Structural Strength

Structural Strength of Ships, Professor Jönsson1

World Maritime University

Professor Jan-Åke Jönsson, WMU

MSEP 407 June 2005


Longitudinal strength is needed for a bridge over troubled waters!


- Old ship? - Too heavy cargo? - Not properly maintained? - Wrong operation when loading?


SOLAS Part A-1 (Structure of Ship) Regulation 3-1: Structural, mechanical and electrical requirements for ships

In addition to the requirements contained elsewhere in the present regulations, ships shall be designed, constructed and maintained in compliance with the structural, mechanical and electrical requirements of a classification society which is recognized by the Administration in accordance with the provisions of regulation XI/ 1, or with applicable national standards of the Administration which provide an equivalent level of safety


International Convention on Load Lines, 1966

Regulation 1: Strength of Hull The Administration shall satisfy itself that the general structural strength

of the hull is sufficient for the draught corresponding to the free-board assigned. Ships built and maintained in conformity with the require ments of a classification society recognized by the Administration may be considered to possess adequate strength.


Hydrostatic Pressure Diagram

p = ρwater·g·d (N)

F = p·A (Nm)


HSC are reinforced to withstand the higher (hydrostatic + hydrodynamic) water pressure. But that is good for other things also!


Transverse strength to sustain the pressure at bottom and hull sides


Green sea on deck requires a strong deck structure


Structure on the deck to facilitate effective tank cleaning


Pressure from both outside and inside of the hull in the cargo area

The loads acting on transverse bulkheadsmay be divided into two types: Pressure loads directly applied to thebulkheads, and concentrated loadstransmitted via girders.Transverse bulkheads have high-rigiditystool rings arranged around them. A stoolring serves various structural purposes, including reduction of girder span,smooth transmission of girder loads totransverse bulkheads to restrain bendingof the girders and to increase the stiffness of these bulkheads against transverse deformation


Typical bulk carrier section

Hopper sided cargo hold with ballast tanks


Typical modern tanker section

Post 1986 Tanker: Wing and double bottom ballast tanks surround the cargo tanks


SOLAS Chapter II-2, Part C – Fire safety measures for cargo ships

6 Protection of cargo tank structure against pressure or vacuum in tankers

6.1 General The venting arrangements shall be so designed and operated as to ensure that neither pressure nor vacuum in cargo tanks shall exceed design parameters and be such as to provide for:

.1 the flow of the small volumes of vapor, air or inert gas mixtures caused by thermal variations in a cargo tank in all cases through pressure/vacuum valves; and

.2 the passage of large volumes of vapor, air or inert gas mixtures during cargo loading and ballasting, or during discharging



6.3 Safety measures in cargo tanks6.3.2 Secondary means for pressure/vacuum relief

A secondary means of allowing full flow relief of vapour, air or inert gas mixtures shall be provided to prevent over-pressure or under-pressure in the event of failure of the arrangements in paragraph 6.1.2. Alternatively, pressure sensors may be fitted in each tank protected by the arrangement required in paragraph 6.1.2, with a monitoring system in the ship's cargo control room or the position- from which cargo operations are normally carried out. Such monitoring equipment shall also provide an alarm facility which is activated by detection of over-pressure or under- pressure conditions within a tank



6.3.4 Pressure/vacuum-breaking devices One or more pressure/vacuum-breaking devices shall be provided to prevent the cargo tanks from being subject to: .1 a positive pressure, in excess of the test pressure of the cargo tank, if the cargo were to be loaded at the maximum rated capacity and all other outlets are left shut; and .2 a negative pressure in excess of 700 mm water gauge if the cargo were to be discharged at the maximum rated capacity of the cargo pumps and the inert gas blowers were to fail.


Deck structure after over pressure in the cargo tank


Still water Shear Forces & Bending Moment

The hydrostatic lift force due to buoyancy and the weight of theship are normally not of equal magnitude in all parts of the ship.This will give rise to vertical shear and bending forces.


Weight curve and displacement curve LOADING CURVE

Bending Moment

Shearing


Influence of the trim on the buoyancy (displacement) curve


Containership splits in two

The afterpart of the 25-year-old container ship CARLA after breaking in two during astorm 100 miles off the Azores. The disaster occurred after the ship's rudder was damaged, leaving her at the mercy of the heavy seas. The 34-man crew, who tookshelter in the stern section, were all taken off by helicopter.The forward half sank after five days, but a tug managed to tow the stern section, carrying 1,000 containers, to Las Palmas.The ship was lengthened 1984, but the vessel's owners denies that the ship had broke

napart along one of the welds.


Racking Hull deformation in heavy sea

Individual waves are creating additional forces


Torsional Forces


Ship motions in a seaway


Sloshing in tanks

In tankers there will be increased loads on the structure in the cargo (andballast) tanks because of motion and sloshing of the fluid.The influence is both longitudinal (surge, heave, pitch) and transverse(heave, sway, roll).


Sloshing in tanks

The magnitude of the influence depends on the size of the tank, thefilling level, mass density and viscosity of the liquid and, of course,the ship's motion and responses at sea.To allow unrestricted filling levels in the tanks it is necessary tospecifically consider the variable liquid pressures on internal

members,such as transverse bulkheads, horizontal stringers and deck girders.


Wash Bulkhead (longitudinal)

Wash Bulkhead is a perforated or partial bulkhead in tank.


