Torsion of Thin Walled Sections Questions and Answers

Answer: C

The assertion is false while the reason, though loosely stated, is true. Twist is linear in length, not cubic; it is bending deflection that carries the cube. Doubling a shaft's length doubles its twist under the same torque.

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 analogy applied. Shear stress corresponds to the slope of the soap film, and at a sharp re-entrant corner the film must fold into the angle, giving a locally very steep slope and hence a high stress. A fillet lets the film curve gently instead, which is why filleting is the standard remedy.

Answer: A

Both statements are true and the second states the result the first summarises. The square is what makes closing a section so effective, and it is why enlarging a cell beats thickening its walls whenever the geometry allows.

Answer: B

The first two are correct. The third is false precisely for a circular section: it is the one case in which the torsion constant and the polar second moment of area coincide, which is why the elementary theory works exactly there.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 give the analogy correctly: the slope of the film is the shear stress and twice the volume beneath it is the torque. Statement 3 confuses slope with height - the height of the film is the stress function itself, and it is its gradient, not its value, that corresponds to stress.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: warping is an axial displacement that leaves the section non-planar, and restraining it generates additional direct stresses. Statement 3 is the exact reverse - the circular shaft is the one common section that does not warp at all, which is precisely what makes the elementary torsion theory exact for it.

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: torsional rigidity is \( GJ \), and it plays the same role in torsion that \( EI \) plays in bending. Statement 3 contradicts the first - torsion strains the material in shear, so the shear modulus is the relevant property, and Young’s modulus does not appear.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: the torsion constant of an open section carries a cube on the wall thickness, and such sections warp freely and so develop large stresses if that warping is restrained. Statement 3 is badly wrong - for a thin open section the torsion constant is a tiny fraction of the polar second moment of area.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 follow from the membrane analogy: at an outside corner the film lies flat against the boundary, so the slope and hence the stress is zero, while at a re-entrant corner it folds sharply and the stress rises. Statement 3 inverts the remedy - filleting reduces the peak stress, which is why it is done.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are correct and they are the same fact from two sides: shear stress and hence the contribution to stiffness grow with radius, so material near the axis earns little and is better placed at the outside. Statement 3 is an approximation rather than a truth - the stress still varies linearly across the wall, and only for a thin wall is it nearly uniform.