practice of inclusion (in mainstream classrooms) has been criticized by advocates and some parents of children with special needs because some of these students require instructional methods that differ dramatically from typical classroom methods. Critics assert that it is not possible to deliver effectively two or more very different instructional methods in the same classroom. As a result, the educational progress of students who depend on different instructional methods to learn often fall even further behind their peers.[24]

Parents of typically developing children sometimes fear that the special needs of a single "fully included" student will take critical levels of attention and energy away from the rest of the class and thereby impair the academic achievements of all students.[24]

Some parents, advocates, and students have concerns about the eligibility criteria and their application. In some cases, parents and students protest the students' placement into special education programs. For example, a student may be placed into the special education programs due to a mental health condition such as obsessive compulsive

disorder, depression, anxiety, panic attacks or ADHD, while the student and his parents believe that the condition is adequately managed through medication and outside therapy. In other cases, students whose parents believe they require the additional support of special education services are denied participation in the program based on the eligibility criteria.[25]

Special CPA compensation models

Pay-per-call

Similar to pay per click, pay per call is a business model for ad listings in search engines and directories that allows publishers to charge local advertisers on a per-call basis for each lead (call) they generate (CPA). Advertiser pays publisher a commission for phone calls received from potential prospects as response to a specific publisher ad.

The term "pay per call" is sometimes confused with click-to-call, the technology that enables the “pay-per-call” business model. Call-tracking technology allows to create a bridge between online and offline advertising. Click-to-call is a service which lets users click a button or link and immediately speak with a customer service representative. The call can either be carried over VoIP, or the customer may request an immediate call back by entering their phone number. One significant benefit to click-to-call providers is that it allows companies to monitor when online visitors change from the website to a phone sales channel.

Pay-per-call is not just restricted to local advertisers. Many of the pay-per-call search engines allows advertisers with a national presence to create ads with local telephone numbers. Pay-per-call advertising is still new and in its infancy, but according to the Kelsey Group, the pay-per-phone-call market is expected to reach US$3.7 billion by 2010

Pay-per-install (PPI)

Advertiser pays publisher a commission for every install by a user of usually free applications bundled with adware applications. Users are prompted first if they really want to download and install this software. Pay per install is included in the definition for pay per action (like cost-per-acquisition), but its relationship to how adware is distributed made the use of this term versus pay per action more popular to distinguish it from other CPA offers that pay for software downloads. The term pay per install is being used beyond the download of adware[1].

Some botnets are known to operate PPI scams to generate money for their operators. Essentially, the compromised computer with the bot agent is instructed to install the software package from a registered PPI source via the bots command and control system. The bot operator then receives payment from the PPI agency and, after a short period of time, uninstalls the software package and installs a new one

1.2 Pricing models in search engine marketing

Pay-per-click (PPC)

Cost-per-click (CPC). Advertiser pays publisher a commission every time a visitor clicks on the advertiser's ad. It is irrelevant (for the compensation) how often an ad is displayed. commission is only due when the ad is clicked

Pay per action (PPA) or cost per action (CPA)

Cost-per-action (CPA). Used by display advertising as pricing mode as early as 1998 [3]. By mid-2007 the CPA/Performance pricing mode (50%) superseded the CPM pricing mode (45%) and became the dominant pricing mode for display advertising

Shared CPM

Shared Cost-per-mil (CPM) is a pricing model in which two or more advertisers share the same ad space for the duration of a single impression (or page view) in order to save CPM costs. Publishers offering a shared CPM pricing model generally offer a discount to compensate for the reduced exposure received by the advertisers that opt to share online ad space in this way. Inspired by the rotating billboards of outdoor advertising, the shared CPM pricing model can be implemented with either refresh scripts (client-side JavaScript) or specialized rich media ad units. Publishers that opt to offer a shared CPM pricing model with their existing ad management platforms must employ additional tracking methods to ensure accurate impression counting and separate click-through tracking for each advertiser that opts to share a particular ad space with one or more other advertisers.

Glossary:

Accommodations. Techniques and materials that allow individuals with LD to complete school or work tasks with greater ease and effectiveness. Examples include spellcheckers, tape recorders, and expanded time for completing assignments.

Assistive Technology. Equipment that enhances the ability of students and employees to be more efficient and successful. For individuals with LD, computer grammar checkers, an overhead projector used by a teacher, or the audiovisual information delivered through a CD-ROM would be typical examples.

Attention Deficit Disorder (ADD). A severe difficulty in focusing and maintaining attention. Often leads to learning and behavior problems at home, school, and work. Also called Attention Deficit Hyperactivity Disorder (ADHD).

Brain Imaging Techniques. Recently developed, noninvasive techniques for studying the activity of living brains. Includes brain electrical activity mapping (BEAM), computerized axial tomography (CAT), and magnetic resonance imaging (MRI).

Brain Injury. The physical damage to brain tissue or structure that occurs before, during, or after birth that is verified by EEG, MRI, CAT, or a similar examination, rather than by observation of performance. When caused by an accident, the damage may be called Traumatic Brain Injury (TBI).

Collaboration. A program model in which the LD teacher demonstrates for or team teaches with the general classroom teacher to help a student with LD be successful in a regular classroom.

Developmental Aphasia. A severe language disorder that is presumed to be due to brain injury rather than because of a developmental delay in the normal acquisition of language.

Direct Instruction. An instructional approach to academic subjects that emphasizes the use of carefully sequenced steps that include demonstration, modeling, guided practice, and independent application.

Dyscalculia. A severe difficulty in understanding and using symbols or functions needed for success in mathematics.

Dysgraphia. A severe difficulty in producing handwriting that is legible and written at an age-appropriate speed.

Dyslexia. A severe difficulty in understanding or using one or more areas of language, including listening, speaking, reading, writing, and spelling.

Dysnomia. A marked difficulty in remembering names or recalling words needed for oral or written language.

Dyspraxia. A severe difficulty in performing drawing, writing, buttoning, and other tasks requiring fine motor skill, or in sequencing the necessary movements.

Learned Helplessness. A tendency to be a passive learner who depends on others for decisions and guidance. In individuals with LD, continued struggle and failure can heighten this lack of self-confidence.

Learning Modalities. Approaches to assessment or instruction stressing the auditory, visual, or tactile avenues for learning that are dependent upon the individual.

Learning Strategy Approaches. Instructional approaches that focus on efficient ways to learn, rather than on curriculum. Includes specific techniques for organizing, actively interacting with material, memorizing, and monitoring any content or subject.

Learning Styles. Approaches to assessment or instruction emphasizing the variations in temperament, attitude, and preferred manner of tackling a task. Typically considered are styles along the active/passive, reflective/impulsive, or verbal/spatial dimensions.

Locus of Control. The tendency to attribute success and difficulties either to internal factors such as effort or to external factors such as chance. Individuals with learning disabilities tend to blame failure on themselves and achievement on luck, leading to frustration and passivity.

Metacognitive Learning. Instructional approaches emphasizing awareness of the cognitive processes that facilitate one's own learning and its application to academic and work assignments. Typical metacognitive techniques include systematic rehearsal of steps or conscious selection among strategies for completing a task.

Minimal Brain Dysfunction (MBD). A medical and psychological term originally used to refer to the learning difficulties that seemed to result from identified or presumed damage to the brain. Reflects a medical, rather than educational or vocational orientation.

Multisensory Learning. An instructional approach that combines auditory, visual, and tactile elements into a learning task. Tracing sandpaper numbers while saying a number fact aloud would be a multisensory learning activity.

Resource Program. A program model in which a student with LD is in a regular classroom for most of each day, but also receives regularly scheduled individual services in a specialized LD resource classroom.

Self-Advocacy. The development of specific skills and understandings that enable children and adults to explain their specific learning disabilities to others and cope positively with the attitudes of peers, parents, teachers, and employers.

Specific Language Disability (SLD). A severe difficulty in some aspect of listening, speaking, reading, writing, or spelling, while skills in the other areas are age-appropriate. Also called Specific Language Learning Disability (SLLD).

Specific Learning Disability (SLD). The official term used in federal legislation to refer to difficulty in certain areas of learning, rather than in all areas of learning. Synonymous with learning disabilities.

Subtype Research. A recently developed research method that seeks to identify characteristics that are common to specific groups within the larger population of individuals identified as having learning disabilities.

Check your progress1. Explain Formex Algebra2. Explain Pricing models in search marketing

Reference:

1. ^ What is special education? from New Zealand's Ministry of Education2. ^ National Council on Disability. (1994). Inclusionary education for students with special needs: Keeping the promise. Washington, DC: Author.3. ^ Swan, William W.; Morgan, Janet L (1993). "The Local Interagency Coordinating Council". Collaborating for Comprehensive Services for Young Children and Their Families. Baltimore: Paul H. Brookes Pub. Co.. ISBN 1557661030. OCLC 25628688. OL 4285012W .4. ^ Beverly Rainforth; York-Barr, Jennifer (1997). Collaborative Teams for Students With Severe Disabilities: Integrating Therapy and Educational Services. Brookes Publishing Company. ISBN 1-55766-291-6. OCLC 25025287.5. ^ Stainback, Susan Bray; Stainback, William C. (1996). Support Networks for Inclusive Schooling: Interdependent Integrated Education. Paul H Brookes Pub Co. ISBN 1-55766-041-7. OCLC 300624925. OL 2219710M .6. ^ Gaylord-Ross, Robert (1989). Integration strategies for students with handicaps. Baltimore: P.H. Brookes. ISBN 1-55766-010-7. OCLC 19130181.7. ^ Gartner, Alan; Dorothy Kerzner Lipsky (1997). Inclusion and School Reform: Transforming America's Classrooms. Brookes Publishing Company. ISBN 1-55766-273-8. OCLC 35848926.8. ^ a b Goodman, Libby (1990). Time and learning in the special education classroom. Albany, N.Y.: State University of New York Press. p. 122. ISBN 0-7914-0371-8. OCLC 20635959.9. ^ Special Education Inclusion10. ^ Smith P (October 2007). "Have we made any progress? Including students with intellectual disabilities in regular education classrooms". Intellect Dev Disabil 45 (5): 297–309. doi:10.1352/0047-6765(2007)45[297:HWMAPI]2.0.CO;2. PMID 17887907.11. ^ James Q. Affleck; Sally Madge, Abby Adams, Sheila Lowenbraun (1988-01). "Integrated classroom versus resource model: academic viability and effectiveness". Exceptional Children: 2. Retrieved 2010-05-29.

Check your progress answers

1. Refer 1.12. Refer 1.2

Unit 2: Application of Formex Algebra

2.1 Introduction

2.2 Methods2.3 Types

2.1 Introduction

A Formex is a numpy array of order 3 (axes 0,1,2) and type Float. A scalar element represents a coordinate (F:uniple).

A row along the axis 2 is a set of coordinates and represents a point (node, vertex, F: signet). For simplicity’s sake, the current implementation only deals with points in a 3-dimensional space. This means that the length of axis 2 is always 3. The user can create formices (plural of Formex) in a 2-D space, but internally these will be stored with 3 coordinates, by adding a third value 0. All operations work with 3-D coordinate sets. However, a method exists to extract only a limited set of coordinates from the results, permitting to return to a 2-D environment

A plane along the axes 2 and 1 is a set of points (F: cantle). This can be thought of as a geometrical shape (2 points form a line segment, 3 points make a triangle, ...) or as an element in FE terms. But it really is up to the user as to how this set of points is to be interpreted.

Finally, the whole Formex represents a set of such elements.

Additionally, a Formex may have a property set, which is an 1-D array of integers. The length of the array is equal to the length of axis 0 of the Formex data (i.e. the number of elements in the Formex). Thus, a single integer value may be attributed to each element. It is up to the user to define the use of this integer (e.g. it could be an index in a table of element property records). If a property set is defined, it will be copied together with the Formex data whenever copies of the Formex (or parts thereof) are made. Properties can be specified at creation time, and they can be set, modified or deleted at any time. Of course, the properties that are copied in an operation are those that exist at the time of performing the operation.

Radiation therapy is an effective treatment for pelvic malignancies.However, 2% to 5% of patients who receive radiation therapy for such a malignancy suffer from severe proctitis. The most troublesome symptom of the proctitis is chronic hemorrhage, and in many cases, repeated transfusions are required. Several materials have been used for the treatment of proctitis,and a 4% formalin solution has been used effectively worldwide for 20 years. However, there is still controversy surrounding the indications and methods involved in formalin therpay.The first formalin treatment for radiation-induced hemorrhagic proctitis (RIHP) in Korea was reported about 10 years ago, and involved a combined method of both formalin instillation and selective formalin application.Since then, however, reports regarding the use of formalin treatment of RIHP are rare in Korea. The aim of this study was to evaluate the therapy and outcome of the combined formalin application therapy since the first reported case in Korea.

Because the Formex class is derived from Geometry, the following Formex methods exist and return the value of the same method applied on the coords attribute: x, y, z, bbox, center, centroid, sizes, dsize, bsphere, distanceFromPlane, distanceFromLine, distanceFromPoint, directionalSize, directionalWidth, directionalExtremes, __str__. Refer to the correponding Coords method for their usage.

2.2 Methods

Also, the following Coords transformation methods can be directly applied to a Formex object or a derived class object. The return value is a new object identical to the original, except for the coordinates, which will have been transformed by the specified method. Refer to the correponding Coords method for the usage of these methods: scale, translate, rotate, shear, reflect, affine, cylindrical, hyperCylindrical, toCylindrical, spherical, superSpherical, toSpherical, bump, bump1, bump2, flare, map, map1, mapd, newmap, replace, swapAxes, rollAxes, projectOnSphere, projectOnCylinder, rot, trl.

element(i)

Return element i of the Formex

point(i, j)

Return point j of element i

coord(i, j, k)

Return coord k of point j of element i

nelems()

Return the number of elements in the formex.

nplex()

Return the number of points per element.

Examples:

1: unconnected points, 2: straight line elements, 3: triangles or quadratic line elements, 4: tetraeders or quadrilaterals or cubic line elements.

ndim()

Return the number of dimensions.

