Shear Flow in Open and Closed Sections Questions and Answers

Answer: C

Correct answer: An increased stalling speed in level flight

Torsional flexibility lowers the divergence speed, lowers the aileron reversal speed and increases the twist under load, all of which follow from the wing twisting more for a given aerodynamic moment. The stalling speed depends on the wing area, the maximum lift coefficient and the weight, and is not a torsional matter at all.

Answer: D

Shear flow analysis produces the wall-by-wall shear distribution under transverse load and torque, and locates the shear centre. Those two results size the skins and webs and feed directly into the aeroelastic behaviour of the wing.

Answer: A

In a tapered box the spar caps are inclined to the axis, so their axial loads have transverse components that relieve part of the applied shear. Ignoring the taper overstates the shear the webs must carry, sometimes appreciably near the root.

Answer: B

Turning a flange around the hole restores stiffness at the edge and lets the shear divert smoothly, and it also stabilises the surrounding web against buckling. Plain square holes at high-shear stations are a reliable way to start a fatigue crack.

Answer: C

Each cap contributes \( 400 \sin 4^\circ = 400 \times 0.0698 = 27.9 \) kN, and two caps give about 56 kN. That much of the applied shear is carried by the caps rather than the web, which a prismatic analysis would miss.

Answer: D

Both are true and the second explains the first. The relief can amount to a significant fraction near the root where the caps are most heavily loaded, so treating a tapered box as prismatic is conservative but wasteful.

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 are the reason flanged holes are used: the flange gives the diverted shear a stiff path round the opening and stabilises the free edge against buckling. Statement 3 is the opposite of practice - a plain square hole puts sharp re-entrant corners into a highly stressed web, which is where fatigue cracks start.

Answer: B

Correct answer: Flanging removes the need to analyse the web at all

Flanging restores local stiffness, stabilises the edge and helps the shear divert smoothly, but the web around a cut-out still needs analysing - arguably more carefully than an unpierced one, since the flow is redistributed and the stress at the hole edge is raised. The flange makes the detail acceptable, not the analysis unnecessary.

Answer: C

For a deep section with most of the area in the flanges, the parabolic variation across the web is slight, so the average flow is an accurate and much quicker working value. For a shallow section the approximation is poorer and the full distribution should be used.

Answer: D

The wall-by-wall flows set the skin and web thicknesses, and the shear centres along the span define the flexural axis about which the wing twists. Both outputs feed directly into aeroelastic clearance as well as static strength.