Additional local forces because of acceleration and vibration

All ships are flexible and can be likened to a hollow rod. When it is subject to the

motion of the sea, the ship bends and twists in several direc tions. The

superstructure and the aft body follow the ship's motion.


DEFLECTION CURVE


Various loads on the structure of a ship


800 tonne grab


Deformation of a container ship in the seaway (deformation magnified)


The ship looks like a beam


The ship is like a beam

For the purpose of calculating the maximum vertical bendingstresses and moment the ship may be considered as a beam(box girder). There are then simple formulas for detecting themaximum stresses.


The hull of a ship is like a beam with various loads and supports


DOUBLE BOTTOM COSTRUCTION


DOUBLE BOTTOM CONSTRUCTION


DISTRIBUTION OF FORCES


DISTRIBUTION OF FORCES

Deflection of the bulkheads will create additional forces in the hull girder


TERMINOLOGY

Girder is a collective term for primary supporting members, usually supporting stiffeners. Other terms used are:

- floor (a bottom transverse girder) - stringer (a horizontal girder)Stiffener is a collective term for a secondary support ing member. Other terms

used are:- frame- bottom longitudinal- inner bottom longitudinal- reversed frame (inner bottom transverse stiffener), side longitudinal- beam- deck longitudinal- bulkhead longitudinal


Oil tanker (large size)Longitudinal framing


Oil tanker (small or medium size) Transverse side framing


SOLAS CHAPTER II-2, Part C: Suppression of fire

Regulation 11: Structural integrity

The purpose of this regulation is to maintain structural

integrity of the ship, preventing partial or whole collapse of

the ship structures due to strength deterioration by heat. For

this purpose, materials used in the ships' structure shall ensure

that the structural integrity is not degraded due to fire.


and


Mechanics of Material

F = A = F/A

dAσF


Elastic limit

Plastic limit Fracture

STRENGTH OF MATERIALS


Mechanical Properties of MetalsPlasticity is the ease with which a material may be bent or moulded into a

given shape.Brittleness is the lack of ductility.Malleability is the property possessed by a metal which allows it to be rolled

or hammered without fracture. Such material must be plastic.Hardness is the measure of a metal's resistance to surface indentation and

abrasion.Fatigue is the loss of ductility and consequent failure at a lower load after

repeated application of alternating stress.Ductility is the property of a material which allows it to be drawn out into

smaller sections.Elasticity is the property by virtue of which a material deformed under load

returns to its original shape when the load is removed. Strength is the ability of the material to resist fracture under load.Toughness is the property whereby a material absorbs energy with-out

fracture or has the ability to resist the propagation of cracks.


Stress

Stresses are of three main types :

(1) Tensile: The forces are acting in such a

direction as to increase the length.

(2) Compressive: The forces are acting in

such a direction as to

decrease the length.

(3) Shear: Two equal forces are acting along

parallel lines and in opposite

directions such that the various

parts of the section tend to slide

one on the other.


If A is the cross-sectional area of the material which is being subjected toequal and opposite forces F, then:

Tensile or compressive stress = force/area σ = F/A [N/mm2]

If the material had an initial length l and the applied force extends or compresses it by an amount x, then:

Strain = change in length / original length ε=x/l [dimensionless, %]

As shown by the dotted lines, changes also occur in the cross-sectional area of the material and thus strains are set up in lateral directions as well as longitudinal directions.


When the material is subject to a longitudinal (axial) force, also a lateral (internal) force will be set up (because of the change of the sectional area and by that the volume)

Lateral strain/ Longitudinal strain = Lateral stress/ Longitudinal stress = Poisson's ratio

Forces in the material


Hooke's Law

For loading within the elastic limit of the material, deformation is directly proportional to the load producing it. Since stress is proportional to load and strain to deformation, then stress is proportional to strain.

The ratio of stress to strain is a constant for a given material. Assuming all strains to lie within the elastic limit so that all stresses follow Hooke's Law, then the intensity of stress, б, at any point is: б = E·x/l = E·ε where E is the modulus of elasticity or Young's modulus

Stress N/mm2

Elongation mm or %


E is not a function of the strength of the material but is a function of its flexibility

E is the modulus of elasticity or Young's modulus

ESTEEL 2·105 N/mm2

EAl 0,69·105 N/mm2

Elx

E


Stress / Strain diagram – Low carbon steel


Stress / Strain Diagram – Low carbon steel


Brittle or fast Fracture

When a tensile stress is applied to a material it normally elongates

elastically until the yield point is reached, then undergoes

plastic deformation and finally fractures

WARNING of FRACTURE

is given by the

ELONGATION and DEFORMATION

of the material


CRACK


Cracking and other signs of Structural Failure

A crack creates a stress concentration that causes the crack to

spread, and further intensify the stress and increase the rate at

which the crack spreads. This process will eventually cause

the structure to fracture.

Cracks usually start at a point where a discontinuity in the

structure has been poorly merged into the neighbouring

structure. An example of this would be corners of hatchways

or access cut-outs that have fillets of insufficient radius.

A crack developing in the main hull structure is a serious

problem that requires fairly immediate repair


Cracking and other signs of Structural Failure


Poor design of a double bottom might result in cracks


Flow holes & air holes in a double bottom tank shall preferably be elliptical and the edges to be smooth ground to avoid cracks

Area of the girder with the highest tension

Very low tension in the center part


BRITTLE FRACTURE

There are a number of significant factors which may give rise to brittle fracture. These are :

Stress Concentration and Notch Effect. A notch in a metal is susceptible to cracking. Although only a single direct stress has been applied to the material, at a notch the Poisson effect will give rise to a triaxial stress system in which the stresses are greater than the original applied stress due to the stress concentration effects of a notch. This will then lead to increased probability of failure.

