WORKSHEET 3
Material Behaviour
Q1
Give units where applicable
a) what is stress? internal force intensity as result of external forces,
force per unit area - Pa, kPa, MPa - 1Pa = 1 N / m2
b) what is strain? change in size or shape relative to original state,
e.g. change in length relative to original length
e = DL / L - dimensionless
c) what is the Modulus of Elasticity, E?
linear relationship between stress and strain
slope of line, d, where tan d = stress /strain
- same units as stress
Q2
A footbridge is supported by 25mm dia. aluminium rod 3 m long. Each
rod carries a load of 40 kN added to its end. Neglecting the self-weight of
the rod and given the Modulus of Elasticity of aluminium as 70,000 MPa:
a) what is the stress in the rod?
area of rod = p x D2 / 4
= p x 25 x 25 / 4 = 490.9 mm2
stress
= Force / Area
= 40000 / 490.9 = 81.5 N/mm2
= 81.5 MPa
(keep units to Newtons, MPa and mm2 for simplicity)
b) what is the strain in the rod?
E = stress / strain
strain = stress / E
= 81.5 / 70,000
= 0.00116 (1.2 x 10-3)
Q2
c) how much does the rod lengthen?
strain = DL / L
DL = L x strain
= 3000 x 0.00116
= 3.5 mm
d) what happens when we take the weight off?
typical yield strength of aluminium is up to 150MPa
so still within elastic range
the rod goes back to its original length
e) Given that the maximum allowable tensile stress for
aluminium is 120 MPa, is the rod strong enough?
stress in rod = 81.5 MPa
max allowable stress of aluminium = 120 MPa
stress in rod < maximum allowable stress
yes - the rod is strong enough
Q3
What does:
a) elastic behaviour mean?
• material responds to stress in linear way.
• the deformation , i.e. strain is linearly proportional to
the stress applied.
• the deformation is reversible.
b) plastic behaviour mean?
• material deformation great with respect to stress applied.
• material can be bent and reshaped - e.g. plasticene.
• deformation is permanent. Still have strength
c) brittle behaviour mean?
• material fails suddenly. Very soon after elastic behaviour
• usually weak in tension - strong in compression
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Q4
Is steel:
a) elastic?
yes - it has a linear relationship between stress
and strain up to the yield stress
b) plastic?
yes - after the elastic range it becomes plastic until
ultimate failure
c) brittle?
no
Draw the stress/strain curves
for:(Mark the yield point, area of
plasticity, and point of failure)
stress
Q5
a) an elasto-plastic material
yield stress
ultimate
failure
elastic plastic strain
range range
stress
b) a brittle material
yield point
failure yield stress
yield point
elastic strain
range
Q6
What are the advantages of elasto-plastic materials?
after the yield stress is reached, large deformations take place
but material does not immediately fail.
can take more stress until ultimate failure.
large deformations - visible to naked eye give warning
that reaching danger stage.
Q7
a) Name two brittle materials
concrete, glass, masonry, brick, cement
b) How does one cure brittleness?
by introducing elastic material to take care
of tensile stresses.
in reinforced concrete steel reinforcement resists
tensile stresses while concrete resists
the compressive stresses
Q8
What does a material with a high value of E do?
• for a given stress it will have less change in size or shape.
• i.e. it will deform less under the same loading conditions
for the same geometrical properties.
• a steel wire of the same diameter and length as a rope
will stretch less under the same load.
• a steel beam will deflect less than a timber or
reinforced concrete beam of the same span
and cross-section given other things being equal.
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Q9
A ground-floor reinforced concrete column in a multi-storey building is 3m
high and carries a load 3.2 MN. Given that the max. allowable compressive
stress for concrete is 30MPa and the Modulus of Elasticity, E, of concrete is
25,000MPa:
a) What dimensions should the column be (nearest 25mm)?
stress = Force / Area
Area = Force / stress
= 3.2 x 106 /30
square column
= √106,667 mm2
= 326.6
round column
= 106,667 mm2
= 350 x 350 mm
pD2 /4 = 106,667
D2
= 135,813
D
= √ 135,813
= 375 mm dia.
Q9
A ground-floor reinforced concrete column in a multi-storey building is 3m
high and carries a load 3.2 MN. Given that the max. allowable compressive
stress for concrete is 30MPa and the Modulus of Elasticity, E, of concrete is
25,000MPa:
b) What is the actual stress in the column?
stress = Force / Area = 3.2 x 106/ (350 x 350)
= 26.12 N/mm2
= 26.1 MPa
c) What is the strain in the column?
Strain = stress / E
= 26.12/25,000
= 0.001
d) By how much does the column shorten?
Strain = change in length / original length
change in length = strain x original length
= 0.001 x 3000
= 3.0 mm
Q10
a) what are safety factors and why do we use them
• factors of safety are factors by which we over-design a structure to
allow a margin of safety
• in building, nothing is exact, nothing is certain
• adequate margins of safety must be used so that failure becomes
extremely unlikely without the building being grossly over-designed
• the minimum margins of safety required are given in Codes of
Practice
b) what do factors of safety allow for?
