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GATE 2019 AE – Question 63

Structures · Flight vehicle structures: torsion, bending and shear of thin-walled sections, loads on aircraft · 2 marks · Numerical answer

A thin closed single-cell section consists of a semicircle of radius 50 mm and the triangular part shown, with axial width 500 mm and total height 100 mm. Wall thickness is 1 mm, shear modulus is 26 GPa and applied torque is 1 kN m. Find the wall shear stress in MPa (one decimal place).

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Correct answer: 17.0 to 17.5

Explanation

The enclosed median-line area is $A=\tfrac12(0.5)(0.1)+\tfrac12\pi(0.05)^2=0.028927$ m². Bredt’s relation gives shear flow q=T/(2A), and τ=q/t. Therefore $\tau=1000/[2(0.028927)(0.001)]=17.29$ MPa, or 17.3. G would be needed for twist, not this stress.

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