Temperature. One of the most important factors is the temperature at which the material must function. The lower the temperature the greater is the probability of brittle fracture. The temperature above which brittle fracture will not occur is called the transitional temperature. This is due to a change in the characteristics of the material with a change in the temperature. In some cases only a difference of a few degrees may determine the difference between a ductile and brittle fracture.


Materials and Material Protection (from DNV regulations)

Requirements for low air temperatures [Class notation dat(—x° C)]

In ships intended to operate for longer periods in areas with low air

temperatures (i.e. regular service during winter to Arctic or Antarctic

water), the materials in exposed structures will be specially considered. In

that case the notation dat(—x° C) will be entered in the Register of Ships

indicating the lowest design ambient air temperature applied as basis for

approval. Design ambient temperature is considered to be comparable with

the lowest monthly isotherm in the area of operation.

For materials subjected to low temperature cargoes, see Pt.5 Ch.5 Sec.2

(Liquefied gas) and Pt.5 Ch.10 Sec.2 (Refrigerated cargoes).


BRITTLE FRACTURE

Plate Thickness. Thick plates generally have higher transitional temperatures plus the increased ability to develop triaxial stresses, i.e. tensional stresses in three dimensions. Due to their thickness there is also the possibility of a lack of metallurgical uniformity occurring within the material, thus affecting the internal stress level.

Stress Loading. Stress systems that vary rapidly, i.e. impact, shock, intense vibration etc., can cause high local stress level and thus increase the probability of fracture.

Metallurgical Composition. The chemical composition of the material may influence the transitional temperature and thus the probability of fracture.


Brittle Fractures

Under the following conditions there is a potential risk for the development of BRITTLE FRACTURES in steel:

High nominal stress level Low temperature High local stress, i.e. a three dimensional stress at a

sufficient high level


Shear Stresses

If the applied force, F, consists of two equal and opposite parallel forces, not in the same line, then there is a tendency for one part to slide over the other or shear across the section. Shear stress is load per unit area.

If the cross-section at X Y, measured parallel to the force F is A, then the average shear stress is = F/A [N/mm2]


Shear Stresses (cont.)

It will be seen that the block, where the force F is applied, distorts, the strain being a measure of the angular distortion of the sides.

Shear strain = (radians)

In pure shear stress systems no change in the volume occurs when the material distorts. It is important to remember with shear stress systems that a stress in one plane is always accompanied by an equal shear stress in a plane at right angles to the first.


In the real case it is always a combination of stresses:

Both longitudinal and shear stress appear at the same time. Various hypothesis for the calculation of the effective (combined) stress have been developed. One of them is von Mises' hypothesis:

222 N/mm3 effective


Causes of cracks in the strength deck and in the shell

NOBODYIS

PERFECT!


Failure modes against which structures must be designed in a gross sense, include:

Hull failureDeck collapseBulkhead collapseCracking and loss of water tightnessGross deflections

stressDesignstressYieldfactorSafety


In a more finite sense, geometry and material failures or strength loss include:

Tearing Fracture Cracking Rupture Explosion Buckling Crippling Tripping CollapseExcessive deflection CorrosionPitting Wastage CreepFatigue Warping ShearingCompressive plastic flow Lamellar tearing

stressDesignstressYieldfactorSafety


Minimum necessary plate thickness

RULE VALUEfor a new ship

SAFETY MARGINbecause of:Inaccurate calculation,varying plate thickness,welding influence

MINIMUM THICKNESSTo maintain sufficient

strength with acceptablesafety margin


About plate thickness tolerances (from DNV Hull Structural Steel Regulations)

General: Where subsequent Rules for material grade are dependent on plate thickness, the requirements are based on the thickness as built.

Guidance note:When the hull plating is being gauged at periodical surveys and the wastage considered in

relation to reductions allowed by the Society, the reductions are based on the nominal thicknesses required by the Rules.

The under thickness tolerances acceptable are to be seen as the lower limit of a total minus-plus standard range which could be met in normal production with a conventional rolling mill settled to produce in average the nominal thickness.

However, with modern rolling mills it might be possible to produce plates to a narrow band of thickness tolerances which could permit to consistently produce material thinner than the nominal thickness, satisfying at the same time the under thickness tolerance given. Therefore in such a case the material will reach earlier the minimum thickness allowable at the hull gaugings.

It is upon the Shipyard and Owner, bearing in mind the above situation, to decide whether, for commercial reasons, stricter under thickness tolerances are to be specified in the individual cases.


The ship itself and all the construction details are like beams

For the purpose of calculating the maximum vertical bendingstresses and moment in the ship (a box girder) and all the

strengthcomponents in it, elementary beam theories may be used to

detectThe maximum stresses.


Beam Strength

When a force, or a system of forces, is imposed upon a beam or girder resulting in a bending moment, the beam will tend to bend by an

amount that will depend on the magnitude of the bending moment.


Three geometric properties of a structure are of importance when considering the longitudinal stress distribution in a beam subjected to bending:

Neutral Axis of the beam is the position of the unstrained layer in longitudinal bending; the neutral axis is coincident with the centroid or centre of gravity of a section.

