An open channel and a closed box of the same wall material differ in torsional stiffness typically by a factor of order
Answer: A
The open section relies on the St Venant mechanism, with its cube on the wall thickness, while the closed one develops a circulating flow round the enclosed area. Three orders of magnitude is common, which is why a slit cut along a torsion tube is so catastrophic.
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Assertion (A): A closed section is vastly stiffer in torsion than an open one of the same material.
Reason (R): A closed cell develops a shear flow circulating round the enclosed area.
Select the correct answer from the options below.
Answer: B
Both are true and the second explains the first. The open section can only resist by St Venant shear varying through the wall thickness, a mechanism carrying a cube on a very small dimension. The difference commonly runs to three orders of magnitude.
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Assertion (A): A transverse load applied at the web of a channel section twists it.
Reason (R): The shear centre of a channel lies outside the section.
Select the correct answer from the options below.
Answer: C
Both statements are true and the second is the reason for the first. The flange shear flows form a couple whose resultant falls outside the material, so a load anywhere on the web leaves a residual torque. Channels are rarely used alone as beams for this reason.
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Assertion (A): Shear flow rather than shear stress is the natural variable in thin-walled analysis.
Reason (R): Shear flow stays constant along a wall whose thickness varies.
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Answer: D
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. Because \( q \) is continuous along a wall whose thickness steps or tapers, the equilibrium equations can be written in terms of a single unknown per panel, whereas the stress changes at every thickness change. The stress is then recovered at the end by dividing by the local thickness.
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Assertion (A): The shear flow in an open section can be found from equilibrium alone.
Reason (R): There is a free edge at which the shear flow is known to be zero.
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Answer: A
Both statements are true and the second explains the first. The known starting value makes the problem determinate, so the flow follows by integrating the first moment of area round the section. A closed section has no such edge and needs a compatibility condition.
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Assertion (A): A boom lying on the neutral axis produces no step in the shear flow.
Reason (R): The step at a boom is proportional to its first moment of area about the neutral axis.
Select the correct answer from the options below.
Answer: B
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. The step is \( VBy/I \), which is proportional to \( By \), the boom’s first moment about the neutral axis. A boom on the axis has \( y = 0 \), so its first moment vanishes and the shear flow passes it unchanged - which is also why such a boom contributes nothing to bending stiffness.
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Assertion (A): The thinnest wall of a closed section under torsion is the critical one.
Reason (R): The shear flow is constant round the cell, so stress varies inversely with thickness.
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Answer: C
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. With \( q \) constant round the cell, \( \tau = q/t \) is greatest where \( t \) is least. Thinning one wall to save weight therefore raises the stress in that wall alone and may make it the critical one, however generous the rest of the box.
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Assertion (A): Warping always produces additional direct stresses in a member under torsion.
Reason (R): Warping is an out-of-plane axial displacement of the cross-section.
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Answer: D
The assertion is false and the reason is true. Warping generates direct stress only when it is restrained, for instance at a built-in end or a heavy fitting. A member free to warp develops no such stresses and pure torsion theory applies unchanged.
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Assertion (A): Closing an open section with a light skin panel is a very efficient structural change.
Reason (R): The panel allows a circulating shear flow to form round the enclosed area.
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Answer: A
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. An open section resists torsion only through the small \( t^3 \) term summed over its walls, but a closed cell resists it through a circulating flow acting on the whole enclosed area. Adding a light skin to close the section can raise the torsional stiffness by two or three orders of magnitude for very little weight.
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Assertion (A): The position of the cut used to solve a closed section affects the final answer.
Reason (R): Cutting the section turns an indeterminate problem into a determinate one.
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Answer: B
The assertion is false and the reason is true. The cut is an analytical device: the redundant flow restored afterwards compensates exactly, so the final distribution is independent of where the cut was made. Choosing a convenient position merely simplifies the arithmetic.
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