WORKSHEET 3 Material Behaviour

1
WORKSHEET 3Material Behaviour
2
Q1
Give units where applicable
internal force intensity as result of external
forces, force per unit area - Pa, kPa, MPa -
1Pa 1 N / m2
change in size or shape relative to original
state, e.g. change in length relative to original
length e DL / L - dimensionless
linear relationship between stress and
strain slope of line, d, where tan d stress
/strain - same units as stress
3
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
area of rod p x D2 / 4
p x 25 x 25 / 4 490.9 mm2
stress Force / Area
81.5 MPa
40000 / 490.9 81.5 N/mm2
(keep units to Newtons, MPa and mm2 for
simplicity)
E stress / strain
strain stress / E
81.5 / 70,000
0.00116 (1.2 x 10-3)
4
Q2
strain DL / L DL L x strain
3.5 mm
3000 x 0.00116
typical yield strength of aluminium is up to
150MPa
so still within elastic range
the rod goes back to its original length
stress in rod 81.5 MPa
max allowable stress of aluminium 120 MPa
stress in rod lt maximum allowable stress
yes - the rod is strong enough
5
Q3
What does

• material responds to stress in linear way.

• the deformation , i.e. strain is linearly
  proportional to
• the stress applied.

• the deformation is reversible.

• material deformation great with respect to
  stress applied.

• material can be bent and reshaped - e.g.
  plasticene.

• deformation is permanent. Still have strength

• material fails suddenly. Very soon after elastic
  behaviour

• usually weak in tension - strong in compression

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6
Q4
Is steel
yes - it has a linear relationship between
stress and strain up to the yield stress
yes - after the elastic range it becomes plastic
until ultimate failure
no
7
Q5
Draw the stress/strain curves for(Mark the yield
point, area of plasticity, and point of
failure)
8
Q6
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.
9
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
10
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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11
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
stress Force / Area
3.2 x 106 /30
Area Force / stress
106,667 mm2
v106,667 mm2
square column
350 x 350 mm
326.6
round column
?D2 /4 106,667
D2 135,813
375 mm dia.
D v 135,813
12
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
stress Force / Area 3.2 x 106/ (350 x 350)
26.12 N/mm2
26.1 MPa
Strain stress / E
26.12/25,000
0.001
Strain change in length / original length
change in length strain x original length
0.001 x 3000
3.0 mm
13
Q10

• 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

• 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

14
Q10

• vary from 1.5 to 2.5
• depend on type of building and material

• 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

15
Q11
What are the advantages and disadvantages of the
following when used as structural materials and
when would you use them
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16
Q11
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

17
Q11
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)

18
Q11
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

19
Q11
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

20
Q11
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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21
Q11
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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22
Q11
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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