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Torsion MCQs – Part 1

15 questions. Tap an option to check it instantly, then read the solution.

Practice SSC JE and other civil engineering exam questions on torsion of shafts: the torsion equation T/J = τ/R = Gθ/L, polar moment of inertia and polar modulus, torsional rigidity, solid versus hollow shafts, shafts in series, power transmitted, combined bending and torsion (equivalent bending moment and torque), thin tubes, non-circular sections and torsional strain energy, plus a few related questions the book places in this chapter. Tap an option to check it, then open the full explanation for each question.

Question 1Medium
To have exactly zero tensile stress at one extreme fibre of a solid circular section (diameter D) under combined direct compressive and bending stress, a normal point load must be placed ______.
Full explanation

Answer: C. beyond a distance of 3D/8 measured towards the centre from the periphery

Zero stress at the far fibre when e = Z/A = D/8, i.e. 3D/8 in from the periphery; any load at or beyond that distance from the edge (closer to the centre) causes no tension.

Question 2Medium
Identify the correct statement related to a circular shaft subjected to pure torsion.
Full explanation

Answer: D. The torque required to produce a twist of one radian per unit length of a shaft is termed torsional rigidity.

T = GJ·(θ/L); with θ/L = 1 rad per unit length, T = GJ — the torsional rigidity.

Question 3Easy
A circular shaft of 20 mm diameter transmits torque. Find the safe torque if the shear stress is not to exceed 30 MPa.
Full explanation

Answer: C. 15000π N·mm

T = τπd³/16 = 30 × π × 8000/16 = 15000π N·mm.

Question 4Easy
Which of the following terms represents the torque that produces a twist of one radian in a shaft of unit length?
Full explanation

Answer: B. Torsional rigidity

GJ = TL/θ; with L = 1 and θ = 1 rad, GJ = T. This is torsional rigidity.

Question 5Easy
A solid circular shaft of diameter 100 mm is subjected to a torque of 8 kN·m. Determine the maximum shear stress induced in the shaft (in N/mm²).
Full explanation

Answer: D. 128/π

τ = 16T/(πD³) = 16 × 8 × 10⁶/(π × 10⁶) = 128/π N/mm² ≈ 40.7 MPa.

Question 6Easy
If D and d are the external and internal diameters of a circular shaft, its polar moment of inertia is:
Full explanation

Answer: D. π(D⁴ − d⁴)/32

J = π(D⁴ − d⁴)/32 — the solid-shaft value for D minus that for d.

Question 7Easy
If Ix and Iy are the moments of inertia of a section about the X and Y axes, the polar moment of inertia of the section is:
Full explanation

Answer: C. Ix + Iy

Perpendicular axis theorem: J = Iz = Ix + Iy.

Question 8Hard
The strain energy stored per unit volume in a hollow shaft under pure torque, when the maximum shear stress is fs, is 17fs²/(64N), where N is the modulus of rigidity. The ratio of inner diameter to outer diameter is:
Full explanation

Answer: C. 1/4

U/V = (fs²/4N)(D² + d²)/D² = 17fs²/64N → (D² + d²)/D² = 17/16 → d/D = 1/4.

Question 9Hard
Channels get twisted symmetrically with regard to their axis ______.
Full explanation

Answer: B. parallel to web

Book key (b): parallel to the web. The question is loosely worded and keys differ.

Question 10Medium
Pick the correct statement(s): A. The bending moment which, acting alone, would produce a maximum stress equal to the major principal stress caused by combined bending and torsion is called the equivalent bending moment. B. The torque which, acting alone, would produce a maximum shear stress equal to the maximum shear stress caused by combined bending and torsion is called the equivalent torque.
Full explanation

Answer: C. Both A and B

Both are standard definitions: Me = ½[M + √(M² + T²)], Te = √(M² + T²).

Question 11Easy
A circular shaft of diameter d and length l is subjected to a torque T and a bending moment M. The ratio of maximum (torsional) shear stress to maximum bending stress is:
Full explanation

Answer: B. T/(2M)

τ/σ = (16T/πd³)/(32M/πd³) = T/2M.

Question 12Medium
For a hollow shaft with external and internal diameters of 10 cm and 5 cm, the torsional section modulus is approximately:
Full explanation

Answer: A. 184 cm³

Zp = π(D⁴ − d⁴)/(16D) = π × 9375/160 ≈ 184 cm³.

Question 13Medium
The moment required to rotate the near end of a prismatic beam through a unit angle, without translation, with the far end fixed, is:
Full explanation

Answer: D. 4EI/L

Rotational (bending) stiffness with the far end fixed = 4EI/L; with the far end hinged = 3EI/L.

Question 14Easy
In a shaft, the shear stress is NOT directly proportional to the:
Full explanation

Answer: C. length of the shaft

τ = GRθ/L — inversely proportional to length.

Question 15Medium
A solid shaft (diameter 20 cm, length 400 cm, modulus of rigidity N = 0.8 × 10⁵ N/mm²) under a twisting moment develops a maximum shear stress of 50 N/mm². The angle of twist in radians is:
Full explanation

Answer: C. 0.025

θ = τL/(NR) = 50 × 4000/(0.8 × 10⁵ × 100) = 0.025 rad. (The exam printed 0.0025; question cancelled.)