Bending of Thin Walled Beams Questions and Answers

Answer: C

The assertion is false and the reason, though vague, is true. The dependence is on the cube of the length, not the square, so doubling the span multiplies the deflection by eight. Getting the power wrong here badly understates how expensive span is.

Answer: D

Both are true and the second explains the first. Scaling the width by the ratio of the moduli produces a single-material section with the same stiffness distribution, after which the familiar formula applies and the stresses are scaled back at the end.

Answer: A

Both statements are true and the second is the reason for the first. A constant moment has zero derivative, so the shear vanishes. The condition is approached in the central span of a four-point bending test, which is why that arrangement is used.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: with no axial force the neutral axis passes through the centroid, and it is perpendicular to the moment only for bending about a principal axis. Statement 3 confuses two things - a symmetry axis is always principal, but the neutral axis coincides with it only when the moment is applied about it.

Answer: C

The first two are correct. The third is false: unlike the second moments of area, the product of inertia can be positive or negative depending on how the material is distributed across the quadrants, and its sign determines which way the neutral axis rotates.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are the idealisation: booms take the direct stress and skin takes the shear. Statement 3 is what is deliberately discarded - a boom’s own centroidal second moment is negligible beside its transfer term \( Ay^2 \), and dropping it is what reduces the calculation to a summation.

Answer: A

All three are correct. The transfer term is positive because the offset is squared, and the theorem works in both directions, so a value known about any axis can be reduced to the centroidal one by subtracting the term.

Answer: B

All three are correct. Principal axes exist for any section whatever, since the product of inertia varies continuously as the axes rotate and must pass through zero; for a symmetric section they simply coincide with the axes of symmetry.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: shear lag leaves the stress lower away from the webs than simple bending theory predicts, and design allows for it by counting only an effective width of flange. Statement 3 reverses the dependence - the effect is worst in wide flanges, since the shear has further to travel from the web.

Answer: D

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: bending stiffness is \( EI \), and \( I \) rises with the square of the distance material is placed from the neutral axis. Statement 3 is exactly what is not true - two sections of identical area can differ in stiffness by an order of magnitude according to where that area sits.