1. BEHAVIOUR OF MATERIALS
stress
strain
elasticity - plasticity - brittleness
safety factors
selecting appropriate materials
1/23

2. STRESS internal forces developed within a structure
due to action of external forces
stress is force intensity -
force per unit area
similar to (internal) pressure
2/23

3. change in size or shape of element to original size or shape
STRAIN
response to stress
have stress --> get strain
strain to do with change in size or shape
ratio of
change in size or shape of element
to original size or shape
3/23

4. STRAIN (cont.1) DL e = L for member subject to simple tensile force
increase in length
original length
dimensionless - millimetres / millimetre
4/23

5. STRAIN (cont2.) except for rubber bands, strains very small
usually not visible
more a material strains under load -
more the structure deflects
5/23

6. STESS & STRAIN SUMMARY force stress strain deformation causes
puts material under
deformation
results in
6/23

7. 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

8. 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

9. MODULUS OF ELASTICITY within elastic range
stress is proportional to strain
strain
stress a
linear relationship (Hooke’s Law)
the modulus of elasticity, E,
is a property of a material
E =
stress
strain
E is stress divided by strain
slope of line (tan a)
same units as stress (MPa)
9/23

10. MODULUS OF ELASTICITY (cont.)
the modulus of elasticity, E, is a property of a material
steel ,000 MPa
modulus of elasticity, E
aluminium ,000 MPa
concrete ,000 MPa (varies)
timber ,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

11. MODULUS OF ELASTICITY (cont.)
the modulus of elasticity, E,
is a property of a material
measures the resistance to deformation
higher E – more resistant to deformation
11/24

12. 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 energy
12/24

13. DUCTILITY - PLASTICITY (cont1.)
yield stress
yield point
elastic
range
stress
strain
ultimate
failure
plastic
range
ultimate deformation of plastic material much greater
than elastic deformation - visible to naked eye
13/24

14. 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
14/24

15. ELASTO - PLASTIC MATERIALS
ductile materials can be used safely
below the yield stress
overstress --> deform dramatically
but don’t immediately break
good warning
15/24

16. SNAP ! BRITTLENESS sudden breaking of atomic bonds
material fails suddenly - like glass
16/24

17. BRITTLENESS (cont.) stress strain brittle failure occurs with
yield point
stress
strain
brittle failure occurs with
little energy absorption
failure
stone, brick, concrete, glass
high compressive strength -
poor tensile strength
most traditional structures designed to
eliminate tensile stresses - domes , vaults
timber not durable - 19thC iron then steel
17/24

18. CURE FOR BRITTLENESS reinforced concrete invented in 2nd half of 19thC
steel bars placed in parts of
concrete that are in tension
concrete cracks but
steel resists the tension
cracks very fine - important that
water does not reach steel
18/24

19. CURE FOR BRITTLENESS (cont.)
add elasto-plastic material
that can resist tension
into brittle material
19/24

20. SELECTING THE RIGHT MATERIAL
timber - not fireproof
strength per volume just less than R.C - much less than steel
strength per weight not much less than steel - long span glulam
stone rarely used today as structural material
brick and block - loadbearing walls
for multistorey buildings of medium height
steel - needs fireproofing, rustproofing
reinforced concrete (R.C.) - slow construction
prestressed concrete (P.C.) - expensive
aluminium - lightweight, expensive
20/24

21. SAFETY FACTORS must ensure that structures do not collapse
must have a margin of safety
factor of safety allows for
imperfections in materials
loads not considered
slightly undersized members
simplifications in assumptions made in analysis
two philosophies
ultimate strength method
elastic method
21/24

22. Ultimate Strength Method
SAFETY FACTORS
Ultimate Strength Method
load that structure carries x a factor of safety
factored load called the Ultimate Load
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
depends on structure and material
22/24

23. SAFETY FACTORS Elastic Method
ensure that actual maximum stress in structure
less than Maximum Permissible Stress
Max Permissible Stress =
Ultimate Stress
Factor of Safety
Maximum Permissible Stress nearly always falls
within elastic range of material
23/24

24. SERVICEABILITY factor of safety ensures that structure does not
collapse under most situations
but also need to avoid excessive deflection
leads to cracking - elements and finishes
excessive deflection - instantaneous / creep
creep - slowly over time - timber, concrete
creep deflection may be 2-3 times as much as
instantaneous deflection
24/24