• uncertain loading conditions - unexpected loads in unexpected places
• uncertain material properties - imperfections in materials, variability
• inexact workmanship - slightly undersized members
• assumptions in theories and imprecise calculations
Q10
c) what value of safety factors do we use in buildings?
• vary from 1.5 to 2.5
• depend on type of building and material
d) would a steel structure require a higher or lower
safety factor than a reinforce concrete structure? Why?
• a steel structure would have a lower factor of safety than a concrete one
• because the properties of steel vary much less than those of concrete.
That is the tolerances are much smaller and thus a smaller
margin of error exists
Q11
What are the advantages and disadvantages
of the following when used as structural materials
and when would you use them:
15/22
Q11
a) timber
advantages
• good in tension & compression - medium strength - yield stress 10-50MPa (as used)
• low weight 600-1000kg/m3 - good strength to weight ratio
• easy to cut to length on site - easily joined
• reasonably inexpensive - except for special e.g. glulam
• may be attractive - use for appearance
disadvantages
• low Modulus of Elasticity 8000-15000MPa - large deformations - creeps
• hard to create rigid joints - pinned and semi-rigid joints
• strength time dependent - varies across grain (except for plywood, particleboard)
•swells with moisture
•small spans (except for glulam)
• flammable (very large sections ok) - when fire resistance not an issue
usage
• framing, post & beam, trusses, panels, floors
• small structures usually - glulam can be used for larger spans
Q11
b) brick / block
advantages
• reasonably inexpensive
• nonflammable - when fire resistance is an issue
• good sound proofing - use for sound isolation (cavity walls)
• may be attractive - use for appearance
disadvantages
• low strength - yield stress 3-20MPa - very weak in tension - brittle
• medium Modulus of Elasticity 10000-25000MPa
• heavy: ~1900 kg/m3
• not waterproof
usage
• use in compression
• walls, piers, footings, retaining walls, arches, vaults(not so much today)
Q11
c) steel
advantages
• high strength - yield stress 250-300MPa up to 1000MPa for high strength wires
• good in tension and compression
• high Modulus of Elasticity 200000 MPa - small deformations
• small variability - lower factor of safety
• can be easily manufactured in many shapes - rolled, cast
disadvantages
• heavy: 7800 kg/m3
• nonflammable but loses strength under heat - needs to be fireproofed
• rusts - needs protection (stainless steel possible but expensive)
• buckling may be a problem - thin elements
• expensive - use efficiently e.g. I-beams
usage
• where tensile strength is required - reinforcement
• for long spans, large loads
• frames mainly but also floor decking & roofing as sheets
Q11
d) reinforced concrete
advantages
• medium strength - yield stress 20-50MPa
• medium Modulus of Elasticity 20000 - 30000 MPa - medium deformations
• nonflammable
• good sound proofing - use for sound isolation (floors)
• can be formed into many shapes
• waterproof if made properly - else needs protection
• generally inexpensive - forms the fabric
disadvantages
• heavy: 2400 kg/m3 - use efficiently
• large variability - lower factor of safety
• slow construction
usage
• medium spans
• frames, slabs, shells, footings, retaining walls
Q11
e) prestressed concrete
advantages
• high strength - yield stress 20-50MPa
• Modulus of Elasticity similar to Reinforced Concrete
• other properties similar to Reinforced Concrete
• smaller sections than Reinforced Concrete - lighter
• often precast - faster construction
disadvantages
• expensive - use efficient shapes
• lighter than R.C. but still fairly heavy
usage
• long spans
• frames, slabs, shells
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Q11
f) aluminium
advantages
• high strength - yield stress varies - up to 150MPa - increased by alloying
• good in tension and compression
• medium Modulus of Elasticity 200000 MPa - small to medium deformations
• light (with respect to strength): 2700 kg/m3 - use for lightweight structures
• corrosion resistant - good in exposed conditions (may need protection)
• can be easily manufactured in many shapes - rolled, drawn, extruded
• may be attractive - use for appearance
• nonflammable but loses strength under heat - needs to be fireproofed
• small variability - lower factor of safety
disadvantages
• expensive - use efficiently
• buckling may be a problem
usage
• long spans, medium loads
• lightweight structures, frames, space frames
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Q11
g) glass
advantages
• low strength as used ~ 15 MPa (due to surface cracks)
• may be used as fibreglass - much stronger - eliminates chance of cracks
• medium to high Modulus of Elasticity 200000 MPa
- small to medium deformations
• transparent - use for functionality / effect
disadvantages
• brittle, poor in tension
• heavy: 2700 kg/m3 - use efficiently
• expensive - use efficiently
usage
• use mainly in compression or small spans
• use where effect is main consideration
• sheets, blocks, roofing, window-walls including lateral support
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