Second Moment of Area or Moment of Inertia of the section (I) is said to be the measure of a beam's ability to resist deflection. It is an indication of how the cross-sectional area is distributed with respect to the neutral axis.

Section Modulus of the cross-section (Z) is a measure of the structural bending strength of the section under consideration. Z = I/ymax


Necessary cutouts shall be made around the neutral axes

A transverse frame in the accomodation, showing the cutouts for cables and pipes, which are needed to ensure a clear headroom of around 2,10m.


Typical crack catching plate strakes in dry cargo ship and tanker


Materials and Material Protection (from DNV Rules)

Material certificates: Rolled steel and aluminium for hull structures are normally to be supplied with DNV material certificates

Hull Structural Steel: Hull materials of various strength groups will be re ferred to as follows:

- NV-NS Normal strength structural steel with yield point not less than 235 N/mm2.- NV-27 High strength structural steel with yield point not less than 265 N/mm2.- NV-32 High strength structural steel with yield point not less than 315 N/mm2.- NV-36 High strength structural steel with yield point not less than 355 N/mm2.- NV-40 High strength structural steel with yield point not less than 390 N/mm2.

The material factor f1 which may be included in the various formulae for scantlings and in expressions giving allowable stresses, is dependent on strength group as follows:

- for NV-NS: f1 = 1,00 - for NV-27: f1 = 1,08 - for NV-32: f1 = 1,28 - for NV-36: fl = 1,39 - for NV-40: f1 = 1,43


DNV rules: Alternative Structural Materials

Aluminum alloy for marine use may be applied in superstructures,

deckhouses, hatch covers, hatch beams and other local items.

In weld zones of rolled or extruded products (heat affected zones) the

mechanical properties given for extruded products may in general be used

as basis for the scantling requirements.

The various formulae and expressions involving the factor fl may normally

also be applied for aluminum alloys when:

f1 =σf/235σf = yield stress in N/mm2 at 0,2 % offset. σf is not to be taken greater than 70 % of the

ultimate tensile strength.


SOLAS: Structure of ships

Regulation 3-2: Corrosion prevention of seawater ballast tanks1 This regulation applies to oil tankers and bulk carriers constructed on or

after 1 July 1998.2 All dedicated seawater ballast tanks shall have an efficient corrosion

prevention system, such as hard protective coatings or equivalent. The coatings should preferably be of a light colour. The scheme for the selection, application and maintenance of the system shall be approved by the Administration, based on the guidelines adopted by the Organization.* Where appropriate, sacrificial anodes shall also be used.___________________________________________________

* Refer to the Guidelines for the selection, application and maintenance of corrosion prevention systems of dedicated seawater ballast tanks adopted by the Organization by resolution A.798(19).


DNV rules for ships:Corrosion Protection and Corrosion Additions.

General: All steel surfaces except in tanks other than ballast tanks are to be protected against corrosion by paint of suitable composition or other effective coating. In tanks for cargo oil and/or water ballast the scantlings or the steel structures are to be increased by corrosion additions.

Corrosion additions:Plates, stiffeners and girders in tanks for water ballast and/or cargo oil and of

holds in dry bulk cargo carriers are to be given a corrosion addition tk as stated in Table D 1.

The requirement to section modulus of stiffeners in tanks for water ballast or cargo oil given in relevant chapters is to be multiplied by a factor:

wk = 1 + 0,05 (tkw + tkf) for flanged sections = 1 + 0,06 tkw for bulbs

tkw = corrosion addition tk with respect to the profile webtkf = corrosion addition tk with respect to the profile flange


Moment of inertia = Second moment of area

Second Moment of Area is said to be an indication of the measure of a beam's ability to resist deflection. It is an indication of how the cross-sectional area is distributed with respect to the neutral axis.

With a given cross-sectional area itis possible to create a number of different sections. One cross-section

could have a greater second moment of area than another because of the greater distances of its flanges from the neutral axis.


Second moment of area = Moment of inertia

The Second Moment of Area (I) of a rectangular section of length l and breadth b about an axis through the centroid (neutral axis) and parallel to the breadth:

where A = area of cross-section NA = neutral axis

4m

12

2

12

3 lAlbI


Theorem of Parallel Axis

The second moment of area, I, of an area about an axis parallel to the axis through the centroid of the area is equal to the second moment of area about the axis through the centroid plus the area multiplied by the square of the distance separating the two axis.

Iyy = I about axis yy Ixx = I about axis xx A = area of cross-section h = distance between axis xx and yy

2xxyy hAII


To Calculate the Section Modulus of a Rectangular Section

2ly

122lA

12lbI

6lA

l2

12lA

yIZ

3

2

Section modulus:

Stress calculation:

ZMσ


Example : In the following figures the area of cross-section is 6 000 mm2. Calculate the second moment of area (I) about the neutral axis, and the section modulus (Z), in each case.


SECTION MODULUS is a measure of the structural bending strength of the

transverse section of a ship and is proportional to D3

hDB

Z

DBI

12

312

3


moment of the force acting at the point about the neutral axis=


Since the beam is in equilibrium then the bending moment (M) must be equal to the total moment of all the forces acting across the area

of the section


Z is used as a standard or modulus of the ability Df a section to withstand bending and the associated stress due to bending

In the above calculation for section modulus it is assumed:(a) the material is homogeneous and has the same value E

(Young's modulus) both in tension and compression.R (b) the beam is initially straight and all longitudinal fibres

bend into circular arcs with a common centre of curvature.transverse cross-sections remain plane and perpendicular to the

neutral axis after bending.the radius of curvature (R) is large compared with the cross-

section dimensions.the stress is purely longitudinal.


