A torsion test determines the shear modulus of a material by measuring
Answer: A
Rearranging the twist expression gives the shear modulus directly from the measured angle, the applied torque, the gauge length and the section's torsion constant. A circular specimen is used so that the torsion constant is known exactly.
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Torsional-flexural buckling is a failure mode of
Answer: B
A column whose section is open and torsionally soft may buckle by twisting and bending together at a load below the Euler value. It is a real design case for angles, channels and tees, and it is another consequence of the feebleness of open sections in torsion.
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A wing carrying a distributed aerodynamic torque along its span will have a rate of twist that
Answer: C
The torque accumulates from tip to root, so it is largest at the root, and with the box also tapering the rate of twist varies along the span. The total tip twist is found by integrating the local rate along the length.
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A shaft carries a bending stress of \( 80 \) MPa and a torsional shear stress of \( 30 \) MPa. The maximum shear stress in the material is nearest to
Answer: D
Correct answer: 50 MPa
The maximum shear stress under combined direct and shear loading is \[ \tau_{max} = \sqrt{\left(\frac{\sigma}{2}\right)^2 + \tau^2} = \sqrt{40^2 + 30^2} \] \[ = \sqrt{2500} = 50\ \mathrm{MPa}. \] Note the halving of the direct stress before squaring - it comes from the radius of Mohr’s circle, and omitting it gives 85 MPa.
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For that same stress state, the larger principal stress is nearest to
Answer: A
The principal stresses are \( \sigma/2 \pm \sqrt{(\sigma/2)^2 + \tau^2} = 40 \pm 50 \), giving \( 90 \) MPa and \( -10 \) MPa. Note that a compressive principal stress appears even though the applied direct stress was wholly tensile.
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A circular specimen of \( J = 6 \times 10^5 \) mm\( ^4 \) and gauge length \( 200 \) mm twists \( 0.001 \) radians under \( 240 \) N m. Its shear modulus is
Answer: B
Rearranging, \( G = TL/(J\theta) \). Working in newtons and millimetres, the numerator is \( 240\,000 \times 200 = 4.8 \times 10^7 \) and the denominator \( 6 \times 10^5 \times 0.001 = 600 \), giving \( 80\,000 \) N/mm\( ^2 \), that is 80 GPa. The value is about right for steel.
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Assertion (A): Open thin-walled columns can fail by torsional-flexural buckling.
Reason (R): Such sections have very low torsional stiffness.
Select the correct answer from the options below.
Answer: C
Both are true and the second explains the first. With little resistance to twist, the column finds a combined twisting and bending mode cheaper than pure Euler bending, and it can fail well below the load a flexural calculation alone would predict.
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Assertion (A): A circular specimen is used for a torsion test to determine shear modulus.
Reason (R): The torsion constant of a circular section is known exactly and equals its polar second moment of area.
Select the correct answer from the options below.
Answer: D
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason is the justification. To extract \( G \) from a measured torque and twist you must know \( J \) exactly, and only for a circular section is it exactly the polar second moment of area. Any other shape warps, so its torsion constant would itself have to be estimated and the modulus would inherit that uncertainty.
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Consider the following statements about combined bending and torsion:
1. The direct and shear stresses are found independently and then combined.
2. A failure criterion resolves them into an equivalent stress.
3. The two stresses may simply be added arithmetically.
Which of the statements given above is or are correct?
Answer: A
Correct answer: 1 and 2 only
Statements 1 and 2 describe the correct procedure: compute the bending and torsional stresses separately, then combine them through a failure criterion such as maximum shear stress or von Mises. Statement 3 is wrong - a direct stress and a shear stress act on different planes and cannot be added arithmetically, which is exactly what the criterion exists to handle.
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Consider the following statements about a wing box under distributed torque:
1. The accumulated torque is largest at the root.
2. The rate of twist varies along the span.
3. The total tip twist is the rate of twist at the root times the span.
Which of the statements given above is or are correct?
Answer: B
Correct answer: 1 and 2 only
Statements 1 and 2 are correct: torque accumulates inboard so it is greatest at the root, and since the rate of twist follows the local torque it varies along the span. Statement 3 would only hold if the rate were constant; the tip twist is the integral of the rate along the span, which for a linearly varying torque is about half that estimate.
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