Stress and Strain

TUTORIAL 6

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what is stress?

Question 1a

internal force intensitya

force per unit area c

internal force b

a or c d

what are the units of stress?

Question 1b

kN, MNa

kPa, MPa c

kN / m, MN /m b

kNm2, MNm2d

what is strain?

Question 2a

a bad back achea

change in size or shapec

response to stress b

b and d e

change in size or shape relative to original stated

b and c f

what are the units of strain?

Question 2b

mm, cm, ma

no units c

kN / m b

kNmd

what is the strain in the cable?

Question 3a

4 mma

8 x 10-4 b

50 kN

5 m

20 mm

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 andGiven that the cable lengthens by 4mm

8 x 10-4 mmc

what is the stress in the cable?

Question 3b

159.2 kPaa

159.2 MPab

50 kN

5 m

20 mm

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 andGiven that the cable lengthens by 4mm

0.15 kPac

is the cable strong enough?

Question 3c

noa

yesb

50 kN

5 m

20 mm

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 andGiven that the cable lengthens by 4mm

Given that the maximum allowable tensile stressfor high-strength steel is 1000 MPa

what factors do we have to take Into consideration?

Question 4a

strength of the columna

slenderness of the columnb

when a column is under load

a and bc

what is the first means of failurewe should check for?

Question 4b

column breaking under compressiona

bucklingb

when a column is under load

what is the stress in the column?

Question 5a

1 MPaa

4 kPa b

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

1 kPac

160 kN

3.5

m

400 mm

what is the strain in the column?

Question 5b

50a

2 x 10-5 b

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

0.00002 mmc

160 kN

3.5

m

400 mm

is the column strong enough?

Question 5c

yesa

no b

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 stressfor the concrete is 20 MPa

160 kN

3.5

m

400 mm

could you reduce the area of the column?

Question 5d

yesa

no b

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

3.5

m

400 mm

maybe c

to what size could you theoreticallyreduce the area of the column?

Question 5e

90 mm x 90 mma

400 mm x 200 mm b

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

160 kN

3.5

m

400 mm

200 mm x 40 mm c

what would be the problem with that?

Question 5f

nonea

it would buckle b

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

160 kN

3.5

m

400 mm

it would be difficult to build c

b and c d

next question

enough !

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

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partly correct

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a thousand times NO! a force is a force – not stress

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enough !

f = F /A – so it’s force distributed over an area

1 kN/m2 = 1 kPa

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that’s force units

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go back to the formulaf = F / A

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enough !

strain is a response to stress andis a relative concept

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No?Then you 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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enough !

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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enough !

Well done !

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f = F / A

check your calculations and units(it’s good practice to keep everything to Newtons and

mm

1 N/mm2 = 1 MPa = 1MN/m2)

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enough !

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

and then think again

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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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enough !

both are important

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enough !

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

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enough !

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/mm2 = 1 MPa = 1 MN/m2

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enough !

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

Check your calculations? What’s ΔL? What’s L?

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e = ΔL / L

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What are the units of strain ??

e = ΔL / L

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enough !

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

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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next question

enough !

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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enough !

according to calculationsA = F / f

Minimum required area = 8000 mm2

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not according to the theoretical calculations

f = F / A A = F / f

the end !

Yes it’s much too slender. It would buckle immediately

Also, how could you pour concrete into such a small area?

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think again !

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