This is the number of coordinates for each point. In the current implementation this is always 3, though you can define 2D Formices by given only two coordinates: the third will automatically be set to zero.

npoints()

Return the number of points in the formex.

This is the product of the number of elements in the formex with the number of nodes per element.

shape()

Return the shape of the Formex.

The shape of a Formex is the shape of its data array, i.e. a tuple (nelems, nplex, ndim).

view()

Return the Formex coordinates as a numpy array (ndarray).

Since the ndarray object has a method view() returning a view on the ndarray, this method allows writing code that works with both Formex and ndarray instances. The results is always an ndarray.

getProp(index=None)

Return the property numbers of the element in index

maxProp()

Return the highest property value used, or None

propSet()

Return a list with unique property values on this Formex.

centroids()

Return the centroids of all elements of the Formex.

The centroid of an element is the point whose coordinates are the mean values of all points of the element. The return value is a Coords object with nelems points.

fuse(repeat=True, nodesperbox=1, rtol=1.0000000000000001e-05, atol=None)

Return a tuple of nodal coordinates and element connectivity.

A tuple of two arrays is returned. The first is float array with the coordinates of the unique nodes of the Formex. The second is an integer array with the node numbers connected by each element. The elements come in the same order as they are in the Formex, but the order of the nodes is unspecified. By the way, the reverse operation of coords,elems = fuse(F) is accomplished by F = Formex(coords[elems])

There is a (very small) probability that two very close nodes are not equivalenced by this procedure. Use it multiple times with different parameters to check. You can also set the rtol /atol parameters to influence the equivalence checking of two points. The default settting for atol is rtol * self.dsize()

toMesh(*args, **kargs)

Convert a Formex to a Mesh.

Converts a geometry in Formex model to the equivalent Mesh model. In the Mesh model, all points with nearly identical coordinates are fused into a single point, and elements are defined by a connectivity table with integers pointing to the corresponding vertex.

info()

Return formatted information about a Formex.

classmethod point2str(clas, point)

Return a string representation of a point

classmethod element2str(clas, elem)

Return a string representation of an element

asFormex()

Return string representation of a Formex as in Formian.

Coordinates are separated by commas, points are separated by semicolons and grouped between brackets, elements are separated by commas and grouped between braces:

>>> F = Formex([[[1,0],[0,1]],[[0,1],[1,2]]])>>> print(F){[1.0,0.0,0.0; 0.0,1.0,0.0], [0.0,1.0,0.0; 1.0,2.0,0.0]}asFormexWithProp()

Return string representation as Formex with properties.

The string representation as done by asFormex() is followed by the words “with prop” and a list of the properties.

2.3 Types

asArray()

Return string representation as a numpy array.

classmethod setPrintFunction(clas, func)

Choose the default formatting for printing formices.

This sets how formices will be formatted by a print statement. Currently there are two available functions: asFormex, asArray. The user may create its own formatting method. This is a class method. It should be used asfollows: Formex.setPrintFunction(Formex.asArray).

setProp(p=None)

Create or destroy the property array for the Formex.

A property array is a rank-1 integer array with dimension equal to the number of elements in the Formex (first dimension of data). You can specify a single value or a list/array of integer values. If the number of passed values is less than the number of elements, they wil be repeated. If you give more, they will be ignored.

If a value None is given, the properties are removed from the Formex.

append(F)

Append the members of Formex F to this one.

This function changes the original one! Use __add__ if you want to get a copy with the sum. >>> F = Formex([[[1.0,1.0,1.0]]]) >>> G = F.append(F) >>> print(F) {[1.0,1.0,1.0], [1.0,1.0,1.0]}

classmethod concatenate(clas, Flist)

Concatenate all formices in Flist.

This is a class method, not an instance method! >>> F = Formex([[[1,2,3]]],1) >>> print(Formex.concatenate([F,F,F])) {[1.0,2.0,3.0], [1.0,2.0,3.0], [1.0,2.0,3.0]}

Formex.concatenate([F,G,H]) is functionally equivalent with F+G+H. The latter is simpler to write for a list with a few elements. If the list becomes large, or the number of

items in the list is not fixed, the concatenate method is easier (and faster). We made it a class method and not a global function, because that would interfere with NumPy’s own concatenate function.

select(idx)

Return a Formex which holds only element with numbers in ids.

idx can be a single element number or a list of numbers or any other index mechanism accepted by numpy’s ndarray

cselect(idx)

Return a Formex without the elements with numbers in ids.

idx can be a single element number or a list of numbers or any other index mechanism accepted by numpy’s ndarray

This is the complementary operation of select

selectNodes(idx)

Return a Formex which holds only some nodes of the parent.

idx is a list of node numbers to select. Thus, if F is a plex 3 Formex representing triangles, the sides of the triangles are given by F.selectNodes([0,1]) + F.selectNodes([1,2]) + F.selectNodes([2,0]) The returned Formex inherits the property of its parent.

points()

Return a Formex containing only the points.

This is obviously a Formex with plexitude 1. It holds the same data as the original Formex, but in another shape: the number of points per element is 1, and the number of elements is equal to the total number of points. The properties are not copied over, since they will usually not make any sense.

The vertices() method returns the same data, but as a Coords object.

vertices()

Return the points of a Formex as a 2dim Coords object.

The return value holds the same coordinate data as the input Formex, but in another shape: (npoints,3).

The points() method returns the same data, but as a Formex.

remove(F)

Return a Formex where the elements in F have been removed.

This is also the subtraction of the current Formex with F. Elements are only removed if they have the same nodes in the same order. This is a slow operation: for large structures, you should avoid it where possible.

whereProp(val)

Return the numbers of the elements with property val.

val is either a single integer, or a list/array of integers. The return value is an array holding all the numbers of all the elements that have the property val, resp. one of the values in val.

If the Formex has no properties, a empty array is returned.

withProp(val)

Return a Formex which holds only the elements with property val.

val is either a single integer, or a list/array of integers. The return value is a Formex holding all the elements that have the property val, resp. one of the values in val. The returned Formex inherits the matching properties.

If the Formex has no properties, a copy with all elements is returned.

splitProp()

Partition a Formex according to its prop values.

Returns a dict with the prop values as keys and the corresponding partitions as values. Each value is a Formex instance. It the Formex has no props, an empty dict is returned.

elbbox()

Return a Formex where each element is replaced by its bbox.

The returned Formex has two points for each element: two corners of the bbox.

unique(rtol=0.0001, atol=9.9999999999999995e-07)

Return a Formex which holds only the unique elements.

Two elements are considered equal when all its nodal coordinates are close. Two values are close if they are both small compared to atol or their difference divided by the second value is small compared to rtol. Two elements are not considered equal if one’s points are a permutation of the other’s.

reverse()

Return a Formex where all elements have been reversed.

Reversing an element means reversing the order of its points. This is equivalent to:

self.selectNodes(arange(self.nplex()-1,-1,-1))test(nodes='all', dir=0, min=None, max=None, atol=0.0)

Flag elements having nodal coordinates between min and max.

This function is very convenient in clipping a Formex in a specified direction. It returns a 1D integer array flagging (with a value 1 or True) the elements having nodal coordinates in the required range. Use where(result) to get a list of element numbers passing the test. Or directly use clip() or cclip() to create the clipped Formex.

The test plane can be defined in two ways, depending on the value of dir. If dir == 0, 1 or 2, it specifies a global axis and min and max are the minimum and maximum values for the coordinates along that axis. Default is the 0 (or x) direction.

Else, dir should be compaitble with a (3,) shaped array and specifies the direction of the normal on the planes. In this case, min and max are points and should also evaluate to (3,) shaped arrays.

nodes specifies which nodes are taken into account in the comparisons. It should be one of the following: - a single (integer) point number (< the number of points in the Formex) - a list of point numbers - one of the special strings: ‘all’, ‘any’, ‘none’ The default (‘all’) will flag all the elements that have all their nodes between the planes x=min and x=max, i.e. the elements that fall completely between these planes. One of the two clipping planes may be left unspecified.

clip(t)

Return a Formex with all the elements where t>0.

t should be a 1-D integer array with length equal to the number of elements of the formex. The resulting Formex will contain all elements where t > 0. This is a convenience function for the user, equivalent to F.select(t>0).

cclip(t)

This is the complement of clip, returning a Formex where t<=0.

mirror(dir=2, pos=0, keep_orig=True)

Reflect a Formex in one of the coordinate directions

This method behaves like reflect(), but adds the reflected part to the original. Setting keep_orig=False makes it behave just like reflect().

centered()

Return a centered copy of the Formex.

resized(size=1.0, tol=1.0000000000000001e-05)

Return a scaled copy of the Formex with given size in all directions.

If a direction has zero size, it is not rescaled.

circulize(angle)

Transform a linear sector into a circular one.

A sector of the (0,1) plane with given angle, starting from the 0 axis, is transformed as follows: points on the sector borders remain in place. Points inside the sector are projected from the center on the circle through the intersection points of the sector border axes and the line through the point and perpendicular to the bisector of the angle. See Diamatic example.

circulize1()

Transforms the first octant of the 0-1 plane into 1/6 of a circle.

Points on the 0-axis keep their position. Lines parallel to the 1-axis are transformed into circular arcs. The bisector of the first quadrant is transformed in a straight line at an angle Pi/6. This function is especially suited to create circular domains where all bars have nearly same length. See the Diamatic example.

shrink(factor)

Shrinks each element with respect to its own center.

Each element is scaled with the given factor in a local coordinate system with origin at the element center. The element center is the mean of all its nodes. The shrink operation is typically used (with a factor around 0.9) in wireframe draw mode to show all elements disconnected. A factor above 1.0 will grow the elements.

replicate(n, vector, distance=None)

Replicate a Formex n times with fixed step in any direction.

Returns a Formex which is the concatenation of n copies, where each copy is equal to the previous one translated over (vector,distance). The first copy is equal to the original. Vector and distance are interpreted just like in the translate() method.

replic(n, step=1.0, dir=0)

Return a Formex with n replications in direction dir with step.

The original Formex is the first of the n replicas.

replic2(n1, n2, t1=1.0, t2=1.0, d1=0, d2=1, bias=0, taper=0)

Replicate in two directions.

n1,n2 number of replications with steps t1,t2 in directions d1,d2 bias, taper : extra step and extra number of generations in direction d1 for each generation in direction d2

rosette(n, angle, axis=2, point=[0.0, 0.0, 0.0])

Return a Formex with n rotational replications with angular step angle around an axis parallel with one of the coordinate axes going through the given point. axis is the number of the axis (0,1,2). point must be given as a list (or array) of three coordinates. The original Formex is the first of the n replicas.

translatem(*args, **kargs)

Multiple subsequent translations in axis directions.

The argument list is a sequence of tuples (axis, step). Thus translatem((0,x),(2,z),(1,y)) is equivalent to translate([x,y,z]). This function is especially conveniant to translate in calculated directions.

extrude(n, step=1.0, dir=0, autofix=True)

Extrude a Formex in one of the axis directions.

Returns a Formex with doubled plexitude.

First the original Formex is translated over n steps of length step in direction dir. Then each pair of subsequent Formices is connected to form a higher plexitude structure.

Currently, this function correctly transforms: point1 to line2, line2 to quad4, tri3 to wedge6, quad4 to hex8.

See the ‘connect’ function for a more versatile tool.

divide(div)

Divide a plex-2 Formex at the values in div.

Replaces each member of the Formex by a sequence of members obtained by dividing the Formex at the relative values specified in div. The values should normally range from 0.0 to 1.0.

As a convenience, if an integer is specified for div, it is taken as a number of divisions for the interval [0..1].

This function only works on plex-2 Formices (line segments).

intersectionWithPlane(p, n)

Return the intersection of a Formex with the plane (p,n).

Currently this only works for plex-2 and plex-3 Formices.

The intersection of the Formex with a plane specified by a point p and normal n is returned. For a plex-2 Formex (lines), the returned Formex will be of plexitude 1 (points). For a plex-3 Formex (triangles) the returned Fomrex has plexitude 2 (lines).

cutWithPlane(p, n, side='', atol=None, newprops=None)

Cut a Formex with the plane(s) (p,n).

..warning :: This method currently only works for plexitude 2 or 3!

• p,`n`: a point and normal vector defining the cutting plane. In case of plexitude 3, p and n can be sequences of points and vector, allowing to cut with multiple planes. Both p and n have shape (3) or (npoints,3).

The default return value is a tuple of two Formices of the same plexitude as the input: (Fpos,Fneg), where Fpos is the part of the Formex at the positive side of the plane (as defined by the normal vector), and Fneg is the part at the negative side. Elements of the input Formex that are lying completely on one side of the plane will return unaltered. Elements that are crossing the plane will be cut and split up into multiple parts.

When side = ‘+’ or ‘-‘ (or ‘positive’or ‘negative’), only one of the sides is returned.

The other arguments (atol,newprops) are currently specific for the plexitude. See the cut2AtPlane and cut3AtPlane, which hold the actual implementation of this method.

split(n=1)

Split a Formex in subFormices containing n elements.

The number of elements in the Formex should be a multiple of n. Returns a list of Formices each comprising n elements.

write(fil, sep=' ', mode='w')

Write a Formex to file.

If fil is a string, a file with that name is opened. Else fil should be an open file. The Formex is then written to that file in a native format, using sep as separator between the coordinates. If fil is a string, the file is closed prior to returning.

classmethod read(clas, fil, sep=' ')

Read a Formex from file.

fil is a filename or a file object. If the file is in a valid Formex file format, the Formex is read and returned. Otherwise, None is returned. Valid Formex file formats are described in the manual.

classmethod fromstring(clas, fil, sep=' ', nplex=1, ndim=3, count=-1)

Create a Formex from coodinates in a string.

This uses the Coords.fromstring() method to read coordinates from a string and restructures them into a Formex of the specified plexitude.

fil: a string containing a single sequence of float numbers separatedby whitespace and a possible separator string.sep: the separator used between the coordinates. If not a space,all extra whitespace is ignored.ndim: number of coordinates per point. Should be 1, 2 or 3 (default).If 1, resp. 2, the coordinate string only holds x, resp. x,y values.count: total number of coordinates to read. This should be a multipleof 3. The default is to read all the coordinates in the string. count can be used to force an error condition if the string does not contain the expected number of values.

