Bending of Thin Walled Beams Questions and Answers

Answer: C

The quantity EI appears throughout beam deflection theory, so stiffness may be raised either by choosing a stiffer material or by distributing the same material further from the neutral axis. In airframes the second route is almost always the cheaper one in weight.

Answer: D

Each element contributes its area times the square of its distance, so material at twice the distance is four times as effective. This is why a spar has heavy caps top and bottom joined by a light web, and why an I-section is the classic bending shape.

Answer: A

That combination appears because the two curvature equations must be solved simultaneously once the product of inertia couples them. It reduces to the simple product when the product of inertia is zero, at which point the general expression collapses back to the familiar formula.

Answer: B

The centroid is the area-weighted mean position, so each boom contributes its area times its coordinate. Simply averaging the positions would be right only if every boom had the same area, which on a real stiffened section is rarely true.

Answer: C

Shear deformation in wide, thin flanges means the direct stress does not reach the value simple theory predicts at points remote from the webs. The effect, known as shear lag, matters on wide wing boxes and is handled by using an effective width rather than the full flange.

Answer: D

The load has to travel into the flange by shear, and that transfer takes distance, so material far from a web is not fully stressed. Designers allow for it by counting only an effective width of skin as working, which is what the boom idealisation of a wing box quietly assumes.

Answer: A

After buckling, the middle of a panel sheds load while the material adjacent to the stiffeners continues to carry stress. Counting an effective width attached to each stiffener reproduces the load the panel really carries and keeps the section properties honest.

Answer: B

Pure bending means the moment is constant, and since shear force is the rate of change of bending moment along the beam, it vanishes. The condition is convenient in theory and is approached in a four-point bending test between the loading points.

Answer: C

Differentiating the moment with respect to position along the beam gives the shear, and differentiating the shear gives the distributed load. The chain lets a whole loading diagram be built up by successive integration from the applied load.

Answer: D

Multiplying the width of one material by the ratio of the moduli produces an equivalent section of a single material with the same stiffness distribution. Ordinary bending theory then applies, and the stresses in the transformed material are scaled back by the same ratio at the end.