S

The value of the section modulus for each flange of a beam permits the calculation of the maximum bending stress to be imposed upon them when the value of the longitudinal bending moment is known.

Each material is associated with a particular value of permissible stress. If the stress level is too high, as determined by the above equa tion, for a given bending moment, then the section modulus must be increased in order that the stress level is reduced. The section modulus may be increased by a redistribution as well as an increase in the cross-sectional area. Using the above equation with a specified bending stress, a given bending moment and a given type of material for the section, then the necessary section modulus may be calcu lated


it is assumed:the material is homogeneous and has the same value E(Young's modulus) both in tension and compression.the beam is initially straight and all longitudinal fibres bend into circular arcs

with a common centre of curvature.transverse cross-sections remain plane and perpendicular to the neutral axis

after bending.the radius of curvature (R) is large compared with the cross‑section dimensions.the stress is purely longitudinal


Deflection in Seaway

it is assumed :(a) the material is homogeneous and has the

same value E (Young's modulus) both in tension and compression.

the beam is initially straight and all longitudinal fibres bend

into circular arcs with a common centre of curvature.

transverse cross-sections remain plane and perpendicular to

the neutral axis after bending.the radius of curvature (R) is large

compared with the cross-section dimensions.

the stress is purely longitudinal.


Lloyd's Society's Regulations for the Classification and Construction of Steel Ships require the calculation of the section modulus or geometric property of rolled or built sections in association with an effective area of attached plating. The calculations may be made directly or, alternatively, the curves in the Society's publication Geometric Properties of Rolled and Built Girders may be used.

Reference to Lloyd's Rules will show that minimum values for section modulus for many structural items are given; i.e. the section modulus must not be less than that given by formula in the rules. Examples are.:

Hull midship section modulus Deck longitudinal Inner bottom longitudinal Transverse side framing Deck beams


DocumentationPlans and particulars.The following plans are normally to be submitted for approval: Midship section including class- and register notations, main particulars

(L, B, D, T, CB), maximum service speed V, see B 100. Deck and double bottom plans including openings. Longitudinal section. Shell expansion and framing including openings and ex-tent of flat part of

bottom forward, watertight bulkheads including openings. Cargo tank structures. Deep tank structures. Engine room structures including tanks and foundations for heavy

machinery components. Afterpeak structures. Forepeak structures. Superstructures and deckhouses including openings. Supporting structure for containers and container securing equipment. Arrangement of cathodic protection in tankers.


Specifications and calculations

Information which is necessary for longitudinal strength calculations: Maximum still water bending moments and shear forces (if different from

standard values) Still water bending moment limits. Mass of light ship and its longitudinal distribution Cargo capacity in t. Buoyancy data Cargo, ballast and bunker distribution.Information which is necessary for local strength cal culations: Minimum and maximum ballast draught and correspond ing trim Load on deck, hatch covers and inner bottom Stowage rate and angle of repose of dry bulk cargo Maximum density of intended tank contents Height of air pipes Mass of heavy machinery components Design forces for cargo securing and container supports Any other local loads or forces which will affect the hull structure.


The Second Moment of Area (I) of a A rectangular section of length 1 and breadth b about

an axis through the centroid (neutral axis) and parallel to the breadth,

where A = area of cross-section NA = neutral axis


The Second Moment of Area (I) of a

A rectangular section of length 1 and breadth b about an axis

through the centroid (neutral axis) and parallel to the

breadth,

where A = area of cross-section NA = neutral axisbNbxxT

hYTheorem of Parallel Axis. The second moment of area, I,

of an area about an axis parallel to the axis through the

centroid of the area is equal to the second moment of area

about the axis through the centroid plus the area

multiplied by the square of the distance separating the two

axis.


For stiffeners and frames we can in general assume that the part of the hull plate to be considered as effective flange is equal to the framing distance, but for normal plate thicknesses not more than 600 mm (300 mm on each side of the stiffener web).


Calculation of Section ModulusConsider material which is distributed over a major length in a longitudinal

direction, e.g. all continuous decks, deck longitudinal, side and bottom shell, bottom longitudinal, tank top plating and centre girder. Deck girders should be included if they continue for a sufficient length amidships.

TRANSVERSE FRAMING

is common in small and

medium size ships


LONGITUDINAL FRAMING

is necessary in big ships to get

enough longitudinal


Torsional Forces


Torsional stresses During Rolling

The hull is subjected to a twisting motion at the ends of roll


The mid ship section of a ship will not be symmetrical, i.e. the neutral axis is unlikely to be at half the depth. There will therefore be two values of Z, Z1 and Z2.

The Ship Girder


Elementary beam theory may justifiably be used in calculations relat ing to the longitudinal bending of ships. Assuming the greatest bend ing moment to occur at or near amidships then the greatest stresses are likely to occur there so that the value of the section modulus (Z) is required for the midship section.The midship section of a ship will not be symmetrical, i.e. the neutral axis is unlikely to be at half the depth. There will therefore be two values of Z, Z 1 and Z2.

