A wing box has an enclosed area of \( 1.2 \) m\( ^2 \) and a skin \( 2 \) mm thick. What torque produces a shear stress of \( 60 \) MPa?
Answer: A
The shear flow is \( 60 \times 10^6 \times 0.002 = 120 \) kN/m, and from \( T = 2Aq \) the torque is \( 2 \times 1.2 \times 120 = 288 \) kN m. Working forward from an allowable stress like this is how a torsion box is sized.
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Assertion (A): Semi-monocoque construction is lighter than a true monocoque of the same strength.
Reason (R): Adding stringers shortens the unsupported length of the skin, so a thinner skin may be used.
Select the correct answer from the options below.
Answer: B
Both are true and the second explains the first. Buckling, not material strength, sets the skin thickness in a shell, and dividing the panels with stiffeners raises the buckling stress sharply. The stringers add weight but the skin saves far more.
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Assertion (A): The hoop stress in a pressurised fuselage is twice the longitudinal stress.
Reason (R): A cylindrical shell resists the pressure over different projected areas in the two directions.
Select the correct answer from the options below.
Answer: C
Both statements are true and the second is the reason for the first. The result is why pressurisation cracks in a fuselage skin characteristically run lengthwise, along the direction of least stress, and why tear straps are laid to arrest exactly that.
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Assertion (A): A domed rear pressure bulkhead is lighter than a flat one of the same strength.
Reason (R): A dome carries the pressure largely in membrane tension rather than in bending.
Select the correct answer from the options below.
Answer: D
Both are true and the second explains the first. Membrane action uses the material uniformly through the thickness, whereas bending uses only the outer fibres effectively. The same argument explains why pressure vessels are round rather than square.
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Assertion (A): Wing ribs are more closely spaced towards the root.
Reason (R): Bending moment and skin compressive stress are highest near the root.
Select the correct answer from the options below.
Answer: A
Both statements are true and the second is the reason for the first. A higher compressive stress demands a shorter panel to avoid buckling, so the rib pitch follows the stress distribution rather than the geometry of the aerofoil.
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Assertion (A): A thin shear web may be allowed to buckle well below its ultimate load.
Reason (R): After buckling it carries load as a field of inclined tension bands.
Select the correct answer from the options below.
Answer: B
Both are true and the second explains the first. Wagner's diagonal tension theory shows the post-buckled web carries far more than its buckling load, provided the flanges and uprights can react the inward pull. Designing for that state rather than against it saves considerable weight.
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Assertion (A): Control surfaces are mass balanced ahead of the hinge line.
Reason (R): Moving the surface's centre of gravity forward decouples its rotation from wing bending.
Select the correct answer from the options below.
Answer: C
Both statements are true and the second is the reason for the first. Coupling between bending and control rotation is a classic flutter mechanism, and mass balance raises the flutter speed above the flight envelope. It is a certification requirement rather than an option.
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Assertion (A): Fail-safe design has largely replaced safe-life design for transport airframes.
Reason (R): Fail-safe structures retire every component at a fixed life regardless of inspection.
Select the correct answer from the options below.
Answer: D
The assertion is true but the reason describes safe-life, not fail-safe. A fail-safe structure provides an alternative load path so that a cracked member is carried until the damage is found by inspection. Safe-life retirement is the approach reserved for parts where redundancy is impractical, such as landing gear.
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Assertion (A): Tear straps are fitted to a pressurised fuselage skin.
Reason (R): They arrest a running crack so that decompression is controlled rather than catastrophic.
Select the correct answer from the options below.
Answer: A
Both are true and the second is the reason for the first. Without them a crack driven by hoop stress can run many frames in an instant. With them the damage is confined to a bay, which is the practical expression of damage tolerance.
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Assertion (A): A stringer run-out is a fatigue-critical detail.
Reason (R): The load the stringer carried must shear into the skin over a short length.
Select the correct answer from the options below.
Answer: B
Both statements are true and the second explains the first. The abrupt transfer produces a local stress peak that fatigue finds readily, which is why run-outs are tapered gradually and why they appear so often in service cracking reports.
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