Shear Flow in Open and Closed Sections Questions and Answers

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. The cells share webs and belong to one continuous structure, so they must twist together. Setting the rate of twist equal for every cell supplies exactly the compatibility equations needed to solve for the individual cell shear flows, which equilibrium alone cannot determine.

Answer: D

Both are true and the second explains the first. Two axes of symmetry fix both coordinates at their intersection. The consequence is that bending and torsion decouple naturally in such a box, which is a considerable analytical convenience.

Answer: A

Both statements are true and the second explains the first. Treating the box as open would leave the redundant constant unaccounted for and give a distribution that does not satisfy compatibility, misplacing the shear flows around the section.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 are correct and follow from each other: \( q = \tau t \), and equilibrium keeps it constant along a wall whose thickness varies. Statement 3 is dimensionally wrong - shear flow is force per unit length, N/mm or kN/m, not force per unit area.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: the shear centre is by definition the point through which a load causes bending without twist, and symmetry requires it to lie on any axis of symmetry. Statement 3 is false in general - for a channel the shear centre lies outside the material altogether, and only in a doubly symmetric section do the two points coincide.

Answer: D

The first two describe the standard method. The third is false: the redundant flow compensates exactly for the cut, so the final distribution is independent of its position. The cut is chosen only for arithmetic convenience.

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 are the Bredt-Batho result: \( q = T/2A \), constant round the cell. Statement 3 misdefines the area, which is that enclosed by the median line of the wall - for a thin box, close to the whole area of the box - and not the cross-sectional area of the material, which is very much smaller.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 are correct and connected: the torsion constant of an open section is \( \sum bt^3/3 \), and that cube on a small thickness is exactly why such sections are so soft in torsion. Statement 3 describes the closed section - an open one cannot form a circulating flow, because there is no closed path for it to circulate round.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 are the idealisation: the booms carry the direct stress and the panels between them carry a constant shear flow, which steps at each boom by \( VBy/I \). Statement 3 inverts the consequence - a boom on the neutral axis has zero first moment and produces no step at all, while the largest steps come from the booms furthest from the axis.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: the cells twist together, and the shared web carries the difference of the two circulating flows. Statement 3 is exactly what makes the multi-cell problem harder than the single-cell one - the cells are coupled through their shared webs and through the common rate of twist, and must be solved simultaneously.