Lesson test: Torsion

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Torsion

1.[2p]
Why does the elementary torsion theory apply only to circular sections?

A circle looks the same after any rotation about the axis, so nothing makes the section warp out of plane

Correct

Only circles can be manufactured accurately enough

The answer is: A circle looks the same after any rotation about the axis, so nothing makes the section warp out of plane

Non-circular sections have no polar second moment of area

The answer is: A circle looks the same after any rotation about the axis, so nothing makes the section warp out of plane

The shear modulus is defined only for round bars

The answer is: A circle looks the same after any rotation about the axis, so nothing makes the section warp out of plane

2.[3p]
A solid shaft of 40 mm diameter carries a torque of 500 N m. What is the maximum shear stress, in MPa?

CorrectNot quite: 39.8

3.[3p]
A shaft transmits 50 kW at 1500 rpm. What torque does it carry, in N m?

CorrectNot quite: 318

4.[2p]
For steel with $E = 210$ GPa and $ν = 0.3$ , what is the shear modulus $G$ , in GPa?

CorrectNot quite: 80.8

5.[2p]
Doubling the diameter of a solid shaft multiplies the torque it can carry at a given surface stress by what factor?

Eight

Correct

Two

The answer is: Eight

Four

The answer is: Eight

Sixteen

The answer is: Eight

6.[2p]
For a given mass of material, a hollow circular shaft carries more torque than a solid one of the same material.

True

Correct

False

The answer is: True

7.[2p]
Where does the shear stress vanish in a shaft under pure torsion?

On the axis, since the shear strain is proportional to radius

Correct

At the outer surface, which is free of load

The answer is: On the axis, since the shear strain is proportional to radius

Nowhere, since the stress is uniform across the section

The answer is: On the axis, since the shear strain is proportional to radius

At the fixed end, which cannot rotate

The answer is: On the axis, since the shear strain is proportional to radius

8.[3p]
Slitting a closed tube along its length does what to its torsional stiffness?

Collapses it by a factor of hundreds, because the shear flow can no longer circulate

Correct

Leaves it unchanged, since the same material is present

The answer is: Collapses it by a factor of hundreds, because the shear flow can no longer circulate

Roughly halves it

The answer is: Collapses it by a factor of hundreds, because the shear flow can no longer circulate

Increases it, because the section is free to warp

The answer is: Collapses it by a factor of hundreds, because the shear flow can no longer circulate

9.[3p]
Match each quantity in the torsion formula to what it describes.

T
J
G
theta

the angle of twist over the length L
the material stiffness in shear
how the area is distributed about the axis
the applied torque

Show the answer

T: the applied torque J: how the area is distributed about the axis G: the material stiffness in shear theta: the angle of twist over the length L

1.[2p] Why does the elementary torsion theory apply only to circular sections?

2.[3p] A solid shaft of 40 mm diameter carries a torque of 500 N m. What is the maximum shear stress, in MPa?

3.[3p] A shaft transmits 50 kW at 1500 rpm. What torque does it carry, in N m?

4.[2p] For steel with E=210 GPa and ν=0.3, what is the shear modulus G, in GPa?

5.[2p] Doubling the diameter of a solid shaft multiplies the torque it can carry at a given surface stress by what factor?

6.[2p] For a given mass of material, a hollow circular shaft carries more torque than a solid one of the same material.

7.[2p] Where does the shear stress vanish in a shaft under pure torsion?

8.[3p] Slitting a closed tube along its length does what to its torsional stiffness?

9.[3p] Match each quantity in the torsion formula to what it describes.

1.[2p]
Why does the elementary torsion theory apply only to circular sections?

2.[3p]
A solid shaft of 40 mm diameter carries a torque of 500 N m. What is the maximum shear stress, in MPa?

3.[3p]
A shaft transmits 50 kW at 1500 rpm. What torque does it carry, in N m?

4.[2p]
For steel with $E = 210$ GPa and $ν = 0.3$ , what is the shear modulus $G$ , in GPa?

5.[2p]
Doubling the diameter of a solid shaft multiplies the torque it can carry at a given surface stress by what factor?

6.[2p]
For a given mass of material, a hollow circular shaft carries more torque than a solid one of the same material.

7.[2p]
Where does the shear stress vanish in a shaft under pure torsion?

8.[3p]
Slitting a closed tube along its length does what to its torsional stiffness?

9.[3p]
Match each quantity in the torsion formula to what it describes.