The return value is a Coords object.

affine(*args, **kargs)

Returns a general affine transform of the Coords object.

mat: a 3x3 float matrix

vec: a length 3 list or array of floats

The returned object has coordinates given by self * mat + vec.

bump(*args, **kargs)

Return a Coords with a bump.

A bump is a modification of a set of coordinates by a non-matching point. It can produce various effects, but one of the most common uses is to force a surface to be indented by some point.

dir specifies the axis of the modified coordinates; a is the point that forces the bumping; func is a function that calculates the bump intensity from distance (!! func(0) should be different from 0) dist is the direction in which the distance is measured : this can be one of the axes, or a list of one or more axes. If only 1 axis is specified, the effect is like function bump1 If 2 axes are specified, the effect is like bump2 This function can take 3 axes however. Default value is the set of 3 axes minus the direction of modification. This function is then equivalent to bump2.

bump1(*args, **kargs)

Return a Coords with a one-dimensional bump.

• dir specifies the axis of the modified coordinates;• a is the point that forces the bumping;• dist specifies the direction in which the distance is measured;• func is a function that calculates the bump intensity from distance and should be

such that func(0) != 0.

bump2(*args, **kargs)

Return a Coords with a two-dimensional bump.

dir specifies the axis of the modified coordinates; a is the point that forces the bumping; func is a function that calculates the bump intensity from distance !! func(0) should be different from 0.

cylindrical(*args, **kargs)

Converts from cylindrical to cartesian after scaling.

dir specifies which coordinates are interpreted as resp. distance(r), angle(theta) and height(z). Default order is [r,theta,z]. scale will scale the coordinate values prior to the transformation. (scale is given in order r,theta,z). The resulting angle is interpreted in degrees.

egg(*args, **kargs)

Maps the coordinates to an egg-shape

flare(*args, **kargs)

Create a flare at the end of a Coords block.

The flare extends over a distance xf at the start (end=0) or end (end=1) in direction dir[0] of the coords block, and has a maximum amplitude of f in the dir[1] direction.

isopar(*args, **kargs)

Perform an isoparametric transformation on a Coords.

This is a convenience method to transform a Coords object through an isoparametric transformation. It is equivalent to:

Isopar(eltype,coords,oldcoords).transform(self)

See plugins.isopar for more details.

map(*args, **kargs)

Return a Coords mapped by a 3-D function.

This is one of the versatile mapping functions. func is a numerical function which takes three arguments and produces a list of three output values. The coordinates [x,y,z] will be replaced by func(x,y,z). The function must be applicable to arrays, so it should only include numerical operations and functions understood by the numpy module. This method is one of several mapping methods. See also map1 and mapd.

Example:

>>> print Coords([[1.,1.,1.]]).map(lambda x,y,z: [2*x,3*y,4*z])[[ 2. 3. 4.]]

map1(*args, **kargs)

Return a Coords where coordinate i is mapped by a 1-D function.

func is a numerical function which takes one argument and produces one result. The coordinate dir will be replaced by func(coord[x]). If no x is specified, x is taken equal to dir. The function must be applicable on arrays, so it should only include numerical operations and functions understood by the numpy module. This method is one of several mapping methods. See also map and mapd.

mapd(*args, **kargs)

Maps one coordinate by a function of the distance to a point.

func a numerical function which takes one argument and produces one result. The coordinate dir will be replaced by func(d), where d is calculated as the distance to point. The function must be applicable on arrays, so it should only include numerical operations and functions understood by the numpy module. By default, the distance d is calculated in 3-D, but one can specify a limited set of axes to calculate a 2-D or 1-D distance. This method is one of several mapping methods. See also map3() and map1().

Example:

E.mapd(2,lambda d:sqrt(10**2-d**2),f.center(),[0,1])

maps E on a sphere with radius 10.

projectOnCylinder(*args, **kargs)

Project Coords on a cylinder with axis parallel to a global axis.

The default cylinder has its axis along the x-axis and a unit radius. No points of the Coords should belong to the axis..

projectOnSphere(*args, **kargs)

Project Coords on a sphere.

The default sphere is a unit sphere at the origin. The center of the sphere should not be part of the Coords.

reflect(*args, **kargs)

Reflect the coordinates in direction dir against plane at pos.

Parameters:

• dir: int: direction of the reflection (default 0)• pos: float: offset of the mirror plane from origin (default 0.0)• inplace: boolean: change the coordinates inplace (default False)

replace(*args, **kargs)

Replace the coordinates along the axes i by those along j.

i and j are lists of axis numbers or single axis numbers. replace ([0,1,2],[1,2,0]) will roll the axes by 1. replace ([0,1],[1,0]) will swap axes 0 and 1. An optionally third argument may specify another Coords object to take the coordinates from. It should have the same dimensions.

rollAxes(*args, **kargs)

Roll the axes over the given amount.

Default is 1, thus axis 0 becomes the new 1 axis, 1 becomes 2 and 2 becomes 0.

rot(*args, **kargs)

Return a copy rotated over angle around axis.

The angle is specified in degrees. The axis is either one of (0,1,2) designating the global axes, or a vector specifying an axis through the origin. If no axis is specified, rotation is around the 2(z)-axis. This is convenient for working on 2D-structures.

As a convenience, the user may also specify a 3x3 rotation matrix, in which case the function rotate(mat) is equivalent to affine(mat).

All rotations are performed around the point [0,0,0], unless a rotation origin is specified in the argument ‘around’.

rotate(*args, **kargs)

Return a copy rotated over angle around axis.

The angle is specified in degrees. The axis is either one of (0,1,2) designating the global axes, or a vector specifying an axis through the origin. If no axis is specified, rotation is around the 2(z)-axis. This is convenient for working on 2D-structures.

As a convenience, the user may also specify a 3x3 rotation matrix, in which case the function rotate(mat) is equivalent to affine(mat).

All rotations are performed around the point [0,0,0], unless a rotation origin is specified in the argument ‘around’.

scale(*args, **kargs)

Return a copy scaled with scale[i] in direction i.

The scale should be a list of 3 scaling factors for the 3 axis directions, or a single scaling factor. In the latter case, dir (a single axis number or a list) may be given to specify the direction(s) to scale. The default is to produce a homothetic scaling.

Example:

>>> print Coords([1.,1.,1.]).scale(2)[ 2. 2. 2.]>>> print Coords([1.,1.,1.]).scale([2,3,4])[ 2. 3. 4.]

shear(*args, **kargs)

Return a copy skewed in the direction dir of plane (dir,dir1).

The coordinate dir is replaced with (dir + skew * dir1).

spherical(*args, **kargs)

Converts from spherical to cartesian after scaling.

• dir specifies which coordinates are interpreted as resp. longitude(theta), latitude(phi) and distance(r).

• scale will scale the coordinate values prior to the transformation.

Angles are interpreted in degrees. Latitude, i.e. the elevation angle, is measured from equator in direction of north pole(90). South pole is -90.

If colat=True, the third coordinate is the colatitude (90-lat) instead.

superSpherical(*args, **kargs)

Performs a superspherical transformation.

superSpherical is much like spherical, but adds some extra parameters to enable the creation of virtually any surface.

Just like with spherical(), the input coordinates are interpreted as the longitude, latitude and distance in a spherical coordinate system.

dir specifies which coordinates are interpreted as resp. longitude(theta), latitude(phi) and distance(r). Angles are then interpreted in degrees. Latitude, i.e. the elevation angle, is measured from equator in direction of north pole(90). South pole is -90. If colat=True, the third coordinate is the colatitude (90-lat) instead.

scale will scale the coordinate values prior to the transformation.

The n and e parameters define exponential transformations of the north_south (latitude), resp. the east_west (longitude) coordinates. Default values of 1 result in a circle.

k adds ‘eggness’ to the shape: a difference between the northern and southern hemisphere. Values > 0 enlarge the southern hemishpere and shrink the northern.

swapAxes(*args, **kargs)

Swap coordinate axes i and j.

Beware! This is different from numpy’s swapaxes() method !

toCylindrical(*args, **kargs)

Converts from cartesian to cylindrical coordinates.

dir specifies which coordinates axes are parallel to respectively the cylindrical axes distance(r), angle(theta) and height(z). Default order is [x,y,z]. The angle value is given in degrees.

toSpherical(*args, **kargs)

Converts from cartesian to spherical coordinates.

dir specifies which coordinates axes are parallel to respectively the spherical axes distance(r), longitude(theta) and latitude(phi). Latitude is the elevation angle measured from equator in direction of north pole(90). South pole is -90. Default order is [0,1,2], thus the equator plane is the (x,y)-plane.

The returned angle values are given in degrees.

transformCS(*args, **kargs)

Perform a CoordinateSystem transformation on the Coords.

This method transforms the Coords object by the transformation that turns the initial CoordinateSystem into the currentCoordinateSystem.

currentCS and initialCS are CoordSystem or (4,3) shaped Coords instances. If initialCS is None, the global (x,y,z) axes are used.

E.g. the default initialCS and currentCS equal to:

0. 1. 0.-1. 0. 0. 0. 0. 1.

0. 0. 0.

result in a rotation of 90 degrees around the z-axis.

This is a convenience function equivalent to:

self.isopar('tet4',currentCS,initialCS)

translate(*args, **kargs)

Translate a Coords object.

The translation vector can be specified in one of the following ways:

• an axis number (0,1,2),• a single translation vector,• an array of translation vectors.

If an axis number is given, a unit vector in the direction of the specified axis will be used. If an array of translation vectors is given, it should be broadcastable to the size of the Coords array. If a distance value is given, the translation vector is multiplied with this value before it is added to the coordinates.

Example:

>>> x = Coords([1.,1.,1.])>>> print x.translate(1)[ 1. 2. 1.]>>> print x.translate(1,1.)[ 1. 2. 1.]>>> print x.translate([0,1,0])[ 1. 2. 1.]>>> print x.translate([0,2,0],0.5)[ 1. 2. 1.]

trl(*args, **kargs)

Translate a Coords object.

The translation vector can be specified in one of the following ways:

• an axis number (0,1,2),• a single translation vector,• an array of translation vectors.

If an axis number is given, a unit vector in the direction of the specified axis will be used. If an array of translation vectors is given, it should be broadcastable to the size of the Coords array. If a distance value is given, the translation vector is multiplied with this value before it is added to the coordinates.

Example:

>>> x = Coords([1.,1.,1.])>>> print x.translate(1)[ 1. 2. 1.]>>> print x.translate(1,1.)[ 1. 2. 1.]>>> print x.translate([0,1,0])[ 1. 2. 1.]>>> print x.translate([0,2,0],0.5)[ 1. 2. 1.]

copy()

Return a deep copy of the object.

classmethod fromfile(clas, fil, sep=' ', nplex=1)

Read the coordinates of a Formex from a file

nnodes()

Return the number of points in the formex.

This is the product of the number of elements in the formex with the number of nodes per element.

rep(n, step=1.0, dir=0)

Return a Formex with n replications in direction dir with step.

The original Formex is the first of the n replicas.

ros(n, angle, axis=2, point=[0.0, 0.0, 0.0])

Return a Formex with n rotational replications with angular step angle around an axis parallel with one of the coordinate axes going through the given point. axis is the number of the axis (0,1,2). point must be given as a list (or array) of three coordinates. The original Formex is the first of the n replicas.

Functions defined in module formex

formex.vectorLength(vec)

Return the lengths of a set of vectors.

vec is an (n,3) shaped array holding a collection of vectors. The result is an (n,) shaped array with the length of each vector.

formex.vectorNormalize(vec)

Normalize a set of vectors.

vec is a (n,3) shaped arrays holding a collection of vectors. The result is a tuple of two arrays:

• length (n): the length of the vectors vec• normal (n,3): unit-length vectors along vec.

formex.vectorPairAreaNormals(vec1, vec2)

Compute area of and normals on parallellograms formed by vec1 and vec2.

vec1 and vec2 are (n,3) shaped arrays holding collections of vectors. The result is a tuple of two arrays: - area (n) : the area of the parallellogram formed by vec1 and vec2. - normal (n,3) : (normalized) vectors normal to each couple (vec1,2). These are calculated from the cross product of vec1 and vec2, which indeed gives area * normal.

Note that where two vectors are parallel, an area zero will results and an axis with components NaN.

formex.vectorPairArea(vec1, vec2)

Compute area of the parallellogram formed by a vector pair vec1,vec2.

vec1 and vec2 are (n,3) shaped arrays holding collections of vectors. The result is an (n) shaped array with the area of the parallellograms formed by each pair of vectors (vec1,vec2).

formex.vectorPairNormals(vec1, vec2)

Compute vectors normal to vec1 and vec2.

vec1 and vec2 are (n,3) shaped arrays holding collections of vectors. The result is an (n,3) shaped array of unit length vectors normal to each couple (edg1,edg2).

formex.vectorTripleProduct(vec1, vec2, vec3)

Compute triple product vec1 . (vec2 x vec3).

vec1, vec2, vec3 are (n,3) shaped arrays holding collections of vectors. The result is a (n,) shaped array with the triple product of each set of corresponding vectors fromvec1,vec2,vec3. This is also the square of the volume of the parallellepid formex by the 3 vectors.

formex.polygonNormals(x)

Compute normals in all points of polygons in x.

x is an (nel,nplex,3) coordinate array representing a (possibly not plane) polygon.

The return value is an (nel,nplex,3) array with the unit normals on the two edges ending in each point.

formex.pattern(s)

Return a line segment pattern created from a string.

