WORKSHEET 3

Material Behaviour

Q1

a) what is stress?

Give units where applicable

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 lengthe = L / L - dimensionless

c) what is the Modulus of Elasticity, E?linear relationship between stress and strainslope of line, where tan = stress /strain

- same units as stress

Q2

a) what is the stress in the rod?

area of rod = x D2 / 4

b) what is the strain in the rod?

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:

stress = Force / Area

= 81.5 MPa

E = stress / strain

strain = stress / E = 81.5 / 70,000 = 0.00116 (1.2 x 10-3)

(keep units to Newtons, MPa and mm2 for simplicity)

= x 25 x 25 / 4 = 490.9 mm2

= 40000 / 490.9 = 81.5 N/mm2

Q2

d) what happens when we take the weight off?

the rod goes back to its original length

typical yield strength of aluminium is up to 150MPa

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

so still within elastic range

strain = L / LL = L x strain = 3.5 mm

c) how much does the rod lengthen?

= 3000 x 0.00116

Q3

a) elastic behaviour mean?

b) plastic behaviour mean?

• material responds to stress in linear way.

• material deformation great with respect to stress applied.

What does:

c) brittle behaviour mean?• material fails suddenly. Very soon after elastic behaviour

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

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

• deformation is permanent. Still have strength

• usually weak in tension - strong in compression

5/22

Q4

a) elastic?

yes - it has a linear relationship between stressand strain up to the yield stress

b) plastic?

Is steel:

yes - after the elastic range it becomes plastic untilultimate failure

c) brittle?

no

Q5

Draw the stress/strain curvesfor:(Mark the yield point, area of plasticity, and point of failure)

a) an elasto-plastic material

b) a brittle material

plasticrange

ultimatefailure

strain

stre

ssyield point

failure

elasticrange

yield stress

yield stressstre

ss

strain

yield point

elasticrange

Q6

What are the advantages of elasto-plastic materials?

after the yield stress is reached, large deformations take placebut material does not immediately fail.

can take more stress until ultimate failure.

large deformations - visible to naked eye give warningthat reaching danger stage.

Q7

a) Name two brittle materials

b) How does one cure brittleness?

concrete, glass, masonry, brick, cement

by introducing elastic material to take careof tensile stresses.

in reinforced concrete steel reinforcement resiststensile 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.

10/22

Q9

stress = Force / Area

a) What dimensions should the column be (nearest 25mm)?

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:

= 3.2 x 106 /30

= 350 x 350 mm

Area = Force / stress = 106,667 mm2

square column = √106,667 mm2

= 326.6

= 375 mm dia.

round column D2 /4 = 106,667

D = √ 135,813 D2 = 135,813

Q9

stress = Force / Area = 3.2 x 106/ (350 x 350)

b) What is the actual stress in the column?

= 26.12 N/mm2 = 26.1 MPa

c) What is the strain in the column?

Strain = stress / E = 26.12/25,000

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:

= 0.001

d) By how much does the column shorten?

Strain = change in length / original length

= 0.001 x 3000 = 3.0 mm

change in length = strain x original length

Q10

b) what do factors of safety allow for?

• 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

a) what are safety factors and why do we use them

• 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 disadvantagesof the following when used as structural materials

and when would you use them:

15/22

Q11

• good in tension & compression - medium strength - yield stress 10-50MPa (as used)

a) timber

• hard to create rigid joints - pinned and semi-rigid joints

• low Modulus of Elasticity 8000-15000MPa - large deformations - creeps

• low weight 600-1000kg/m3 - good strength to weight ratio

• strength time dependent - varies across grain (except for plywood, particleboard)

• flammable (very large sections ok) - when fire resistance not an issue

• easy to cut to length on site - easily joined• reasonably inexpensive - except for special e.g. glulam• may be attractive - use for appearance

advantages

disadvantages

•swells with moisture

•small spans (except for glulam)

• framing, post & beam, trusses, panels, floors usage

• small structures usually - glulam can be used for larger spans

Q11

• low strength - yield stress 3-20MPa - very weak in tension - brittle

b) brick / block

• medium Modulus of Elasticity 10000-25000MPa• heavy: ~1900 kg/m3

• nonflammable - when fire resistance is an issue

• not waterproof

• reasonably inexpensive

• may be attractive - use for appearance

• good sound proofing - use for sound isolation (cavity walls)

advantages

disadvantages

usage• use in compression• walls, piers, footings, retaining walls, arches, vaults(not so much today)

Q11

• high strength - yield stress 250-300MPa up to 1000MPa for high strength wires • good in tension and compression

c) steel

• high Modulus of Elasticity 200000 MPa - small deformations

• heavy: 7800 kg/m3

• nonflammable but loses strength under heat - needs to be fireproofed

• small variability - lower factor of safety

• expensive - use efficiently e.g. I-beams

• can be easily manufactured in many shapes - rolled, cast

• rusts - needs protection (stainless steel possible but expensive)

advantages

disadvantages

usage• where tensile strength is required - reinforcement

• buckling may be a problem - thin elements

• for long spans, large loads

• frames mainly but also floor decking & roofing as sheets

Q11

• medium strength - yield stress 20-50MPa

d) reinforced concrete

• medium Modulus of Elasticity 20000 - 30000 MPa - medium deformations

• heavy: 2400 kg/m3 - use efficiently

• nonflammable

• large variability - lower factor of safety

• waterproof if made properly - else needs protection • can be formed into many shapes• good sound proofing - use for sound isolation (floors)

• generally inexpensive - forms the fabric

• slow construction

advantages

disadvantages

usage

• medium spans• frames, slabs, shells, footings, retaining walls

Q11

• high strength - yield stress 20-50MPa

e) prestressed concrete

• Modulus of Elasticity similar to Reinforced Concrete

• expensive - use efficient shapes

advantages

disadvantages

usage

• long spans

• other properties similar to Reinforced Concrete

• smaller sections than Reinforced Concrete - lighter

• often precast - faster construction

• lighter than R.C. but still fairly heavy

• frames, slabs, shells

20/22

Q11

• high strength - yield stress varies - up to 150MPa - increased by alloying

f) aluminium

• medium Modulus of Elasticity 200000 MPa - small to medium deformations• light (with respect to strength): 2700 kg/m3 - use for lightweight structures

• nonflammable but loses strength under heat - needs to be fireproofed• small variability - lower factor of safety

• expensive - use efficiently

• may be attractive - use for appearance

• can be easily manufactured in many shapes - rolled, drawn, extruded

• corrosion resistant - good in exposed conditions (may need protection)

advantages

disadvantages

usage

• good in tension and compression

• buckling may be a problem

• long spans, medium loads• lightweight structures, frames, space frames

21/22

Q11

• low strength as used ~ 15 MPa (due to surface cracks)

g) glass

• may be used as fibreglass - much stronger - eliminates chance of cracks

• heavy: 2700 kg/m3 - use efficiently

• expensive - use efficiently

• medium to high Modulus of Elasticity 200000 MPa - small to medium deformations

advantages

disadvantages

usage

• brittle, poor in tension

• use mainly in compression or small spans

• use where effect is main consideration

• transparent - use for functionality / effect

• sheets, blocks, roofing, window-walls including lateral support22/22