BEHAVIOUR OF MATERIALS

stress

strain

elasticity - plasticity - brittleness

safety factors

selecting appropriate materials

1/23

STRESS

internal forces developed within a structure due to action of external forces

stress is force intensity -

similar to (internal) pressure

force per unit area

2/23

STRAIN

response to stress

ratio ofchange in size or shape of element

to original size or shape

have stress --> get strain

strain to do with change in size or shape

3/23

STRAIN (cont.1)

for member subject to simple tensile force

dimensionless - millimetres / millimetre

strain =increase in length

original length e =LL

4/23

STRAIN (cont2.)

except for rubber bands, strains very small usually not visible

more a material strains under load - more the structure deflects

5/23

STESS & STRAIN SUMMARY

force

stress

causes

strain

puts material under

deformation

results in

6/23

BEHAVIOUR OF MATERIALS

how materials respond to stress (i.e. how they strain) determined by whether they are:

elastic or plastic

properties of materials only explicable in terms of internal forces in the material at the molecular or atomic level

7/23

ELASTICITY

until you damage the molecular structure the material remains elastic

it recovers when the load is removed

the spring in a weighing scale deforms in proportion to the load, and

returns to zero when you step off

8/23

MODULUS OF ELASTICITY

the modulus of elasticity, E, is a property of a material

E =stress

strain E is stress divided by strain slope of line (tan )

same units as stress (MPa)

within elastic range stress is proportional to strain

linear relationship (Hooke’s Law)strain

stre

ss

9/23

MODULUS OF ELASTICITY (cont.)

the modulus of elasticity, E, is a property of a material

steel 200,000 MPa

modulus of elasticity, E

aluminium 70,000 MPa

concrete 25,000 MPa (varies)

timber 10,000 MPa (varies a lot)

steel bar 1m long under stress of 150 MPa extends 0.75mm

too small to see by eye - measured by micrometer 10/23

MODULUS OF ELASTICITY (cont.)

the modulus of elasticity, E, is a property of a material

11/24

measures the resistance to deformation

higher E – more resistant to deformation

DUCTILITY - PLASTICITY

as long as atomic bonds unbroken material remains elastic & recovers original size and shape

when break atomic bonds material fails in one of two ways - plastic (ductile) or brittle

in ductile material, material deforms permanently

material can be greatly bent and reshaped (plasticene)

no loss in strength

eventually fracture occurs but after lot of energy12/24

DUCTILITY - PLASTICITY (cont1.)

stre

ss

strainplasticrange

ultimatefailure

ultimate deformation of plastic material much greater than elastic deformation - visible to naked eye

yield stress

yield point

elasticrange

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DUCTILITY - PLASTICITY (cont2.)

ductility - able to deform permanently prior to fracture

most materials ductile at low stresses

most metals ductile (not cast iron)

need also strength

wrought iron highly ductile but not very strong

high-carbon steel very strong but less ductile

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ELASTO - PLASTIC MATERIALS

ductile materials can be used safely below the yield stress

overstress --> deform dramatically

good warning

but don’t immediately break

15/24

BRITTLENESS

sudden breaking of atomic bonds

material fails suddenly - like glass

SNAP !

16/24

BRITTLENESS (cont.)

brittle failure occurs with little energy absorption

stone, brick, concrete, glass

high compressive strength - poor tensile strength

yield point

failure

stre

ss

strain

most traditional structures designed to eliminate tensile stresses - domes , vaults timber not durable - 19thC iron then steel

17/24

CURE FOR BRITTLENESS

reinforced concrete invented in 2nd half of 19thC

steel bars placed in parts of concrete that are in tension

cracks very fine - important that water does not reach steel

concrete cracks but steel resists the tension

18/24

CURE FOR BRITTLENESS (cont.)

add elasto-plastic material that can resist tension

into brittle material

19/24

SELECTING THE RIGHT MATERIAL

timber - not fireproof

stone rarely used today as structural material

steel - needs fireproofing, rustproofing

brick and block - loadbearing walls

strength per volume just less than R.C - much less than steel

strength per weight not much less than steel - long span glulam

for multistorey buildings of medium height

reinforced concrete (R.C.) - slow construction

prestressed concrete (P.C.) - expensive

aluminium - lightweight, expensive 20/24

SAFETY FACTORS

must ensure that structures do not collapse

must have a margin of safety

factor of safety allows for imperfections in materials

two philosophies

elastic method

loads not considered

slightly undersized members

simplifications in assumptions made in analysis

ultimate strength method

21/24

SAFETY FACTORS Ultimate Strength Method

load that structure carries x a factor of safety

factor of safety must be greater than 1.0 1.0 would mean that structure collapses as soon as service load put on

factors of safety for buildings vary from 1.5 to 2.5

factored load called the Ultimate Load

depends on structure and material

22/24

SAFETY FACTORS Elastic Method

ensure that actual maximum stress in structure less than Maximum Permissible Stress

Maximum Permissible Stress nearly always falls within elastic range of material

Max Permissible Stress = Ultimate Stress

Factor of Safety

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SERVICEABILITY

factor of safety ensures that structure does not collapse under most situations

excessive deflection - instantaneous / creep

but also need to avoid excessive deflection

leads to cracking - elements and finishes

creep - slowly over time - timber, concrete

creep deflection may be 2-3 times as much as instantaneous deflection

24/24