This function creates a list of line segments where all points lie on a regular grid with unit step. The first point of the list is [0,0,0]. Each character from the input string is interpreted as a code specifying how to move to the next point. Currently defined are the following codes: 1..8 move in the x,y plane 9 remains at the same place 0 = goto origin [0,0,0] + = go back to origin without creating a line segment When looking at the plane with the x-axis to the right, 1 = East, 2 = North, 3 = West, 4 = South, 5 = NE, 6 = NW, 7 = SW, 8 = SE. Adding 16 to the ordinal of the character causes an extra move of +1 in the z-direction. Adding 48 causes an extra move of -1. This means that ‘ABCDEFGHI’, resp. ‘abcdefghi’, correspond with ‘123456789’ with an extra z +/-= 1. This gives the following schema:

z+=1 z unchanged z -= 1

F B E 6 2 5 f b e | | | | | | C----I----A 3----9----1 c----i----a | | | | | | G D H 7 4 8 g d h

The special character ‘/’ can be put before any character to make the move without making a connection. The effect of any other character is undefined.

The resulting list is directly suited to initialize a Formex.

formex.mpattern(s)

This is like pattern, but allowing lists with more than 2 points.

Subsequent points are included in the same list until a ‘-‘ occurs. A ‘+’ or ‘-‘ character splits lists. After a ‘-‘, the list starts at the last point of the previous list. After a ‘+’, the list starts again at the origin. All lists should have equal length if you want to use the resulting list to initialize a Formex.

formex.pointsAt(F, t)

Return the points of a plex-2 Formex at times t.

F is a plex 2 Formex and t is an array with F.nelems() float values which are interpreted as local parameters along the edges of the Formex, such that the first node has value 0.0 and the last has value 1.0. The return value is a coords.Coords array with the points at values t.

formex.intersectionLinesWithPlane(F, p, n, atol=0.0001)

Return the intersection lines of a plex-3 Formex with plane (p,n).

F is a Formex of plexitude 3. p is a point specified by 3 coordinates. n is the normal vector to a plane, specified by 3 components. atol is a tolerance factor defining whether an edge is intersected by the plane.

formex.cut2AtPlane(F, p, n, side='', atol=None, newprops=None)

Returns all elements of the Formex cut at plane.

F is a Formex of plexitude 2. p is a point specified by 3 coordinates. n is the normal vector to a plane, specified by 3 components.

The return value is:

• with side = ‘+’ or ‘-‘ or ‘positive’or ‘negative’ : a Formex of the same plexitude with all elements located completely at the positive/negative side of the plane(s) (p,n) retained, all elements lying completely at the negative/positive side removed and the elements intersecting the plane(s) replaced by new elements filling up the parts at the positive/negative side.

• with side = ‘’: two Formices of the same plexitude, one representing the positive side and one representing the negative side.

To avoid roundoff errors and creation of very small elements, a tolerance can be specified. Points lying within the tolerance distance will be considered lying in the plane, and no cutting near these points.

formex.cut3AtPlane(F, p, n, side='', atol=None, newprops=None)

Returns all elements of the Formex cut at plane(s).

F is a Formex of plexitude 3. p is a point or a list of points. n is the normal vector to a plane or a list of normal vectors. Both p and n have shape (3) or (npoints,3).

The return value is:

• with side = ‘+’ or ‘-‘ or ‘positive’or ‘negative’ : a Formex of the same plexitude with all elements located completely at the positive/negative side of the plane(s) (p,n) retained, all elements lying completely at the negative/positive side removed and the elements intersecting the plane(s) replaced by new elements filling up the parts at the positive/negative side.

• with side = ‘’: two Formices of the same plexitude, one representing the positive side and one representing the negative side.

Let be the signed distance of the vertices to a plane. The elements located completely

at the positive or negative side of a plane have three vertices for which .

The elements intersecting a plane can have one or more vertices for which . These vertices are projected on the plane so that their distance is zero.

If the Formex has a property set, the new elements will get the property numbers defined in newprops. This is a list of 7 property numbers flagging elements with following properties:

1. no vertices with , triangle after cut

2. no vertices with , triangle 1 from quad after cut

3. no vertices with , triangle 2 from quad after cut

4. one vertex with , two vertices at pos. or neg. side

5. one vertex with , one vertex at pos. side, one at neg.

6. two vertices with , one vertex at pos. or neg. side

7. three vertices with

formex.cutElements3AtPlane(F, p, n, newprops=None, side='', atol=0.0)

This function needs documentation.

Should it be called by the user? or only via cut3AtPlane? For now, lets suppose the last, so no need to check arguments here.

newprops should be a list of 7 values: each an integer or None side is either ‘+’, ‘-‘ or ‘’

formex.connect(Flist, nodid=None, bias=None, loop=False)

Return a Formex which connects the formices in list.

Flist is a list of formices, nodid is an optional list of nod ids and bias is an optional list of element bias values. All lists should have the same length. The returned Formex has a plexitude equal to the number of formices in list. Each element of the Formex consist of a node from the corresponding element of each of the formices in list. By default this will be the first node of that element, but a nodid list may be given to specify the node id to be used for each of the formices. Finally, a list of bias values may be given to specify an

offset in element number for the subsequent formices. If loop==False, the order of the Formex will be the minimum order of the formices in Flist, each minus its respective bias. By setting loop=True however, each Formex will loop around if its end is encountered, and the order of the result is the maximum order in Flist.

formex.interpolate(F, G, div, swap=False)

Create interpolations between two formices.

F and G are two Formices with the same shape. v is a list of floating point values. The result is the concatenation of the interpolations of F and G at all the values in div. An interpolation of F and G at value v is a Formex H where each coordinate Hijk is obtained from: Hijk = Fijk + v * (Gijk-Fijk). Thus, a Formex interpolate(F,G,[0.,0.5,1.0]) will contain all elements of F and G and all elements with mean coordinates between those of F and G.

As a convenience, if an integer is specified for div, it is taken as a number of divisions for the interval [0..1]. Thus, interpolate(F,G,n) is equivalent with interpolate(F,G,arange(0,n+1)/float(n))

The swap argument sets the order of the elements in the resulting Formex. By default, if n interpolations are created of an m-element Formex, the element order is in-Formex first (n sequences of m elements). If swap==True, the order is swapped and you get m sequences of n interpolations.

Glossary:

Absolute Value the absolute value of a number is the distance the number is from the zero point on the number line. The absolute value of a number or an expression is always greater than or equal to zero (i.e. nonnegative).

Addition a mathematical process to to combine numbers and/or variables into an equivalent quantity, number or algebraic expression Adding integers To ADD integers with the same sign, add their absolute values. Give the result the same sign as the integers.

To ADD integers with different signs, SUBTRACT the lesser absolute value from the greater absolute value. Give the result the same sign as the integer with the greater absolute value.

Addition (and Subtraction) Property for Inequality

For all numbers a, b, and c, the following are true:

1. If a > b, then a + c > b + c and a - c > b - c

2. If a < b, then a + c < b + c and a - c < b - c

In words, if the same number or expression is added or subtracted from both sides of a true inequality, the new inequality is also true.see lesson

AdditiveIdentity Property

For any number a,

a + 0 = 0 + a

In words, adding zero to a number leaves the number unchanged, hence the "identical" number.

Additive Inverse Property

For every number a, a + (-a) = 0

e.g.

5 + ? = 0 5 + (-5) = 0

-17 + ? = 0 -17 + 17 = 0

In words, if the opposite of a number is added to the original number, the sum is equal to zero.

Algebra a language that helps translate real-life situations into mathematical form so that we can analyze change and answer the question "What if?" Algebraic Expression an expression consisting of one or more numbers and variables along with one or more arithmetic operations. Arithmetic Operation a mathematical process of addition, subtraction, multiplication or division.

Axes Two perpendicular number lines that are

used to locate points in a coordinate plane. By convention, the x-axis is the horizontal

line and the y-axis is the vertical line.

Best-Fit Line

A line drawn so it is close to most or all of the data points in a graph.

A best-fit line is described as strong or weak depending on how close the data points are on average.

see lesson

Binomial The sum of two monomials. Boundary

A boundary line of an inequality is a

line that separates the coordinate plane into half-planes.

Coefficient The numerical factor in a term. In the term 4x, 4 is the coefficient. In the

term

4x

/5

;

4

/5

is the coefficient. Note that

4x

/5

can also be written as (

4

/5

)x. Complex

fraction A fraction that has one or more fractions in the numerator or denominator. Compound Event A compound event consists of two or more simple events (i.e. the tossing of two or more coins).

Compound Inequality Two inequalities connected by AND

or OR. Consistent A system of equations is said to be consistent when it has at least one

ordered pair that satisfies both equations. Constants A monomial term that lacks a variable component.

Coordinate Plane

the plane containing the x- and y- axes. Counting Numbers

The set of counting (aka

"natural") numbers can be expressed as {1,2,3,...}. This set is identical to the set of

whole numbers, less the number zero. Counting numbers are not negative.Degree of a monomial The degree of a monomial is the sum of the exponents of its variables. Degree of a polynomial The degree of a polynomial is the degree of the term of the greatest monomial degree. Dependent (equations) A system of equations that has an infinite number of solutions Dependent Event An occurrence or outcome that is affected by previous occurrences or outcomes. The probability of drawing a red or black card from a deck of cards is affected by the colors of cards previously drawn. see independent event Dependent Variable When solving an equation for a given variable, that variable becomes the dependent variable. That is, its value depends upon the domain values chosen for the other variable. The dependent variable represents the range and is graphed on the y-axis (see independent variable). Difference The result of a subtraction operation. Order matters! The difference of 6 and 3 equals 3. The difference of 3 and 6 equals -3. Difference of Squares Two perfect squares separated by a subtraction sign: a2 - b2 & x2 - 49 are both examples of the difference of squares.

Check your progress

1. Explain methods of the Application formex algebra

2. Explain types

Reference:

1. ^ National Council on Disability. (1994). Inclusionary education for students with

special needs: Keeping the promise. Washington, DC: Author.

12. ^ Swan, William W.; Morgan, Janet L (1993). "The Local Interagency Coordinating Council". Collaborating for Comprehensive Services for Young Children and Their Families. Baltimore: Paul H. Brookes Pub. Co.. ISBN 1557661030. OCLC 25628688. OL 4285012W .13. ^ Beverly Rainforth; York-Barr, Jennifer (1997). Collaborative Teams for Students With Severe Disabilities: Integrating Therapy and Educational Services. Brookes Publishing Company. ISBN 1-55766-291-6. OCLC 25025287.14. ^ Stainback, Susan Bray; Stainback, William C. (1996). Support Networks for Inclusive Schooling: Interdependent Integrated Education. Paul H Brookes Pub Co. ISBN 1-55766-041-7. OCLC 300624925. OL 2219710M .15. ^ Gaylord-Ross, Robert (1989). Integration strategies for students with handicaps. Baltimore: P.H. Brookes. ISBN 1-55766-010-7. OCLC 19130181.16. ^ Gartner, Alan; Dorothy Kerzner Lipsky (1997). Inclusion and School Reform: Transforming America's Classrooms. Brookes Publishing Company. ISBN 1-55766-273-8. OCLC 35848926.17. ^ a b Goodman, Libby (1990). Time and learning in the special education classroom. Albany, N.Y.: State University of New York Press. p. 122. ISBN 0-7914-0371-8. OCLC 20635959.18. ^ Special Education Inclusion19. ^ Smith P (October 2007). "Have we made any progress? Including students with intellectual disabilities in regular education classrooms". Intellect Dev Disabil 45 (5): 297–309. doi:10.1352/0047-6765(2007)45[297:HWMAPI]2.0.CO;2. PMID 17887907.20. ^ James Q. Affleck; Sally Madge, Abby Adams, Sheila Lowenbraun (1988-01). "Integrated classroom versus resource model: academic viability and effectiveness". Exceptional Children: 2. Retrieved 2010-05-29.

21. ^ Bowe, Frank (2004). Making Inclusion Work. Upper Saddle River, N.J: Prentice Hall. ISBN 0-13-017603-6. OCLC 54374653.22. ^ a b c d Karen Zittleman; Sadker, David Miller (2006). Teachers, Schools and Society: A Brief Introduction to Education with Bind-in Online Learning Center Card with free Student Reader CD-ROM. McGraw-Hill Humanities/Social Sciences/Languages. pp. 48, 49, 108, G–12. ISBN 0-07-323007-3.23. ^ Warnock Report (1978). "Report of the Committee of Enquiry into the Education of Handicapped Children and Young People", London.24. ^ Wolffe, Jerry. (20 December 2010) What the law requires for disabled students The Oakland Press.25. aq ar Pepper, David (25 September 2007) Assessment for disabled students: an international comparison. UK: Ofqual's Qualifications and Curriculum Authority, Regulation & Standards Division. (Report).26. ^ Busuttil-Reynaud, Gavin and John Winkley [www.jisc.ac.uk/uploaded_documents/eAssess-Glossary-Extended-v1-01.pdf e-Assessment Glossary (Extended)]. UK: Joint Information Systems Committee and Ofqual's Qualifications and Curriculum Authority. (Report).

Check your progress answers

1. Refer 2.2

2. Refer 2.3

Unit 3: FORMIAN for generation of configuration

3.1 Introduction3.2 A Simple make file3.3 A more complex make file3.4 Various types 3.5 Uses3.6 Method

Introduction

Varax domes are special lattice domes built up of a network of equilateral triangles of straight or curved beams and a decking supported by straight purlins. The geometry of a typical varax dome is obtained by projecting the plane network of equilateral triangles onto the spherical surface of the dome. The projection is defined by rays that originate at

the centre of the sphere. Thus, all beam elements and structural nodes lie in great circle planes and have the same radius of curvature.

Formian is a special program developed at the Space Structures Research Center, University of Surrey, UK, to generate coordinates for advanced space structures [1,2]. It is based on formex algebra [3] and has been proven to be a powerful tool. However, the Formian program cannot handle the special features of varax domes. It is necessary to implement new functions related to varax domes within it, which is the focus of this paper. After having done so, all other functions and tools in the Formian program are available for application to varax domes.

Functions and procedures for generating varax dome configurations have been developed and implemented into this professional program for space structures, Formian, to be able to generate any shape of varax domes and to use the results as input variables to a finite element program for analysis purposes. Thus, the Formian program used in this paper is adapted to be applicable also to varax domes. The details of the computer functions and programming are found in [4,5]. In this paper, the procedures and applications of this Formian program adapted to varax domes are described and illustrated.

