Shear Flow in Open and Closed Sections Questions and Answers

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: warping is the axial displacement that leaves the section non-planar, and it is harmless until it is restrained - at a built-in end, say - whereupon direct stresses arise. Statement 3 is wrong: open sections warp more freely than closed ones, and thin-walled open sections are where restrained warping matters most.

Answer: B

The four cases cover most of what airframe work meets. Note how differently the shear centre behaves: outside the material for a channel, at the leg junction for an angle, and at the centroid for a doubly symmetric box.

Answer: C

These four relations carry most of the arithmetic in the topic. The contrast between the second and fourth is the important one: closed-section capacity depends on thickness linearly, open-section stiffness on its cube.

Answer: D

Correct answer: A-2, B-1, C-4, D-3

The four steps trace the method. A closed section is one degree redundant in shear, so it is cut to make it determinate; the redundant flow is then restored to satisfy compatibility; equating the rates of twist supplies the extra equations a multi-cell box needs; and locating the shear centre decides whether a given transverse load will twist the member at all.

Answer: A

Correct answer: A-2, B-1, C-4, D-3

Each change follows from a different part of the theory. Closing an open section replaces a \( t^3 \) resistance with a Bredt-Batho one, raising the stiffness by orders of magnitude. Halving an open wall thickness cuts \( J \) by eight, since it goes as \( t^3 \). Doubling the enclosed area halves the flow at a given torque, since \( q = T/2A \). And thinning one wall of a closed box raises the stress there, since \( q \) is unchanged.

Answer: B

Correct answer: A-2, B-1, C-4, D-3

Four definitions, each precise. Shear flow is stress times thickness, a force per unit length. The shear centre is the point through which a load causes no twist. Warping is the axial displacement leaving the section non-planar. And the redundant shear flow is the constant restored after cutting a closed cell to make it determinate.

Answer: C

Correct answer: Cutting a longitudinal slit along a closed tube

A slit destroys the closed path, so the circulating flow can no longer form and the tube falls back on the \( \sum bt^3/3 \) resistance of an open section - a collapse of two or three orders of magnitude for a cut that removes almost no material. The other three changes all increase the stiffness.

Answer: D

Correct answer: It always lies within the material of the section

The shear centre is a geometric property and can lie well outside the material. For a channel it sits on the far side of the web from the flanges, in the air; for an angle it lies at the intersection of the two legs. This is exactly why a channel twists so readily under a load applied at its web.

Answer: A

Correct answer: It is largest where the wall is thickest

The shear flow is constant round the cell, so it is neither largest nor smallest anywhere. The quantity that varies is the shear stress \( q/t \), and that is largest in the thinnest wall - the opposite of what the incorrect statement suggests. The other three statements are all true.

Answer: B

The flow depends only on the torque and the enclosed area. Thickness affects the stress and the rate of twist, but the flow itself is fixed by equilibrium and is the same however the material is distributed round the cell.