TUTORIAL 6

Stress and Strain

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Question 1a

what is stress?

a

b

c

d

internal force intensity internal force force per unit area a or c

Question 1b

what are the units of stress?

a

b

c

d

kN, MN kN / m, MN /m kPa, MPa kNm 2, MNm 2

Question 2a

what is strain?

a

b

c

d

e

f

a bad back ache response to stress change in size or shape change in size or shape relative to original state b and d b and c

Question 2b

what are the units of strain?

a

b

c

d

mm, cm, m kN / m no units kNm

Question 3a

a 20mm ø high-strength steel cable 5 m long has a weight of 50 kN at its end. Neglecting the self-weight of the cable and Given that the cable lengthens by 4mm 20 mm 50 kN

a

b

c

what is the strain in the cable?

4 mm 8 x 10 -4 8 x 10 -4 mm

Question 3b

a 20mm ø high-strength steel cable 5 m long has a weight of 50 kN at its end. Neglecting the self-weight of the cable and Given that the cable lengthens by 4mm 20 mm 50 kN

a

b

c

what is the stress in the cable?

159.2 kPa 159.2 MPa 0.15 kPa

Question 3c

a 20mm ø high-strength steel cable 5 m long has a weight of 50 kN at its end. Neglecting the self-weight of the cable and Given that the cable lengthens by 4mm Given that the maximum allowable tensile stress for high-strength steel is 1000 MPa 20 mm 50 kN

is the cable strong enough?

a

b

no yes

Question 4a

when a column is under load

what factors do we have to take Into consideration?

a b

c

strength of the column slenderness of the column a and b

Question 4b

when a column is under load

what is the first means of failure we should check for?

a

b

column breaking under compression buckling

Question 5a

160 kN a reinforced concrete column , 400 x 400 mm and 3.5 m high is subject to a load of 160 kN 400 mm Given that the column shortens by 0.07 mm

what is the stress in the column?

a

b

c

1 MPa 4 kPa 1 kPa

Question 5b

160 kN a reinforced concrete column , 400 x 400 mm and 3.5 m high is subject to a load of 160 kN 400 mm Given that the column shortens by 0.07 mm

what is the strain in the column?

a

b

c

50 2 x 10 -5 0.00002 mm

Question 5c

a reinforced concrete column , 400 x 400 mm and 3.5 m high is subject to a load of 160 kN Given that the column shortens by 0.07 mm Given that the maximum allowable stress for the concrete is 20 MPa

is the column strong enough?

a

b

yes no

160 kN 400 mm

Question 5d

a reinforced concrete column , 400 x 400 mm and 3.5 m high is subject to a load of 160 kN Given that the column shortens by 0.07 mm Given that the column is understressed 160 kN 400 mm

could you reduce the area of the column?

a

b

c

yes no maybe

Question 5e

a reinforced concrete column , 400 x 400 mm and 3.5 m high is subject to a load of 160 kN Given that the column shortens by 0.07 mm

to what size could you theoretically reduce the area of the column?

400 mm 160 kN

a

b

c

90 mm x 90 mm 400 mm x 200 mm 200 mm x 40 mm

Question 5f

Given that you want to reduce the column to 90 mm x 90mm

what would be the problem with that?

a

b c

d

none it would buckle it would be difficult to build b and c

160 kN 400 mm

f = F /A – so it’s force distributed over an area that means it’s the intensity of the force, not the force itself

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enough !

partly correct

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a thousand times NO !

a force is a force – not stress

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f = F /A – so it’s force distributed over an area 1 kN/m 2 = 1 kPa

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that’s force units

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go back to the formula f = F / A

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strain is a response to stress and is a relative concept

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Then you No?

are the pain

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I don’t like that the change is just the deformation – not the strain

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length over length means strain is dimensionless

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e = ΔL / L this is length over length

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where’s the force in e = ΔL / L ?

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0.0008 is also correct but 8 x 10 -4 gives a better feel

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e = ΔL / L what’s ΔL, what’s L, what are the units for strain?

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what are the units for strain ?

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Well done !

f = F / A check your calculations and units (it’s good practice to keep everything to Newtons and mm 1 N/mm 2 = 1 MPa = 1MN/m 2 )

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actual stress of 159 MPa is much less than max allowable stress of 1000 MPa

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and then think again What’s the actual stress? What’s the maximum allowable stress?

Is the actual stress less or more than the max allowable stress?

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both are important

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we always check to see if a column is slender and would buckle first

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Right on ! f = F / A

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How did you get that?

f = F / A What’s the force? What’s the area?

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check your calculations and your units?

It’s good practice to keep everything to Newtons and mms 1 N/mm 2 = 1 MPa = 1 MN/m 2

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0.00002 is also correct but 2 x 10 -5 follow is easier to

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enough !

e = ΔL / L Check your calculations? What’s ΔL? What’s L?

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e = ΔL / L What are the units of strain ??

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actual stress of 1 MPa is much less than max allowable stress of 20 MPa

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enough !

What’s the actual stress? What’s the maximum allowable stress?

Is the actual stress less than or greater than the max allowable stress?

SO ?

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it depends on how much we reduce it by

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If it’s understressed that means the area is greater than needs be

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according to calculations A = F / f Minimum required area = 8000 mm 2

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not according to the theoretical calculations f = F / A  A = F / f

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Yes it’s much too slender. It would buckle immediately Also, how could you pour concrete into such a small area?

the end !

think again !

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