The principles and procedures for generating different configurations of varax domes are presented in the paper. The computer schemes necessary to accomplish these kinds of dome shapes are illustrated. Varax domes with different numbers of sectors, different numbers of divisions of the arc length and the bottom beam, and with and without an apex ring are presented. Also, different arrangements of the purlins are illustrated as are applications of inherent Formian functions to generate special shape effects on varax domes.

”For programmers drowning in a sea of constantly changing source code, software configurationmanagement promises to be a much-needed lifeboat.” [Cronk, p. 45] As the software development process grows larger and more complex configuration management is almost a necessity to developing high quality products. In a paper by Salvatore Salamone several reasons have been established of why having a Configuration Management system is a good idea.

The reasons he lists are that it masks complexity of the network from users, reduces user options making LAN support easier, reduces training costs, facilitates changes when applications move or devices are added to the network, keeps users from trying to run programs their PCs cannot support, enforces uniform corporate image in customer service settings, and tightens securities. He goes on to give some good examples of situations where each of these apply [Salamone, p. 160]. With today’s fast paced technology the process of software development is becoming a larger and a more complex process. To manage this complexity, Configuration Management systems have moved to the forefront for controlling and managing the process of software development.

There are many desirable features of a Configuration Management system. Many of the features do exist in current CM systems although some exist more than others and

no single system seems to contain all the features desired [Dart, pp. 3-4]. Three qualities currently exist in many configuration management systems. They are version control, a check-out/check-in facility, and a buffered-compare program [Buckley, p. 56]. ”Version control is the ability to store multiple versions of the same file under controlled, restricted-access conditions. [Buckley, p. 56]” The check-out/check-in capability keeps more than one user from modifying the same file. The buffered-compare program compares the old and new files and provides as output ”a complete delineation of the additions and deletions. [Buckley, p. 59]” There are also four desirable capabilities which would be good to have in a CM system. These are establishing a standards-checking program, implementing an automated problem-reporting system, automating the generation of configuration status accounting reports and providing an automated metrics acquisition and reporting capability [Buckley, p. 59].

The features come from both the management and product side of the software development process. A standards-checking program checks all files to make sure they all conform to project standards and will generate a problem report if one is found that doesn’t conform. The automated problem-reporting system is somewhat self explanatory. It will keep the project on track by getting problems reported quickly. The next desirable feature, automating the generation of configuration status accounting reports, gives details such as the status of change proposals and the revision levels of configuration documentation. This feature is desirable for larger projects such as in industry where the projects can become quite large.

Finally, the desirable feature of providing an automated metrics acquisition and reporting capability provides reports on two types of metrics, those ”relating to the software configuration management process itself, and project metrics providing insight into the software development process.” [Buckley, p. 61] The majority of these features do exist in different CM systems, for instance Aide-De-Camp (ADC) is an existing system which provides change sets for distribution of change. This system also integrates problem reports and change requests providing some of the features from the management side of the process.Another existing CM system is Adele.

Adele has basic features of datamodeling, interface checking, and representing families of products [Dart, p. 32]. ”Since the system knows of the dependency graph, it can assist in composing a configuration. [Dart, p. 32]” Through this, the system can detect incomplete or inconsistent descriptions. Another existing system offering some desirable features is CCC, Softool’s Change and Configuration Tool. Also offering some management features, CCC provides conventions that go along with the waterfall model which is widely used in industry today. It offers online support of documentation standards and change requests [Dart, p. 32].

A system which offers more features is DSEE, Domain Software Engineering Environment. ”DSEE provides derived object code management as well as source version control, system modeling, configuration threads, version selection based attributes, releases of configurations, system building, (reusable) object pools, task lists for tracking tasks to be done and those completed, and alerts for notifying users for certain events.

[Dart, p. 34]” This system offers features from both the management side and the product side of the process. Finally, just to mention a couple more systems of the many existing, we have RCS and DMS which are both version control systems, DMS being for files distributed across different platforms [Dart, pp. 11-12].

When considering the design of a Configuration Management system, one needs to think carefully of the criteria for choosing a software configuration management system. The system needs to offer features that are desirable in the market and will help a company develop the best software with the lowest overhead. It has been established that there are two main cost factors that must be considered when a company is deciding on a Configuration Management system, one ”the hardware resources necessary to achieve acceptable performance” and two ”the human resources needed to administer and maintain the SCM system. [Midha, p. 163]”

These things must be considered to create a product that will excel in the marketplace and to have a product be chosen over other Configuration Management systems. Looking toward the future of Configuration Management it has been discovered that the software development process upon which Configuration Management has been built is evolving to a new level. In industry today and in the recent past the Waterfall Model is widely used in the software development process but ”the software industry however, is now tackling problems that the waterfall model cannot handle. [Bersoff, p. 106]” With these problems new models will be developed which will cause a change in needs from a Configuration Management system. New needs will arise and new systems will need to be developed to accommodate those needs.

The product described below is one which offers some of the established features of a CM system along with the advantage of product development with a team spread out across a network. The product’s features are more towards the product side of the process and more away from the upper management side. One of the major objectives of the Configuration Management System is that it should be a logical extension of Make. Before moving any further in the specification of the system, it would be appropriate to introduce some sample makefiles that will be used as a reference point for further discussion.

In addition, the scrutinization of these existing makefiles should ensure that the final design is complete and contains all of the functionality of the existing Make system. This approach seems to be a logical starting point for specifying the total system due to the fact that many design decisions must take into account the current functionality of makefiles while also providing network accessibility for the system. The introduction of these makefiles will also provide a means for introducing and defining several key terms that will be frequently used from this point forward.

3.2 A Simple Makefile

The makefile shown next in Figure 3.1 was taken from the GnuMake Online Manual. This makefile introduces the dependencies surrounding a sample executable, called EDIT. Although this example is clearly referring to a system programmed in the C programming language, the final Configuration Management system should be language independent. The second example will portray an arbitrary system that is not based on any specific programming language. As shown in Figure 3.2, EDIT has eight dependencies, each of which has a list of their own subsequent dependencies. EDIT has associated with it a command for compiling and creating itself, as do EDIT’s nine dependencies. Any node in the tree which has any commands associated with it is referred to as a goal. All other nodes are referred to as files. This concept will be explained in more detail in Section 3.3. As the makefile from Figure 3.1 is scrutinized further, it becomes apparent that makefiles have uses other than strictly stating compilation rules. The clean command contained within the makefile is independent of the EDIT executable and all of its sub-dependencies.

Thus it can be said that the clean command is an independent goal. In this case, clean serves the purpose of removing all of the object files and therefore has nothing to do with compilation. This concept becomes an important factor in design decisions. The final implementation clearly must have the ability to deal with several, sometimes independent, goals. The entire system contained in the makefile in Figure 3.1 can be graphically represented with the following model. Certainly, this model should be used as an example of the graphical representation that should be produced by the Configuration Management system and available to the user. The specific methodology for producing this model from the given dependencies is left to the programmer, as this methodology would vary depending on the language by which the representation is created. Figure 3.2 simply serves as a prototype of what may be implemented.

Looking at this representation, it should be noted that each circle represents a goal and each square represents a file. In addition, the clean function is properly represented as an independent goal, with no connections to EDIT itself. Although a traversal down the y-axis of this picture implies a deeper dependency and therefore a difference in the compilation order is implied, the same is not true for the x-axis. Nodes on the same level of the y-axis (i.e. main, kbd, command, etc.) can be compiled in any possible order, or all in parallel, if possible. Therefore, a traversal to the left or right on the x-axis carries no implications for compilation order. Finally, although this example does not depict the case where a file has a goal as its dependant, that case is certainly allowed and will be clearly represented in the next, more complex, example makefile.

Formaldehyde is an organic compound with the formula CH2O. It is the simplest aldehyde, hence its systematic name methanal.

Formaldehyde is a colorless gas with a characteristic pungent odor. It is an important precursor to many other chemical compounds, especially for polymers. In 2005, annual world production of formaldehyde was estimated to be 23 million tonnes (50 billion pounds). Commercial solutions of formaldehyde in water, commonly called formalin, were formerly used as disinfectants and for preservation of biological specimens.

In view of its widespread use, toxicity and volatility, exposure to formaldehyde is a significant consideration for human health

A More Complex Makefile

The purpose of the previous makefile was to provide a simple example, which can be referenced throughout the remainder of the text. The example lacked complexity, however, and it is therefore the goal of the next example makefile presented in Figure 3.3 to illustrate the extent to which the final Configuration Management system may be used. It further depicts the system’s capability for dealing with such cases.

Three top-level goals : SYSTEM, PRINT, and SIZE. The *.fil extension is merely a generic representation of any given source file. Similarly, the *.obj extension refers to any object file. These extensions were contrived to illustrate the fact that this system is intended to be platform independent, therefore any arbitrary language may be implemented in the makefile. While PRINT and SIZE are independent goals, the SYSTEM goal contains an intricate web of dependencies, which is best portrayed in the following graphical representation,

This complex set of dependencies will become useful when the compilation methodology is explained later in Section 4.7. For now, it should simply be noted that files have as dependants both files and goals, sometimes simultaneously; and this is also the case for goals.

Forms of formaldehyde

Formaldehyde is more complicated than many simple carbon compounds because it adopts different forms. Formaldehyde is a gas at room temperature, but the gas readily converts to a variety of derivatives, which are often used in industry in place of the gas.

One important derivative is the cyclic trimer metaformaldehyde or trioxane (CH2O)3. There is also an infinite polymer called paraformaldehyde.

When dissolved in water, formaldehyde combines with water to form methanediol or methylene glycol H2C(OH)2. The diol also exists in equilibrium with a series of oligomers (short polymers), depending on the concentration and temperature.

A saturated water solution, that contains about 40% formaldehyde by volume or 37% by mass, is called "100% formalin". A small amount of stabilizer, such as methanol, is usually added to limit oxidation and polymerization. A typical commercial grade formalin may contain 10–12% methanol in addition to various metallic impurities.

Glossary:

allegory (AL-eh-GOR-ee): a narrative that serves as an extended metaphor. Allegories are written in the form of fables, parables, poems, stories, and almost any other style or genre. The main purpose of an allegory is to tell a story that has characters, a setting, as well as other types of symbols, that have both literal and figurative meanings. The difference between an allegory and a symbol is that an allegory is a complete narrative that conveys abstract ideas to get a point across, while a symbol is a representation of an idea or concept that can have a different meaning throughout a literary work (A Handbook to Literature). One well-known example of an allegory is Dante’s The Divine Comedy. In Inferno, Dante is on a pilgrimage to try to understand his own life, but his character also represents every man who is in search of his purpose in the world (Merriam Webster Encyclopedia of Literature). Although Virgil literally guides Dante on his journey through the mystical inferno, he can also be seen as the reason and human wisdom that Dante has been looking for in his life. See A Handbook to Literature, Merriam Webster’s Encyclopedia of Literature. Machella Caldwell, Student, University of North Carolina at Pembroke

alliteration (a-LIT-uh-RAY-shuhn): a pattern of sound that includes the repetition of consonant sounds. The repetition can be located at the beginning of successive words or inside the words. Poets often use alliteration to audibly represent the action that is taking place. For instance, in the Inferno, Dante states: "I saw it there, but I saw nothing in it, except the rising of the boiling bubbles" (261). The repetition of the "b" sounds represents the sounds of bubbling, or the bursting action of the boiling pitch. In addition, in Sir Phillip Sidney's Astrophel and Stella, the poet states: "Biting my truant pen, beating myself for spite" (Line 13). This repetition of the "t" sound represents the action of the poet; one can hear and visualize his anguish as he bites the pen. Also in Astrophel and Stella, the poet states, "Oft turning others' leaves, to see if thence would flow, / Some fresh and fruitful showers upon my sunburn'd brain" (7-8). Again, the poet repeats the "fr" sounds to emphasize the speaker's desire for inspiration in expressing his feelings. Poets may also use alliteration to call attention to a phrase and fix it into the reader's mind; thus, it is useful for emphasis. Therefore, not only does alliteration provide poetry or prose with a unique sound, it can place emphasis on specific phrases and represent the action that is taking place. See A Handbook to Literature, Literature: An Introduction to Fiction, Poetry, and Drama. Stacey Ann Singletary, Student, University of North Carolina at Pembroke

allusion (a-LOO-zhuhn): a reference in a literary work to a person, place, or thing in history or another work of literature. Allusions are often indirect or brief references to

well-known characters or events. Specific examples of allusions can be found throughout Dante’s Inferno. In a passage, Dante alludes to the Greek mythological figures, Phaethon and Icarus, to express his fear as he descends from the air into the eighth circle of hell. He states:

I doubt if Phaethon feared more - that time he dropped the sun-reins of his father's chariot and burned the streak of sky we see today -

or if poor Icarus did - feeling his sides unfeathering as the wax began to melt, his father shouting: "Wrong, your course is wrong" (Canto XVII: 106-111).

