Lesson test: Strain and stiffness

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Strain and stiffness

1.[3p]
A steel bar 3 m long with a cross-sectional area of 500 mm² carries 50 kN in tension. Taking $E = 210$ GPa, what is its extension in millimetres?

CorrectNot quite: 1.43

2.[2p]
A steel member works at a stress of 105 MPa. What is its strain, in microstrain, taking $E = 210$ GPa?

CorrectNot quite: 500

3.[3p]
A steel bar is held between immovable walls and heated by 25 K. Taking $E = 210$ GPa and $α = 12 \times 10^{- 6}$ per kelvin, what compressive stress does it develop, in MPa?

CorrectNot quite: 63

4.[3p]
Two members of different materials are forced to shorten by the same amount. Which carries the larger share of the load?

The stiffer one, since equal strain means stress in proportion to Young's modulus

Correct

The stronger one, since strength decides how much load a member takes

The answer is: The stiffer one, since equal strain means stress in proportion to Young's modulus

The larger one, since load divides in proportion to area alone

The answer is: The stiffer one, since equal strain means stress in proportion to Young's modulus

They share equally, because they deform equally

The answer is: The stiffer one, since equal strain means stress in proportion to Young's modulus

5.[2p]
The thermal stress in a fully restrained bar depends on its length.

True

The answer is: False

False

Correct

6.[3p]
Match each material to its approximate Young's modulus.

Steel
Aluminium
Concrete
Timber along the grain

210 GPa
10 GPa
30 GPa
70 GPa

Show the answer

Steel: 210 GPa Aluminium: 70 GPa Concrete: 30 GPa Timber along the grain: 10 GPa

7.[2p]
Heat treating a steel raises its yield strength substantially. What happens to its Young's modulus?

It barely changes, because stiffness comes from the interatomic bonds rather than the microstructure

Correct

It rises in the same proportion as the strength

The answer is: It barely changes, because stiffness comes from the interatomic bonds rather than the microstructure

It falls, because the material becomes more brittle

The answer is: It barely changes, because stiffness comes from the interatomic bonds rather than the microstructure

It doubles, which is why treated steels are used for springs

The answer is: It barely changes, because stiffness comes from the interatomic bonds rather than the microstructure

8.[2p]
For a material with Poisson's ratio 0.5, what is the fractional change in volume under load?

CorrectNot quite: 0

9.[3p]
Which statements about the axial extension formula $δ = N L / A E$ are correct?

Select all that apply

It treats the bar as a spring of stiffness $A E / L$

Correct

It assumes the material is still on the straight part of its stress-strain curve

Correct

It supplies the extra equations that statically indeterminate structures need

Correct

It holds up to the point where the bar breaks

The answer is: It treats the bar as a spring of stiffness $AE/L$, It assumes the material is still on the straight part of its stress-strain curve, It supplies the extra equations that statically indeterminate structures need

1.[3p] A steel bar 3 m long with a cross-sectional area of 500 mm² carries 50 kN in tension. Taking E=210 GPa, what is its extension in millimetres?

2.[2p] A steel member works at a stress of 105 MPa. What is its strain, in microstrain, taking E=210 GPa?

3.[3p] A steel bar is held between immovable walls and heated by 25 K. Taking E=210 GPa and α=12×10-6 per kelvin, what compressive stress does it develop, in MPa?

4.[3p] Two members of different materials are forced to shorten by the same amount. Which carries the larger share of the load?

5.[2p] The thermal stress in a fully restrained bar depends on its length.

6.[3p] Match each material to its approximate Young's modulus.

7.[2p] Heat treating a steel raises its yield strength substantially. What happens to its Young's modulus?

8.[2p] For a material with Poisson's ratio 0.5, what is the fractional change in volume under load?

9.[3p] Which statements about the axial extension formula δ=NL/AE are correct?

1.[3p]
A steel bar 3 m long with a cross-sectional area of 500 mm² carries 50 kN in tension. Taking $E = 210$ GPa, what is its extension in millimetres?

2.[2p]
A steel member works at a stress of 105 MPa. What is its strain, in microstrain, taking $E = 210$ GPa?

3.[3p]
A steel bar is held between immovable walls and heated by 25 K. Taking $E = 210$ GPa and $α = 12 \times 10^{- 6}$ per kelvin, what compressive stress does it develop, in MPa?

4.[3p]
Two members of different materials are forced to shorten by the same amount. Which carries the larger share of the load?

5.[2p]
The thermal stress in a fully restrained bar depends on its length.

6.[3p]
Match each material to its approximate Young's modulus.

7.[2p]
Heat treating a steel raises its yield strength substantially. What happens to its Young's modulus?

8.[2p]
For a material with Poisson's ratio 0.5, what is the fractional change in volume under load?

9.[3p]
Which statements about the axial extension formula $δ = N L / A E$ are correct?