The Ship Girder


Take a section in way of openings.Consider material which is distributed over a

major length in a longitudinal direction, e.g. all continuous decks, deck longitudinal, side and bottom shell, bottom longitudinal, tank top plat ing and centre girder. Deck girders should be included if they continue for a sufficient length amidships.

Two quantities are required, similar to previous calculations:

the position of the neutral axis, the second moment of area of the total area of the material about the neutral axis.

Calculation of Section Modulus


Concentrated Load, where the load is considered to act at some point in the length of the beam.Distributed Load, where the load is distributed over the length of the beam. It may be uniformly distributed or vary from point to point along the length of the beam. There will be a tendency for the beam to bend or sag.

Types of Load


E.g. a uniformly loaded beam, simply supported at its ends, has a maximum bending moment at its centre with zero moments at its ends. If the ends are fixed the maximum bending moment reduces by a third and is at the ends.

Brackets are important !

2/2412 321 LxforQLMandQLMM


Stress concentration to the toe of the bracket



32

cmmσ

sp1000lZ

Rules for Ships , Pt.3 Ch.2 Sec.8 — Page 35

304 Brackets are normally to be fitted at ends of non‑continuous stiffeners.

C 400 Stiffeners on watertight bulkheads401 The section modulus requirement is given by:

p = p1 as given in table B1 for watertight bulkheads = 160 for collision bulkhead = 220 for other watertight bulkheads m = 16 for member fixed at both ends = 12 for member fixed at one end (lower) and simply supported at the other = 8 for member simply supported at both ends The m-value may be adjusted for members with boundary conditions not corresponding to the above specification.



C 200 End connections of stiffeners.201 Normally all types of stiffeners (longitudinals, beams, frames, bulkhead stiffeners) are to be connected at their ends, in special cases, however, sniped ends may be allowed.202 The arm lengths of brackets for stiffeners not taking part in longitudinal strength may normally be taken as

mmtZca

c = 70 for flanged brackets = 75 for unflanged bracketsZ = rule section modulus in cm3 of stiffenert = thickness of bracket in mm. The arm length (a) is in no case to be taken less than 2 times the depth of the stiffener.Brackets to be flanged if free lengths exceed 50 t.The connection between stiffener and bracket is to be so designed that the effective section modulus is not reduced below the requirement for the stiffener.


Tripping bracket


Because of the arm length it

is necessary with a flange

or a supporting flat bar


WHY ? HOWFinding the shearing force and bending moment

in a beam or a ship at various conditions


ILLC Regulation 10: Information to be supplied to the MasterThe master of every new ship shall be supplied with sufficient information, in an approved form, to enable him to arrange for the loading and ballasting of his ship in such a way as to avoid the creation of any unacceptable stresses in the ship‘s structure.


The shearing force at any section of a beam is the sum of the vertical forces acting on one side or the other of the section.

F is called the shearing force. F = R1—W1—W2

F = W3+W4—R2

therefore, R1—W1—W2 = W3 + W4—R2

Shearing Force


A shearing force diagram is one which shows the variation of the shearing force along the length of the beam.


The bending moment at any section in a beam is defined as the sum of the moments, about that section, of all the forces acting on one side or on the other side of that section.

Moment to left of section X Y is equal to the moment to the right of section X Y since the beam is in a state of equilibrium.

Bending moment: M = R1d3 - W l d l - W2d2

Bending Moment


The bending moment diagram shows the variation in the bending moment along the length of the beam.

BENDING MOMENT diagram

R1= W/2 R1= W/2

Mmax= R ·L/2 = W·L/4


Graphical Representation

The shearing force and bending moment in the beam are shown graphically by plotting the values of the shearing force and bending moment at points along the beam. Such curves indicate where fracture is most likely to occur; that is at points where the shearing force or bending moment has its maximum value.

1. Increase in the bending moment between two sections is given by the area under the shearing force curve between those sec tions;

2. Generally zero shearing force corresponds to a maximum or minimum bending moment;

3. Peaks in the bending moment diagram frequently occur at points of concentrated loads or reactions;

4. Area of the shear force diagram above the baseline equals the area below the baseline.


Loading diagram, shearing force diagram and bending moment diagram for a beam which is loaded with a uniform weight (w tonnes per unit length) and which is freely supported at its two ends.

Loading diagram Shearing force diagram Bending moment diagram


Loading diagram, shearing force diagram and bending moment diagram for a beam which is loaded with a concentrated weight v at L/2 and which is freely supported at its two ends

Loading diagram Shearing force diagram Bending moment diagram


The combined effect of two different types of load on a beam (e.g. the light weight and engine weight in a ship) is found by adding the two load cases.

Final combined Loading diagram Shearing force diagram Bending moment diagramfor a beam which is loaded with a uniform weight (w tonnes per unit length) and a concentrated weight v at L/2 and which is freely supported at its two ends.

Combined diagram


Contributing Factors1. section modulus2. material yield strength3. stiffening system design4. quality control in construction Controllable?1. yes, alter scantlings2. yes, change material (caution: fatigue and buckling)3. yes, add more and/or stronger stiffeners (cost!)4. somewhat, high precision construction is very expensive

Variables: Strengths


A floating ship is supported throughout its length by the upthrust due to buoyancy; the forces acting downwards are due to the weight distribution within the ship.

The buoyancy will vary along the length of the ship as a result of the change in the ship's shape throughout its length. The weight distribution likewise varies throughout the length of the ship.