Allusions are often used to summarize broad, complex ideas or emotions in one quick, powerful image. For example, to communicate the idea of self-sacrifice one may refer to Jesus, as part of Jesus' story portrays him dying on the cross in order to save mankind (Matthew 27:45-56). In addition, to express righteousness, one might allude to Noah who "had no faults and was the only good man of his time" (Genesis 6:9-22). Furthermore, the idea of fatherhood or patriarchial love can be well understood by alluding to Abraham, who was the ancestor of many nations (Genesis 17:3-6). Finally, Cain is an excellent example to convey banishment, rejection, or evil, for he was cast out of his homeland by God (Genesis 4:12). Thus, allusions serve an important function in writing in that they allow the reader to understand a difficult concept by relating to an already familiar story. See A Handbook to Literature, Literature: An Introduction to Fiction, Poetry, and Drama. Stacey Ann Singletary, Student, University of North Carolina at Pembroke

antagonist (an-TAG-uh-nist): a character in a story or poem who deceives, frustrates, or works again the main character, or protagonist, in some way. The antagonist doesn’t necessarily have to be an person. It could be death, the devil, an illness, or any challenge that prevents the main character from living “happily ever after." In fact, the antagonist could be a character of virtue in a literary work where the protagonist represents evil. An antagonist in the story of Genesis is the serpent. He convinces Eve to disobey God, setting off a chain of events.that leads to Adam and Eve being banished from paradise. In the play Othello by William Shakespeare, the antagonist is Iago. Throughout the play, he instigates conflicts and sows distrust among the main characters, Othello and Desdemona, two lovers who have risked their livelihood in order to elope. Iago is determined to break up their marriage due to his suspicions that Othello has taken certain liberties with his wife. See Benet’s Reader’s Encyclopedia. Victoria Henderson, Student, University of North Carolina at Pembroke

aside (uh-SIDE): an actor’s speech, directed to the audience, that is not supposed to be heard by other actors on stage. An aside is usually used to let the audience know what a character is about to do or what he or she is thinking. For example, in Othello, Iago gives several asides, informing the audience of his plans and how he will try to achieve his goals. Asides are important because they increase an audience's involvement in a play by giving them vital information pertaining what is happening, both inside of a character's

mind and in the plot of the play. See A Handbook to Literature, The Concise Oxford Dictionary of Literary Terms, Merriam Webster’s Encyclopedia of Literature. Dawn Oxendine, Student, University of North Carolina at Pembroke

haracter (KARE-ec-ter): a person who is responsible for the thoughts and actions within a story, poem, or other literature. Characters are extremely important because they are the medium through which a reader interacts with a piece of literature. Every character has his or her own personality, which a creative author uses to assist in forming the plot of a story or creating a mood. The different attitudes, mannerisms, and even appearances of characters can greatly influence the other major elements in a literary work, such as theme, setting, and tone. With this understanding of the character, a reader can become more aware of other aspects of literature, such as symbolism, giving the reader a more complete understanding of the work. The character is one of the most important tools available to the author. In the ballad "Edward," for instance, the character himself sets the tone of the ballad within the first stanza. After reading the first few stanzas, one learns that Edward has murdered his father and is very distraught. His attitude changes to disgust and finally to despair when he realizes the consequences he must face for his actions. An example of the attitudes and personalities of characters determining the theme is also seen in the book of Genesis. The proud personality of Cain and the humble personality of Abel help create the conflict for this story. Cain and Abel were brothers, possibly twins, who displayed intense sibling rivalry. God was not pleased with Cain's offerings, but found pleasure in Abel's offerings. Provoked by God's displeasure with him, Cain murdered his own brother out of jealousy. Victoria Henderson, Student, University of North Carolina at Pembroke

connotation (KAH-nuh-TAE-shun): an association that comes along with a particular word. Connotations relate not to a word's actual meaning, or denotation, but rather to the ideas or qualities that are implied by that word. A good example is the word "gold." The denotation of gold is a malleable, ductile, yellow element. The connotations, however, are the ideas associated with gold, such as greed, luxury, or avarice. Another example occurs in the Book of Genesis. Jacob says: “Dan will be a serpent by the roadside, a viper along the path, that bites the horse’s heels so that its rider tumbles backward" (Gen 49:17). In this passage, Dan is not literally going to become a snake. However, describing Dan as a "snake" and "viper" forces the reader to associate him with the negative qualities that are commonly associated with reptiles, such as slyness, danger, and evil. Dan becomes like a snake, sly and dangerous to the riders. Writers use connotation to make their writing more vivid and interesting to read. See A Dictionary of Literary Terms and Literary Theory. Jennifer Lance, Student, University of North Carolina at Pembroke

couplet (KUP-let): a style of poetry defined as a complete thought written in two lines with rhyming ends. The most popular of the couplets is the heroic couplet. The heroic couplet consists of two rhyming lines of iambic pentameter usually having a pause in the middle of each line. One of William Shakespeare’s trademarks was to end a sonnet with a couplet, as in the poem “Shall I Compare Thee to a Summer’s Day”:

So long as men can breathe or eyes can see, So long as lives this, and this gives life to thee.

By using the couplet Shakespeare would often signal the end of a scene in his plays as well. An example of a scene’s end signaled by a couplet is the end of Act IV of Othello. The scene ends with Desdemona’s lines:

Good night. Good night. Heaven me such uses send. Not to pick bad from bad, but by bad mend.

See A Handbook to Literature, Benet’s Reader’s Encyclopedia, Mirriam-Webster’s Encyclopedia of Literature, Literature: An Introduction to Fiction, Poetry, and Drama. Monica Horne, Student, University of North Carolina at Pembroke

denotation (DEE-no-TAE-shuhn): the exact meaning of a word, without the feelings or suggestions that the word may imply. It is the opposite of “connotation” in that it is the “dictionary” meaning of a word, without attached feelings or associations. Some examples of denotations are:

1. heart: an organ that circulates blood throughout the body. Here the word "heart" denotes the actual organ, while in another context, the word "heart" may connote feelings of love or heartache. 2. sweater: a knitted garment for the upper body. The word "sweater" may denote pullover sweaters or cardigans, while “sweater” may also connote feelings of warmness or security.

Denotation allows the reader to know the exact meaning of a word so that he or she will better understand the work of literature. See Literature: An Introduction to Fiction, Poetry, and Drama, A Glossary of Literary Terms, A Dictionary of Literary Terms and Literary Theory, Webster’s Dictionary. Shana Locklear, Student, University of North Carolina at Pembroke

denouement (day-noo-mon): literally meaning the action of untying, a denouement is the final outcome of the main complication in a play or story. Usually the climax (the turning point or "crisis") of the work has already occurred by the time the denouement occurs. It is sometimes referred to as the explanation or outcome of a drama that reveals all the secrets and misunderstandings connected to the plot. In the drama Othello, there is a plot to deceive Othello into believing that his wife, Desdemona, has been unfaithful to him. As a result of this plot, Othello kills his wife out of jealousy, the climax of the play. The denounement occurs soon after, when Emilia, who was Desdemona's mistress, proves to Othello that his wife was in fact honest, true, and faithful to him. Emilia reveals to Othello that her husband, Iago, had plotted against Desdemona and tricked Othello into believing that she had been unfaithful. Iago kills Emilia in front of Othello, and she dies telling Othello his wife was innocent. As a result of being mad with grief, Othello plunges a dagger into his own heart. Understanding the denouement helps the reader to see how the final end of a story unfolds, and how the structure of stories works to affect

our emotions. See Encyclopedia of Literature, Miriam Webster. Shelby Locklear, Student, University of North Carolina at Pembroke

dialogue (di-UH-log): The conversation between characters in a drama or narrative. A dialouge occurs in most works of literature. For example, many ballads demonstrate a ocnversation between two or more characters. In the anonymous ballad, "Sir Patrick Spens", we are able to observe the dialogue between Sir Patrick Spens and his mirry men. In the verses 21-24, "Mak hast, mak haste, my mirry men all, Our guid schip sails the morne: O say na sae, my master deir, for I feir a deadline storme," dialogue can be seen. According to A Handbook of Literature, dialogue serves several functions in literature. It moves the action along in a work and it also helps to characterize the personality of the speakers, which vary depending on their nationalities, jobs, social classes, and educations. It also gives literature a more natural, conversational flow, which makes it more readable and enjoyable. By showcasing human interaction, dialogue prevents literature from being nothing more than a list of descriptions and actions. Dialogue varies in structure and tone depending on the people participating in the conversation and the mood that the author is trying to maintain in his or her writing. See A Handbook to Literature,The American Heritage Dictionary. Ramon Gonzalez, Student, University of North Carolina at Pembroke

didactic (di-DAK-tik): refers to literature or other types of art that are instructional or informative. In this sense The Bible is didactic because it offers guidance in moral, religious, and ethical matters. It tells stories of the lives of people that followed Christian teachings, and stories of people that decided to go against God and the consequences that they faced. The term "didactic" also refers to texts that are overburdened with instructive and factual information, sometimes to the detriment of a reader's enjoyment. The opposite of "didactic" is "nondidactic." If a writer is more concerned with artistic qualities and techniques than with conveying a message, then that piece of work is considered to be nondidactic, even if it is instructive. See Encyclopedia of Literature, Benet's Readers Encyclopedia. Jennifer Baker, University of North Carolina at Pembroke

Check your progress

1. Explain A simple make a file

2. Explain Various types

Reference

1.^ Greenwood CR (May 1991). "Longitudinal analysis of time, engagement, and achievement in at-risk versus non-risk students". Except Child 57 (6): 521–35. PMID 2070811.

2.^ Ellis, Edwin (2002). "Watering Up the Curriculum for Adolescents with Learning Disabilities, Part I: Goals of the Knowledge Dimension". WETA. Retrieved 2010-04-21.

3.Carol A. Breckenridge; Candace Vogler (2001). "The Critical Limits of Embodiment: Disability's Criticism". Public Culture. Duke Univ Press. pp. 349–357.

4.^ Amanda M. Vanderheyden; Joseph C Witt, Gale Naquin (2003). "Development And Validation Of A Process For Screening Referrals To Special Education". School Psychology Review (Research and Read Books, Journals, Articles at Questia Online Library) 32

5..^ "Disability standards for education".

6.^ Robert Holland (2002-06-01). "Vouchers Help the Learning Disabled". School Reform News (The Heartland Institute).

7.^ "Special education needs, Special needs education".

8.^ Management of Inclusion. The SENCO Resource Centre, part 3.

9.^ Karen Zittleman; Sadker, David Miller (2006). Teachers, Schools and Society: A Brief Introduction to Education with Bind-in Online Learning Center Card with free Student Reader CD-ROM. McGraw-Hill Humanities/Social Sciences/Languages. pp. 48, 49, 108, G–12. ISBN 0-07-323007-3.

10.^ Priscilla Pardini (2002). "The History of Special Education". Rethinking Schools 16 (3).

11.^ a b Blanchett, W. J. (2009). A retrospective examination of urban education: From "brown" to the resegregation of African Americans in special education--it is time to "go for broke". Urban Education, 44(4), 370-388.

12.^ Tejeda-Delgado, M. (2009). Teacher efficacy, tolerance, gender, and years of experience and special education referrals. International Journal of Special Education, 24(1), 112-119.

13.^ Ladson-Billings, Gloria (1994). The dreamkeepers: successful teachers of African American children. San Francisco: Jossey-Bass Publishers. ISBN 1-55542-668-9. OCLC 30072651.

14.^ Cortiella, C. (2009). The State of Learning Disabilities. New York, NY: National Center for Learning Disabilities.

Check your progress answers

1. refer 3.2

2. refer 3.4

Unit 4: Case Studies using Formex Algebra

4.1 Introduction4.2 Pyformex4.3 Case study4.4 Hotel hesperia’s glazed dome

4.4.1 Generation of the geomentry using pyformex4.4.2 Facetted shell structure of glass

4.5 Types of cases4.6 Algebra4.7 Elementry Algebra4.8 Polynomials4.9 Abstract algebra4.10 Objects called algebra

4.1 Introduction

Since more than a decade, the application of glass in buildings has been gradually expanding from cladding and infill applications towards primary load-bearing building components. Examples of such relatively transparent components are

i) glass beams that support a glass roof or floor,ii) glass fins that act as stiffeners against wind loads on a façade,iii) glass columns, iv) folded glass plate structures [15] andv) glass domes.

In this last category, some examples exist in recent glass-building history, e.g. the self-supporting glass-and-cable dome presented by Glasbau Seele at the 1998 glasstec fair in Düsseldorf [17]; the built prototype for a garden pavilion with flat, replaceable trapezoidal monolithic glass panels at Delft University of Technology [5], [16], [17]; the conceptual study for a ring grid dome with incorporated sun shading textiles in Aachen [17], the structurally bonded spherical dome with doublecurved laminated glass panels, created by Blandini and Sobek at Stuttgart University (ILEK) [1], [4]; and recently the glazed dome of the EVO restaurant on top of the Hesperia Tower hotel in Barcelona [14].

4.2 pyFormex

pyFormex was developed by Verhegghe at Ghent University for the automated design of spatial structures and the generation of complex three-dimensional geometries by means of sequences of mathematical transformations [9]. Furthermore, pyFormex can be useful for structural analysis purposes, for operations on surface models or simply for generating illustrations. pyFormex is a Python implementation of Formex algebra, pioneered by Nooshin [12].

It implements most features of the Formian language [9], but has far wider aspirations. Being an open source project and programmed in Python, pyFormex is fully open to quickly create extensions, including analysis modules, interfaces with other programs, customizations of the GUI. Python also allows for a much neater scripting language, where logically named operators perform different action depending on the operands. Because of all this, the field of applications of pyFormex has quickly broadened way beyond that of spatial structures. Originally developed in a Linux environment, pyFormex can be used, however, in a Windows environment as well.

The software is based on a script, from which a whole construction can be generated using only a limited number of command lines [8]. Typical Formex operations used in scripts are related to copying, translating, rotating, scaling, etcetera. The major advantage of this modus operandi is that parameters (e.g. dimensions,

material properties, ...) can easily be replaced and consequently a multitude of different configurations of the same geometry can be generated in a limited period of time. Also because of the scripting, there is virtually no limitation to the geometries that pyFormex can generate other than one’s own imagination (see online examples, [7]).

The development of pyFormex is an ongoing process, presented as an open source project: the program can be used, studied, modified and distributed under the conditions of the GNU Genral Public License (GPL) [6]. For the time being, the program is already in use in both a research and educational context. Future developments of this tool include interactive tools, surface and volume meshing, post-processing, distribution and installation.

pyFormex is a program for generating, transforming and manipulating large geometrical models of 3D structures by sequences of mathematical operations. Thanks to a powerful (Python based) scripting language, pyFormex is very well suited for the automated design of spatial frame structures. It provides a wide range of operations on surface meshes, like STL type triangulated surfaces. There are provisions to import medical scan images. pyFormex can also be used as a pre- and post-processor for Finite Element analysis programs. Finally, it might be used just for creating some nice graphics.

