Structural Strength

Structural Strength of Ships, Professor Jnsson1

World Maritime University

Professor Jan-ke Jnsson, 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 Conventionon 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 requirements

of a classification society recognized by the Administration may be

considered to possess adequate strength.


Hydrostatic Pressure Diagram

p = watergd (N)

F = pA (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 bulkheads

may be divided into two types:

Pressure loads directly applied to the

bulkheads, and concentrated loads

transmitted via girders.

Transverse bulkheads have high-rigidity

stool rings arranged around them. A stool

ring serves various structural purposes,

including reduction of girder span,

smooth transmission of girder loads to

transverse bulkheads to restrain bending

of 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


SOLAS Chapter II-2, Part C

Fire safety measures for cargo ships

6.3 Safety measures in cargo tanks

6.3.2 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


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

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 the

ship 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 brokenapart 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 (and

ballast) 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, the

filling 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 to

specifically 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 directions. 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 bending

stresses and moment the ship may be considered as a beam

(box girder). There are then simple formulas for detecting the

maximum 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 supporting 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

dAF


Elastic lim

it

Plastic lim

it Fractu

re

STRENGTH OF MATERIALS


Mechanical Properties of Metals

Plasticity 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 to

equal and opposite forces F, then:

Tensile or compressive stress = force/area = 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 =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, , at any point is:

= Ex/l = E

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 2105 N/mm2

EAl 0,69105 N/mm2

El

xE


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 failure

Deck collapse

Bulkhead collapse

Cracking and loss of water tightness

Gross deflections

stressDesign

stressYieldfactorSafety


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

loss include:

Tearing Fracture Cracking

Rupture Explosion Buckling

Crippling Tripping Collapse

Excessive deflection Corrosion

Pitting Wastage Creep

Fatigue Warping Shearing

Compressive plastic flow Lamellar tearing

stressDesign

stressYieldfactorSafety


Minimum necessary plate thickness

RULE VALUE

for a new ship SAFETY MARGIN

because of:

Inaccurate calculation,

varying plate thickness,

welding influence

MINIMUM THICKNESS

To maintain sufficient

strength with acceptable

safety 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 bending

stresses and moment in the ship (a box girder) and all the strength

components in it, elementary beam theories may be used to detect

The 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 referred 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.




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 =f/235

f = yield stress in N/mm2 at 0,2 % offset. f 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 tanks

1 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 web

tkf = 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 it

is 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

2

xxyy hAII


To Calculate the Section Modulus of a

Rectangular Section

2

ly

12

2lA12

lbI

6

lA

l

2

12

lA

y

IZ

3

2

Section modulus:

Stress calculation:

Z

M


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

h

DBZ

DBI

12

3

12

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 equation, 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 calculated


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


Documentation

Plans 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 calculations:

Minimum and maximum ballast draught and corresponding 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.



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



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 Modulus

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 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

relating to the longitudinal bending of ships. Assuming the

greatest bending 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 plating 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 LxforQL

MandQL

MM


Stress concentration to

the toe of the bracket



32

cmm

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 bulkheads

401 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

mmt

Zca

c = 70 for flanged brackets

= 75 for unflanged brackets

Z = rule section modulus in cm3 of stiffener

t = 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 ? HOW

Finding the shearing force and bending momentin a beam or a ship at various conditions


ILLC Regulation 10: Information to be supplied to the Master

The 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 ships 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 = R1W1W2

F = W3+W4R2

therefore, R1W1W2 = W3 + W4R2

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/2Mmax= R L/2 = WL/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 sections;

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




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



for 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 Factors

1. section modulus

2. material yield strength

3. stiffening system design

4. quality control in construction

Controllable?

1. yes, alter scantlings

2. 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 weight

in 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 causing

SHEAR FORCES

and

BENDING MOMENTS


Example: A barge is of rectangular

construction; length 80 metre, breadth 10

metre, depth 6 metre, floating at a draught

of 3 metre in fresh water. It is divided

transversely into four equal

compartments; the two centre

compartments are to be uniformly loaded

with 400 tonne cargo in each. Draw the

curves of load, shear force and bending

moment for the loaded condition.


S.F= shear force=

(vertical forces)=

Area under the load curve


B.M. = bending moment =

Area under the shear force curve


Variable: Stillwater Bending Moment


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


Heavy sea will increase the structural loads


The Calculation of Ship's Strength Curves

When investigating the basic strength of the vessel the stresses induced in the

ship girder, as would be expected, are greater when floating amongst waves

than in still water. The two most severe conditions are the hogging and

sagging conditions. The three conditions which must be examined are :

A. the still water condition,

B. the hogging condition, and

C. 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 obtained

by subtracting the weight values from the buoyancy values and plotting the

resultant 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 = 0.607

STANDARD 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 Curve

consider 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 continuous 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

distributed 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 geometry 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 represented by the formula:

max. 0.607 wave bending moment = b .B . L2.5 x 10- 3

where 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 amidships

Bf= moment of buoyancy forward of amidships

Wa = moment of weight aft of amidships

Ba = moment of buoyancy aft of amidships

W= total displacement of vessel.

Bending moment amidships is given by :

BM=WfBf=WaBa

It 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 2

The 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+0.041

0.03L 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 position 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+Wa

where Wf= moment of weight forward of amidships Wa = moment of weight

aft of amidships

and Mb = mean moment of buoyancy W.c.L 2

where W = displacement in tonnes c= mean position of L C B L = length of

ship, in metre.

Still Water Bending Moment S.W.B.M.=MwMb


(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 10-3

where 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


1. environmental condition (waves)

2. operating conditions (speed, heading, operating area)

3. hull form

4. weight distribution (specifically, radii of gyration)

Controllable?

1. no, natural forces

2. marginal, requires restricting operation of ship

3. 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


1. environmental conditions

2. operating conditions

3. weight distribution (gyradius)

4. shape of hull near bow (bow flare and flat of bottom

forward)

Controllable?

1. no, natural forces

2. marginal, requires restricting operation of ship

3. marginal, very difficult to reduce radii of gyration

4. 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 y = 235 Nlmm2. If steel of higher yield strength is used,

reduced scantlings may be accepted


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 construction

Hull 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 category of strength.

Structural Strength

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Transcript of Structural Strength