If a ship could be divided into a number of sections and each section allowed to float freely then the sections would take on the positions as shown by the dotted sections i.e. a state of equilibrium will be reached when buoyancy equals weight.The difference between the upward (buoyancy) and downward (weight) forces results in a load on the ship girder. Since the load varies throughout the length of the ship an overall bending moment is produced with the associated shear forces.A ship may be regarded as a hollow beam or box girder subjected to a varying loading rate due to distribution of buoyancy and weightin a longitudinal direction. The loading on the ship girder depends on the buoyancy to weight difference. It is only necessary to find the load, i.e. the difference between the buoyancy and weight over the length of the ship, and then treat as a freely supported beam.


The variety in load and buoyancy forces from stem to stern are causingSHEAR FORCES

andBENDING MOMENTS


Example: A barge is of rectangular constr

uction; length 80 metre, breadth 10 metre,

depth 6 metre, floating at a draught of 3 m

etre in fresh water. It is divided transverse

ly into four equal compartments; the two

centre compartments are to be uniformly l

oaded with 400 tonne cargo in each. Draw

the curves of load, shear force and bendin

g moment for the loaded condition.


S.F= shear force=

Σ(vertical forces)=

Area under the load curve


B.M. = bending moment =

Area under the shear force curve


Variable: Stillwater Bending Moment

Contributing Factors

1. weight distribution

2. hull form (buoyancy distribution)

Controllable?

1. yes, modifying weights to match buoyancy distribution

2. yes mostly, procedures for obtaining a desired sectional area curve by

changing hull shape are well defined and widely understood, only

limitation is mission-driven constraints on required volumes at different

locations

Structural Strength of Ships, Professor Jönsson147Heavy sea will increase the structural loads


The Calculation of Ship's Strength Curves

When investigating the basic strength of the vessel the stresses in duced in the ship girder, as would be expected, are greater when floating amongst waves than in still water. The two most severe con ditions are the hogging and sagging conditions. The three conditions which must be examined are :

A. the still water condition,B. the hogging condition, andC. the sagging condition.For a given loaded condition the weight curve will remain constant but the

buoyancy curves for the still water condition and the two extreme wave profile conditions, given by the hogging and sagging conditions, will vary.

The variations in the relative distribution of buoyancy and weight will give rise to different bending moments.

The load curve is obtainedby subtracting the weight values from the buoyancy values and plot ting the res

ultant difference. Integration of the load curve will give the shear force curve which may then be integrated to obtain the bending moment curve.


Information from a loading computer


The Buoyancy Curve

In carrying out the strength calculation for a ship, in addition to the still water condition, the vessel is assumed to be floating in a regular series of

trochoidal waves having a length from crest to crest equal to the length of the vessel and a depth from crest to trough of 0.607s/(L), where L is the

length of the vessel in metres.A trochoid is the locus of a point, of radius r, inside a rolling circle of radius

R. To give the required wave profile, the circle rolls along beneath a horizontal baseline.

R = L 2r = 0.607STANDARD TROCHOIDAL WAVE PROFILE


Bonjean Curves

These are simply curves of transverse sectional area plotted against draught and are prepared from the Body Plan of the vessel by calculating the transverse sectional areas progressively to the various waterlines.

By this means a complete series of transverse section areas over the length of the vessel is obtained, thus enabling the displacement to any unusual waterline to be readily obtained.


Standard Trochoidal Wave Profile

The shape of the appropriate wave is positioned on the sheer pro-file of the vessel which shows the Bonjean curves at each station.

Using such curves the buoyancy per metre run cut off by the wave can be obtained and plotted to give the buoyancy curve.


BONJEAN CURVES

It is necessary for equilibrium to place the wave at a draught and trim such that;the buoyancy (upthrust or displacement) equals the weight.the centre of buoyancy and centre of gravity lie in the same vertical transverse

plane.The position of the wave to meet the above two conditions can be found by a

process of trial and error.


The weight Curveconsider the weight curve to be composed of:a) a continuous curve over the length of the

ship, representing the weight to the uppermost continuous deck of steel etc.

b) local weights, which include items above the uppermost con tinuous deck together with local additions to the basic underdeck weight.

Given the total light weight of the vessel, the procedure is to deduct the sum of all the local weights, distribute the remainder under a standard curve which depends on the -block coefficient and then add the correctly distributed local weights to the basic weight curve. The local weights, i.e. forecastle, bridge, poop etc., are generally distri buted as a rectangle or triangle over their appropriate length in the vessel.


Shear Force and Bending Moment Curves

1. Divide the length of the ship into a number of equal parts.

2. Calculate the average weight per metre for each of the sections.

3. Calculate the average buoyancy per metre for each of the sections.

4. Draw the curve of loads as a series of rectangles.

5. Successive integration of the load curve will give the values for the

shearing force and bending moment curves.

Check that the total weight and total buoyancy are equal and they have the

same fore and aft position for the L CB and L C G.


Typical strength curves


Longitudinal Strength Standards by Rule Formulae have been devised to represent the standard calculation and to specify

mini-mum section module.The rules are based on the division of the total bending moment into two parts :A. the still water bending moment.B. the wave bending moment.The wave bending moment is that due to the superimposing of a wave onto the

still water condition. It is determined by the geo metry of the ship and the wave and is in no way influenced by the disposition of the cargo.

For a 0° 607wave, the wave bending moment can be repre sented by the formula:max. 0.607 wave bending moment = b .B . L2.5 x 10- 3where b is a constant depending on the block coefficient.The above expression was used by Murray in his method for determining the

longitudinal bending moment amidships, on a ship inwaves.