Using pyFormex, the topology of the elements and the final geometrical form can be decoupled. Often, topology is created first and then mapped onto the geometry. Through the scripting language, the user can define any sequence of transformations, built from provided or user defined functions. This way, building parametric models becomes a natural thing.

pyFormex is a Python implementation of Formex algebra. Using pyFormex, it is very easy to generate large geometrical models of 3D structures by a sequence of mathematical transformations. It is especially suited for the automated design of spatial structures. But it can also be used for other tasks, like operating on 3D geometry obtained from other sources, or for finite element pre- and postprocessing, or just for creating some nice pictures.

By writing a simple script, a large and complex geometry can be created by copying, translating, rotating, or otherwise transforming geometrical entities. pyFormex will interpret the script and draw what you have created. This is clearly very different from the traditional (mostly interactive) way of creating a geometrical model, like is done in most CAD packages. There are some huge advantages in using pyFormex:

• It is especially suited for the automated design of spatial frame structures. A dome, an arc, a hypar shell, ..., when constructed as a space frame, can be rather difficult and tedious to draw with a general CAD program; using scripted mathematical transformations however, it may become a trivial task.

• Using a script makes it very easy to apply changes in the geometry: you simply modify the script and re-execute it. You can easily change the value of a geometrical parameter in any way you want: set it directly, interactively ask it from the user, calculate it from some formula, read it from a file, etcetera. Using CAD, you would have often have to completely redo your drawing work. The power of scripted geometry building is illustrated in figure Same script, different domes: all these domes were created with the same script, but with different values of some parameters.

4.3 Case studies

A case study is a research method common in social science. It is based on an in-depth investigation of a single individual, group, or event. Case studies may be descriptive or explanatory. The latter type is used to explore causation in order to find underlying principles.[1][2] They may be prospective, in which criteria are established and cases fitting the criteria are included as they become available, or retrospective, in which criteria are established for selecting cases from historical records for inclusion in the study.

Rather than using samples and following a rigid protocol (strict set of rules) to examine limited number of variables, case study methods involve an in-depth, longitudinal (over a long period of time) examination of a single instance or event: a case. They provide a systematic way of looking at events, collecting data, analyzing information, and reporting the results. As a result the researcher may gain a sharpened understanding of why the instance happened as it did, and what might become important to look at more extensively in future research. Case studies lend themselves to both generating and testing hypotheses.[3]

Another suggestion is that case study should be defined as a research strategy, an empirical inquiry that investigates a phenomenon within its real-life context. Case study research means single and multiple case studies, can include quantitative evidence, relies on multiple sources of evidence and benefits from the prior development of theoretical propositions. Case studies should not be confused with qualitative research and they can be based on any mix of quantitative and qualitative evidence. Single-subject research provides the statistical framework for making inferences from quantitative case-study data.[2][4] This is also supported and well-formulated in (Lamnek, 2005): "The case study is a research approach, situated between concrete data taking techniques and methodologic paradigms."

4.4 Hotel Hesperia’s glazed dome

The Hesperia Tower is a hotel situated in the district of Bellvitge in L'Hospitalet de Llobregat, Catalonia, Spain.

It has a tower of 28 storeys and 105 metres (344 ft). It was the tallest building in L'Hospitalet until the Plaza Europa Towers were constructed. It is topped by a glass dome that contains a revolving restaurant headed by chef Santi Santamaria. It was designed by the British architect Richard Rogers together with Luis Alonso and Sergi Balaguer. It has 280 rooms, a 5,000 square metres (53,800 sq ft) sq m congress centre, and a sports centre.

A tile is a manufactured piece of hard-wearing material such as ceramic, stone, metal, or even glass. Tiles are generally used for covering roofs, floors, walls, showers, or other objects such as tabletops. Alternatively, tile can sometimes refer to similar units made from lightweight materials such as perlite, wood, and mineral wool, typically used for wall and ceiling applications. Less precisely, the modern term can refer to any sort of construction tile or similar object, such as rectangular counters used in playing games (see tile-based game). The word is derived from the French word tuile, which is, in turn, from the Latin word tegula, meaning a roof tile composed of fired clay.

Tiles are often used to form wall and floor coverings, and can range from simple square tiles to complex mosaics. Tiles are most often made from porcelain, fired clay or ceramic with a hard glaze, but other materials are also commonly used, such as glass, metal, cork, and stone. Tiling stone is typically marble, onyx, granite or slate. Thinner tiles can be used on walls than on floors, which require thicker, more durable surfaces.

4.4.1 Generation of the geometry using pyFormex

A part from its unique location at 95 m atop a hotel tower, the relatively large size and high geometric complexity of the Hotel Hesperia’s glazed dome make it a very interesting example of a recent construction on which some of the possibilities of pyFormex can be illustrated a posteriori The interested reader can find a detailed description of the project in literature [14].visualises the according step-by-step generation of the structure.

A shell structure made of glass combines a light-weight structural concept with glass’ high permeability to light. If the geometry of the structure is plane-based facetted (plate shell structure), the glass elements will be plane panes, and these glass panes will comprise the primary load-bearing structure. A plate shell structure is contrary to a triangulated facetted shell structure, where the shell action is concentrated in the edges and vertices of the geometry, thereby resulting in the need for a triangulated lattice structure outlining the edges of the geometry.

These two structural principles (plate shells and triangulated lattice shells) may not differ in complexity regarding the topology, but when it comes to the practical generation of the geometry, e.g. in CAD, the plate shell is far more troublesome to handle than the triangulated geometry. The free software tool “pyFormex”, developed at Ghent University, has been used to accommodate a parametric generation of plate shell structures. This generation includes the basic facetted shell geometry, joint areas that reproduce given connection characteristics, loads and boundary conditions. From

pyFormex the model is exported to the finite element analysis software Abaqus as a Python script, which translates the information to an Abaqus CAE-model. In pyFormex the model has been prepared for applying the meshing in Abaqus, by allocation of edge seeds, and by defining geometry sets for easy handling.

4.4.2 Facetted shell structure of glass

Bagger et al. already pointed out that facetted shell structures are feasible to create highly transparent glass constructions without additional supporting structure: loads should basically be taken by in-plane stresses in the glass facets and transferred from one facet to another by distributed forces along the edges [1]. Even though many practical issues currently could still be questioned (e.g. high costs for manufacturing polygonal glass panes with high geometrical precision, development of suitable edge connection methods, erection methods,…), the idea seems very valuable from a theoretical point of view. Obviously, in such a concept all facets of a glass construction should by perfectly planar.

One might be tempted to use the same simple approach as for the Hesperia example: subdividing the facets of the icosahedron in a hexagonal base pattern and then projecting it on a sphere. While this leads to a nice hexagonal dome, the hexagons in it are not fully planar.

An average, or typical, case is often not the richest in information. In clarifying lines of history and causation it is more useful to select subjects that offer an interesting, unusual or particularly revealing set of circumstances. A case selection that is based on representativeness will seldom be able to produce these kinds of insights.

When selecting a subject for a case study, researchers will therefore use information-oriented sampling, as opposed to random sampling. Outlier cases (that is, those which are extreme, deviant or atypical) reveal more information than the putatively representative case. Alternatively, a case may be selected as a key case, chosen because of the inherent interest of the case or the circumstances surrounding it. Or it may be chosen because of researchers' in-depth local knowledge; where researchers have this local knowledge they are in a position to “soak and poke” as Fenno puts it, and thereby to offer reasoned lines of explanation based on this rich knowledge of setting and circumstances.

Facetted shell structure of glass

Anne Bagger & Jeppe Jönsson & Henrik Almegaard, BYG-DTU, Technical University of Denmark & Ture Wester, Royal Danish Academy of Arts, School of Architecture

In shell structures, which are appropriately shaped and supported, bending stresses are minimized, and loading is transferred primarily via in plane stresses (membrane stresses). This allows for a better utilization of the capacity of the structural material, since stresses

are distributed evenly over the thickness of the structure in stead of concentrated at the surfaces. The stiffness to weight ratio of a shell structure is remarkably good, since the absorption of loads is provided by the overall global shape of the structure, and not a local sectional area. Glass is already widely used for load carrying structural members like fins, beams and columns.

The structural use of glass is troubled by a brittle behaviour of the material, and a limited capacity for carrying tension forces. However, these characteristics can be taken into account in the design process in various ways. If the glass is used as the load carrying material in a shell structure, bending can be avoided, and the stress level can be minimized to a remarkably low level. In order to avoid the high production cost of doubly curved glass, facetted glass shell structures are considered.

The faceting of a given curved surface can be done in many ways, but if the procedure is subjected to specific constraints, certain advantageous characteristics can be achieved. A plane-based faceting, where all vertices have three adjoining facets, results in a structure which carries load via in-plane stresses distributed in the facets, and the distributed shear along the edges. This corresponds well to glass being the load carrying material, since stress concentrations are avoided.

4.5 Types of cases

Three types of cases may thus be distinguished:

1. Key cases2. Outlier cases3. Local knowledge cases

Whatever the frame of reference for the choice of the subject of the case study (key, outlier, local knowledge), there is a distinction to be made between the subject and the object of the case study. The subject is the “practical, historical unity” through which the theoretical focus of the study is being viewed. The object is that theoretical focus – the analytical frame. Thus, for example, if a researcher were interested in US resistance to communist expansion as a theoretical focus, then the Korean War might be taken to be the subject, the lens, the case study through which the theoretical focus, the object, could be viewed and explicated.

Beyond decisions about case selection and the subject and object of the study, decisions need to be made about purpose, approach and process in the case study. Thomas thus proposes a typology for the case study wherein purposes are first identified (evaluative or exploratory), then approaches are delineated (theory-testing, theory-building or illustrative), then processes are decided upon, with a principal choice being between whether the study is to be single or multiple, and choices also about whether the study is to be retrospective, snapshot or diachronic, and whether it is nested, parallel or sequential. It is thus possible to take many routes through this typology, with, for example, an exploratory, theory-building, multiple, nested study, or an evaluative, theory-

testing, single, retrospective study. The typology thus offers many permutations for case study structure.

A critical case can be defined as having strategic importance in relation to the general problem. A critical case allows the following type of generalization, ‘If it is valid for this case, it is valid for all (or many) cases.’ In its negative form, the generalization would be, ‘If it is not valid for this case, then it is not valid for any (or only few) cases.’

The case study is also effective for generalizing using the type of test that Karl Popper called falsification, which forms part of critical reflexivity. Falsification is one of the most rigorous tests to which a scientific proposition can be subjected: if just one observation does not fit with the proposition it is considered not valid generally and must therefore be either revised or rejected. Popper himself used the now famous example of, "All swans are white," and proposed that just one observation of a single black swan would falsify this proposition and in this way have general significance and stimulate further investigations and theory-building. The case study is well suited for identifying "black swans" because of its in-depth approach: what appears to be "white" often turns out on closer examination to be "black."

For Galileo Galilei’s rejection of Aristotle’s law of gravity was based on a case study selected by information-oriented sampling and not random sampling. The rejection consisted primarily of a conceptual experiment and later on of a practical one. These experiments, with the benefit of hindsight, are self-evident. Nevertheless, Aristotle’s incorrect view of gravity dominated scientific inquiry for nearly two thousand years before it was falsified. In his experimental thinking, Galileo reasoned as follows: if two objects with the same weight are released from the same height at the same time, they will hit the ground simultaneously, having fallen at the same speed. If the two objects are then stuck together into one, this object will have double the weight and will according to the Aristotelian view therefore fall faster than the two individual objects. This conclusion seemed contradictory to Galileo. The only way to avoid the contradiction was to eliminate weight as a determinant factor for acceleration in free fall. Galileo’s experimentalism did not involve a large random sample of trials of objects falling from a wide range of randomly selected heights under varying wind conditions, and so on. Rather, it was a matter of a single experiment, that is, a case study.(Flyvbjerg, 2006, p. 225-6) [2]

Galileo’s view continued to be subjected to doubt, however, and the Aristotelian view was not finally rejected until half a century later, with the invention of the air pump. The air pump made it possible to conduct the ultimate experiment, known by every pupil, whereby a coin or a piece of lead inside a vacuum tube falls with the same speed as a feather. After this experiment, Aristotle’s view could be maintained no longer. What is especially worth noting, however, is that the matter was settled by an individual case due to the clever choice of the extremes of metal and feather. One might call it a critical case, for if Galileo’s thesis held for these materials, it could be expected to be valid for all or a large range of materials. Random and large samples were at no time part of the picture.

However it was Galileo's view that was the subject of doubt as it was not reasonable enough to be the Aristotelian view.

4.6 Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

Elementary algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers, such as addition. This can be done for a variety of reasons, including equation solving. Algebra is much broader than elementary algebra and studies what happens when different rules of operations are used and when operations are devised for things other than numbers. Addition and multiplication can be generalized and their precise definitions lead to structures such as groups, rings and fields, studied in the area of mathematics called abstract algebra.

Algebra may be divided roughly into the following categories:

• Elementary algebra, in which the properties of operations on the real number system are recorded using symbols as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied. This is usually taught at school under the title algebra (or intermediate algebra and college algebra in subsequent years). University-level courses in group theory may also be called elementary algebra.

• Abstract algebra, sometimes also called modern algebra, in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated.

• Linear algebra, in which the specific properties of vector spaces are studied (including matrices);

• Universal algebra, in which properties common to all algebraic structures are studied.

• Algebraic number theory, in which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.

• Algebraic geometry applies abstract algebra to the problems of geometry.• Algebraic combinatorics, in which abstract algebraic methods are used to study

combinatorial questions.

In some directions of advanced study, axiomatic algebraic systems such as groups, rings, fields, and algebras over a field are investigated in the presence of a geometric

structure (a metric or a topology) which is compatible with the algebraic structure. The list includes a number of areas of functional analysis:

• Normed linear spaces• Banach spaces• Hilbert spaces• Banach algebras• Normed algebras• Topological algebras• Topological groups

4.7 Elementary algebra

Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often denoted by symbols (such as a, x, or y). This is useful because:

• It allows the general formulation of arithmetical laws (such as a + b = b + a for all a and b), and thus is the first step to a systematic exploration of the properties of the real number system.

