Torsion of Thin Walled Sections Questions and Answers

Answer: C

Where the axial displacements the section wants to make are resisted, direct stresses appear that pure torsion theory does not predict. A circular shaft is the exception, since it wants to make no such displacements in the first place.

Answer: D

Preventing the section from warping forces axial strains and hence direct stresses, largest at the restraint and decaying along the member. Open sections, which warp freely, suffer these stresses most severely when built in.

Answer: A

Vlasov added a warping term to the classical torsion theory, introducing the warping constant and the bimoment. It is essential for open sections built into rigid supports, where the St Venant solution alone would badly underestimate the stresses.

Answer: B

The direct stresses from restrained warping have zero resultant force and zero resultant bending moment, yet they are real and can be large. The bimoment is the generalised force that quantifies them, and it has no counterpart in elementary strength of materials.

Answer: C

Shear stress grows with radius, so material near the axis contributes little while adding weight. Removing it and redistributing the same mass to a larger radius raises the polar second moment substantially for the same weight.

Answer: D

The membrane analogy makes this immediate: the film is steepest where it meets the boundary furthest from the centre of the hole, that is at the middle of the long side. At a corner the film is flat against the boundary and the stress is actually zero.

Answer: A

The membrane over a corner lies flat against the boundary on two sides, so its slope, and hence the stress, vanishes. This is the outside corner of a rectangle; a re-entrant corner is the opposite case and concentrates stress severely.

Answer: B

The membrane must fold sharply into a re-entrant corner, giving a very steep slope and a high stress. A generous fillet eases the fold and reduces the peak, which is why such corners are always radiused in a machined fitting.

Answer: C

Bending gives direct stress and torsion gives shear stress, and both are found independently for a linearly elastic member. They are then combined at the critical point using a failure criterion such as maximum shear stress or von Mises.

Answer: D

The slit destroys the circulating shear flow and leaves only the St Venant mechanism, so the stiffness collapses by orders of magnitude. Bending stiffness, by contrast, is barely touched, which makes the demonstration a striking one.