Still Water Bending Moment (S.W.B.M.)

Let Wf= moment of weight forward of amidshipsBf= moment of buoyancy forward of amidships

Wa = moment of weight aft of amidshipsBa = moment of buoyancy aft of amidships

W= total displacement of vessel.Bending moment amidships is given by :

BM=Wf—Bf=Wa—BaIt is possible to evaluate the above equation by calculating in detail the

magnitude of the various quantities.Mean weight moment, Mw= Wf + Wa/ 2


The mean buoyancy moment can be obtained from the formula:Mean buoyancy moment = W x mean LCB of fore and aft bodies 2The value of the mean LCB has been found by analysing a large number of ships

and the following formulae have been obtained in terms of the block coefficient (Cb) and the length of the ship (L).


Formula for LCB

Mean LCB=C x L

The value of the block coefficient in the above table is at a draught of 0.06L

and the formulae can be applied up to a trim of 0.01L.

Draught C

0.06L 0.179Cb+0.063

0.05L 0.189Cb + 0.052

0.04L 0.199Cb+0.0410.03L 0.209Cb+0.030


Still Water Bending Moment (S.W.B.M.)

The bending moment amidships, in terms of the mean moments of weight and buoyancy about mid ships, is then given by:

S.W.B.M. =Wf+Wa/2- W/2 . C. L, where C is as above.If the mean weight moment is greater than the mean buoyancy moment, the

ship hogs, and if vice versa, the ship sags.


This can be shown to depend upon wave height, wave length and the beam of the ship. If the wave height is taken to be proportional to and the wave length is taken as equal to the length of the ship (L), then it has been found that the wave bending moment may be expressed:

Wave bending moment= b • L2' 5 • B x 10- 3 tonne metre,where b is a constant depending upon the block coefficient and posi tion of the

wave crests, i.e. whether the ship is hogging (crest amid-ships) or sagging (crests at ends).

Wave Bending Moment (W.B.M.).


S

Values of b at load draught for various block coefficients.Table for values of b

Cb Hogging Sagging

0.80 10.555 11.821

0.78 10.238 11.505

0.76 9.943 11.188.

0.74 9.647 10.850

0.72 9.329 10.513

0.70 9.014 10.175

0.68 8.716 9.858

0.66 8.402 9.541

0.64 8.106 9.204

0.62 7.790 8887

0.60 7.494 8 571


S

Summary. The total bending moment on a ship may be divided into two parts:

(1) Still Water Bending Moment (S.W.B.M.). This may be obtained by taking the differences of the moments of weight and buoyancy about amidships.

Wf+Wawhere Wf= moment of weight forward of amidships Wa = moment of weight

aft of amidshipsand Mb = mean moment of buoyancy W.c.L 2where W = displacement in tonnes c= mean position of L C B L = length of sh

ip, in metre.Still Water Bending Moment S.W.B.M.=Mw—Mb


(2) Wave Bending Moment (W.B.M.). This is caused by the passage of a wave and has been found by analysis to be,

W.B.M.=b:L2.5B x 10-3where b =a constant depending on the block coefficient L =length of ship, in

metre B = breadth of ship, in metre.The values of the S.W.B.M. and W.B.M. may be added algebraically to give

the total bending moment.


Variable: Wave Moment

Contributing Factors1. environmental condition (waves)2. operating conditions (speed, heading, operating area)3. hull form4. weight distribution (specifically, radii of gyration) Controllable?1. no, natural forces2. marginal, requires restricting operation of ship3. marginal, cause/effect relationship not well understood,

restricted by mission-driven limitations (e.g. cargo requirements and shape of holds)

4. marginal, very difficult to reduce radii of gyration


Variable: Dynamic Moment

Contributing Factors1. environmental conditions2. operating conditions3. weight distribution (gyradius)4. shape of hull near bow (bow flare and flat of bottomforward) Controllable?1. no, natural forces2. marginal, requires restricting operation of ship3. marginal, very difficult to reduce radii of gyration4. yes, interactions well understood, changes are localized


Structural Design Principles

Loading conditions.

Static loads are derived from loading conditions submitted by the builder or

standard conditions prescribed in the Rules.

Unless specifically stated dry cargoes are assumed to be general cargo or bulk

cargo (coal, grain) stowing at 0,7 t/na3 liquid cargoes are- assumed to have

density equal to or less than that of seawater.

The requirements given in Sec.5-12 refer to structures made of mild steel

with yield strength бy = 235 Nlmm2. If steel of higher yield strength is

used,

reduced scantlings may be accepted


The end


Compositely Framed Oil tanker


Longitudinally Framed Oil Tanker


Single Bottom Construction


Transversely Framed Double Bottom Construction


Longitudinally Framed Double Bottom Construction


Bulk carrier Double Bottom Construction


Deck Construction


Rolled steel products for hull constructionHull structural steel is a rolled product with

three commonly used ,strength grades measured in yield point: 235N/ mm2 (mild steel), 315N/mm2 and 355Ni mm- (high-tensile steel) although high-tensile steel of 390N/mm- grade has also been put into commercial use recently.

In addition to strength, hull structural steel requires good impact properties (toughness) and outstanding weld ability dc-oxidation largely depends on fine-killed steel. Impact properties are subject to three-level requirements for each cate gory of strength.

Structural Strength

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