• It allows the reference to "unknown" numbers, the formulation of equations and the study of how to solve these. (For instance, "Find a number x such that 3x + 1 = 10" or going a bit further "Find a number x such that ax+b=c". This step leads to the conclusion that it is not the nature of the specific numbers that allows us to solve it, but that of the operations involved.)

• It allows the formulation of functional relationships. (For instance, "If you sell x tickets, then your profit will be 3x − 10 dollars, or f(x) = 3x − 10, where f is the function, and x is the number to which the function is applied.")

4.8 Polynomials

A polynomial is an expression that is constructed from one or more variables and constants, using only the operations of addition, subtraction, and multiplication (where repeated multiplication of the same variable is standardly denoted as exponentiation with a constant nonnegative integer exponent). For example, x2 + 2x − 3 is a polynomial in the single variable x.

An important class of problems in algebra is factorization of polynomials, that is, expressing a given polynomial as a product of other polynomials. The example polynomial above can be factored as (x − 1)(x + 3). A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.

4.9Abstract algebra

Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts.

Sets: Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets: a collection of all objects (called elements) selected by property, specific for the set. All collections of the familiar types of numbers are sets. Other examples of sets include the set of all two-by-two matrices, the set of all second-degree polynomials (ax2 + bx + c), the set of all two dimensional vectors in the plane, and the various finite groups such as the cyclic groups which are the group of integers modulo n. Set theory is a branch of logic and not technically a branch of algebra.

Binary operations: The notion of addition (+) is abstracted to give a binary operation, ∗ say. The notion of binary operation is meaningless without the set on which the operation is defined. For two elements a and b in a set S, a ∗ b is another element in the set; this condition is called closure. Addition (+), subtraction (-), multiplication (×), and division (÷) can be binary operations when defined on different sets, as is addition and multiplication of matrices, vectors, and polynomials.

Identity elements: The numbers zero and one are abstracted to give the notion of an identity element for an operation. Zero is the identity element for addition and one is the identity element for multiplication. For a general binary operator ∗ the identity element e must satisfy a ∗ e = a and e ∗ a = a. This holds for addition as a + 0 = a and 0 + a = a and multiplication a × 1 = a and 1 × a = a. Not all set and operator combinations have an identity element; for example, the positive natural numbers (1, 2, 3, ...) have no identity element for addition.

Inverse elements: The negative numbers give rise to the concept of inverse elements. For addition, the inverse of a is −a, and for multiplication the inverse is 1/a. A general inverse element a−1 must satisfy the property that a ∗ a−1 = e and a−1 ∗ a = e.

Associativity: Addition of integers has a property called associativity. That is, the grouping of the numbers to be added does not affect the sum. For example: (2 + 3) + 4 = 2 + (3 + 4). In general, this becomes (a ∗ b) ∗ c = a ∗ (b ∗ c). This property is shared by most binary operations, but not subtraction or division or octonion multiplication.

Commutativity: Addition and multiplication of real numbers are both commutative. That is, the order of the numbers does not affect the result. For example: 2+3=3+2. In general, this becomes a ∗ b = b ∗ a. This property does not hold for all binary operations. For example, matrix multiplication and quaternion multiplication are both non-commutative.

GroupsMain article: Group (mathematics)See also: Group theory and Examples of groups

Combining the above concepts gives one of the most important structures in mathematics: a group. A group is a combination of a set S and a single binary operation ∗, defined in any way you choose, but with the following properties:

• An identity element e exists, such that for every member a of S, e ∗ a and a ∗ e are both identical to a.

• Every element has an inverse: for every member a of S, there exists a member a−1

such that a ∗ a−1 and a−1 ∗ a are both identical to the identity element.• The operation is associative: if a, b and c are members of S, then (a ∗ b) ∗ c is

identical to a ∗ (b ∗ c).

If a group is also commutative—that is, for any two members a and b of S, a ∗ b is identical to b ∗ a—then the group is said to be Abelian.

For example, the set of integers under the operation of addition is a group. In this group, the identity element is 0 and the inverse of any element a is its negation, −a. The associativity requirement is met, because for any integers a, b and c, (a + b) + c = a + (b + c)

The nonzero rational numbers form a group under multiplication. Here, the identity element is 1, since 1 × a = a × 1 = a for any rational number a. The inverse of a is 1/a, since a × 1/a = 1.

The integers under the multiplication operation, however, do not form a group. This is because, in general, the multiplicative inverse of an integer is not an integer. For example, 4 is an integer, but its multiplicative inverse is ¼, which is not an integer.

The theory of groups is studied in group theory. A major result in this theory is the classification of finite simple groups, mostly published between about 1955 and 1983, which is thought to classify all of the finite simple groups into roughly 30 basic types.

Rings and fieldsMain articles: ring (mathematics) and field (mathematics)See also: Ring theory, Glossary of ring theory, Field theory (mathematics), and glossary of field theory

Groups just have one binary operation. To fully explain the behaviour of the different types of numbers, structures with two operators need to be studied. The most important of these are rings, and fields.

A ring has two binary operations (+) and (×), with × distributive over +. Under the first operator (+) it forms an Abelian group. Under the second operator (×) it is associative, but it does not need to have identity, or inverse, so division is not allowed. The additive (+) identity element is written as 0 and the additive inverse of a is written as −a.

Distributivity generalises the distributive law for numbers, and specifies the order in which the operators should be applied, (called the precedence). For the integers (a + b) × c = a × c + b × c and c × (a + b) = c × a + c × b, and × is said to be distributive over +.

The integers are an example of a ring. The integers have additional properties which make it an integral domain.

A field is a ring with the additional property that all the elements excluding 0 form an Abelian group under ×. The multiplicative (×) identity is written as 1 and the multiplicative inverse of a is written as a−1.

The rational numbers, the real numbers and the complex numbers are all examples of fields.

4.10 Objects called algebras

The word algebra is also used for various algebraic structures:

• Algebra over a field or more generally Algebra over a ring• Algebra over a set• Boolean algebra• Heyting algebra• F-algebra and F-coalgebra in category theory• Relational algebra• Sigma-algebra• T-Algebras of monads.

Glossary:

abc conjectureThe abc conjecture of Masser and Oesterlé attempts to state as much as possible about repeated prime factors in an equation a + b = c. For example 3 + 125 = 128 but the prime powers here are exceptional.

Arakelov theoryArakelov theory is an approach to arithmetic geometry that explicitly includes the 'infinite primes'.

Arithmetic of abelian varietiesSee main article arithmetic of abelian varieties

Artin L-functionsArtin L-functions are defined for quite general Galois representations. The introduction of étale cohomology in the 1960s meant that Hasse-Weil L-functions (q.v.) could be regarded as Artin L-functions for the Galois representations on l-adic cohomology groups.

Bad reductionSee good reduction.

Birch and Swinnerton-Dyer conjecture

The Birch and Swinnerton-Dyer conjecture on elliptic curves postulates a connection between the rank of an elliptic curve and the order of pole of its Hasse-Weil L-function. It has been an important landmark in Diophantine geometry since the mid-1960s, with important results such as the Coates–Wiles theorem, Gross–Zagier theorem and Kolyvagin's theorem

Bombieri–Lang conjectureEnrico Bombieri, Serge Lang and Paul Vojta have conjectured that algebraic varieties of general type do not have Zariski dense subsets of K-rational points, for K a finitely-generated field. This circle of ideas includes the understanding of analytic hyperbolicity and the Lang conjectures on that, and the Vojta conjectures. An analytically holomorphic algebraic variety V over the complex numbers is one such that no holomorphic mapping from the whole complex plane to it exists, that is not constant. Examples include compact Riemann surfaces of genus g > 1. Lang conjectured that V is analytically holomorphic if and only if all subvarieties are of general type.

Canonical heightThe canonical height on an abelian variety is a height function that is a distinguished quadratic form. See Néron-Tate height.

Chabauty's methodChabauty's method, based on p-adic analytic functions, is a special application but capable of proving cases of the Mordell conjecture for curves whose Jacobian's rank is less than its dimension. It developed ideas from Thoralf Skolem's method for an algebraic torus. (Other older methods for Diophantine problems include Runge's method.)

Crystalline cohomologyCrystalline cohomology is a p-adic cohomology theory in characteristic p, introduced by Alexander Grothendieck to fill the gap left by étale cohomology which is deficient in using mod p coefficients in this case. It is one of a number of theories deriving in some way from Dwork's method (q.v.), and has applications outside purely arithmetical questions.

Diagonal formsDiagonal forms are some of the simplest projective varieties to study from an arithmetic point of view (including the Fermat varieties). Their local zeta-functions are computed in terms of Jacobi sums. Waring's problem is the most classical case.

Dwork's methodBernard Dwork used distinctive methods of p-adic analysis, p-adic algebraic differential equations, Koszul complexes and other techniques that have not all been absorbed into general theories such as crystalline cohomology (q.v.). He first proved the rationality of local zeta-functions, the initial advance in the direction of the Weil conjectures (q.v.)

Étale cohomologyThe search for a Weil cohomology (q.v.) was at least partially fulfilled in the étale cohomology theory of Alexander Grothendieck and Michael Artin. It provided a proof of the functional equation for the local zeta-functions, and was basic in the formulation of the Tate conjecture (q.v.) and numerous other theories.

Fermat's last theoremFermat's last theorem, the most celebrated conjecture of Diophantine geometry, was proved by Andrew Wiles and Richard Taylor.

Flat cohomologyFlat cohomology is, for the school of Grothendieck, one terminal point of development. It has the disadvantage of being quite hard to compute with. The reason that the flat topology has been considered the 'right' foundational topos for scheme theory goes back to the fact of faithfully-flat descent, the discovery of Grothendieck that the representable functors are sheaves for it (i.e. a very general gluing axiom holds).

Function field analogyIt was realised in the nineteenth century that the ring of integers of a number field has analogies with the affine coordinate ring of an algebraic curve or compact Riemann surface, with a point or more removed corresponding to the 'infinite places' of a number field. This idea is more precisely encoded in the theory that global fields should all be treated on the same basis. The idea goes further. Thus elliptic surfaces over the complex numbers, also, have some quite strict analogies with elliptic curves over number fields.

Geometric class field theoryThe extension of class field theory-style results on abelian coverings to varieties of dimension at least two is often called geometric class field theory.

Good reductionFundamental to local analysis in arithmetic problems is to reduce modulo all prime numbers p. In the typical situation this presents little difficulty for almost all p; for example denominators of fractions are tricky, in that reduction modulo a prime in the denominator looks like division by zero, but that rules out only finitely many p per fraction. With a little extra sophistication, homogeneous coordinates allow clearing of denominators by multiplying by a common scalar. For a given, single point one can do this and not leave a common factor p. However singularity theory enters: a non-singular point may become a singular point on reduction modulo p, because the Zariski tangent space can become larger when linear terms reduce to 0 (the geometric formulation shows it is not the fault of a single set of coordinates). Good reduction therefore excludes a finite set S of primes for a given variety V, assumed smooth, such that there is otherwise a smooth reduced Vp over Z/pZ. The theory is subtle, in the sense that the freedom to change variables to try to improve matters is rather unobvious: see Néron model, potential good reduction, Tate curve, semistable abelian variety, semistable elliptic curve, Ogg-Néron-Shafarevich criterion, Serre-Tate theorem.

Grothendieck-Katz conjectureThe Grothendieck-Katz p-curvature conjecture applies reduction modulo primes to algebraic differential equations, to derive information on algebraic function solutions. It is an open problem as of 2005. The initial result of this type was Eisenstein's theorem.

Check your progress:

Explain casestudy of formex algebraExplain types of casesExplain Elementry algebra

Reference:

1. ^ (Boyer 1991, "Europe in the Middle Ages" p. 258) "In the arithmetical theorems in Euclid's Elements VII-IX, numbers had been represented by line segments to which letters had been had been attached, and the geometric proofs in al-Khwarizmi's Algebra made use of lettered diagrams; but all coefficients in the equations used in the Algebra are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry."2. ^ Florian Cajori (2010). "A History of Elementary Mathematics – With Hints on Methods of Teaching". p.34. ISBN 1-4460-2221-83. ^ "A Brief History of Zero and Indian Numerals". Brusselsjournal.com. 2009-09-29. Retrieved 2010-09-24.4. ^ Victor J Katz (March 6, 1998), A History of Mathematics: An Introduction (2nd Edition (Paperback) ed.), Addison Wesley, ISBN 0-321-01618-15. ^ Roshdi Rashed (November 2009), Al Khwarizmi: The Beginnings of Algebra, Saqi Books, ISBN 0-86356-430-56. ^ Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications.7. ^ Diophantus, Father of Algebra8. ^ History of Algebra9. ^ Carl B. Boyer, A History of Mathematics, Second Edition (Wiley, 1991), pages 178, 18110. ^ Carl B. Boyer, A History of Mathematics, Second Edition (Wiley, 1991), page 22811. ^ (Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation."12. ^ (Boyer 1991, "The Arabic Hegemony" p. 230) "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwarizmi's exposition that his readers must have had little difficulty in mastering the solutions."13. ^ Gandz and Saloman (1936), The sources of al-Khwarizmi's algebra, Osiris i, p. 263–277: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra

in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers".14. ^ Rashed, R.; Armstrong, Angela (1994), The Development of Arabic Mathematics, Springer, pp. 11–2, ISBN 0-7923-2565-6, OCLC 2918192615. ^ O'Connor, John J.; Robertson, Edmund F., "Sharaf al-Din al-Muzaffar al-Tusi", MacTutor History of Mathematics archive, University of St Andrews.16. ^ Victor J. Katz, Bill Barton; Barton, Bill (October 2007), "Stages in the History of Algebra with Implications for Teaching", Educational Studies in Mathematics (Springer Netherlands) 66 (2): 185–201 [192], doi:10.1007/s10649-006-9023-7

Check your progress answers

Refer 4.3Refer 4.5Refer 4.7