Bending of Thin Walled Beams Questions and Answers

Answer: C

The first two are correct. The third gets the units wrong: dividing a fourth power by a length leaves a cube, so the section modulus is in cubic millimetres. It is the second moment of area that carries the fourth power.

Answer: D

These four relations connect the loading to the stress and the deflection, and between them cover most elementary beam work. Note the cube on the length in the deflection result, which is what makes span so expensive in stiffness.

Answer: A

Correct answer: It has units of length to the fourth power

The section modulus is \( I/y \), which is length to the fourth divided by length - so its units are length cubed. That is precisely what makes it a modulus rather than a second moment, and it is why dividing the applied moment by it gives a stress.

Answer: B

The plastic modulus is the first moment of the two half-areas about the equal-area axis, corresponding to a fully plastic hinge. It exceeds the elastic value, and the ratio between them is the shape factor, about 1.5 for a rectangle.

Answer: C

The elastic modulus is \( bh^2/6 \) and the plastic modulus is \( bh^2/4 \), so the ratio is \( 6/4 = 1.5 \). An I-section, with its material already concentrated in the flanges, gives a shape factor much closer to one, typically around 1.15.

Answer: D

Both statements are true and the second explains the first. Since the flanges are already close to fully stressed when the extreme fibre yields, little extra capacity remains to be unlocked by full plasticity, so the plastic and elastic moduli are close together.

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: the plastic modulus exceeds the elastic one, and their ratio for a rectangle is 1.5. Statement 3 reverses the comparison - an I-section has most of its material already at the extreme fibres, so plasticity adds little and its shape factor is only about 1.15, well below the rectangle’s.

Answer: B

Nothing about the physics changes, but the geometry allows powerful simplifications: walls can be treated as lines, stringers as points, and skin as carrying shear alone. Those idealisations turn an awkward integration into arithmetic while losing very little accuracy.

Answer: C

Bending analysis converts the moments that load analysis produced into stresses at specific points of specific members, and locates the critical one. Everything downstream, from material allowables to fatigue life, is applied at that point.

Answer: D

Once the section is fully plastic it sustains the plastic moment while rotating freely, which is the mechanism plastic collapse analysis is built on. First yield at the extreme fibre occurs earlier, at the smaller elastic moment.