GATE 2025 AE – Question 60

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

Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is__ (rounded off to two decimal places).

Design A is a closed section made of a semicircle of radius 1 cm followed by a rectangle that is 4 cm long (from the centre of the semicircle) and 2 cm high. Design B has the same semicircle and the same 2 cm height, runs straight for 4 cm from the centre of the semicircle, and then tapers to a point over a further 2 cm.

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Correct answer: 1.20 to 1.22

Explanation

For a thin-walled closed section $T = 2A_mt\tau$, where $A_m$ is the enclosed area. The thickness and allowable shear stress are the same, so the maximum torque is proportional to the enclosed area. $A_A = \frac{\pi}{2} + 4 \times 2 = 9.571$ cm$^2$. For B there is also a triangle of base 2 cm and height 2 cm, so $A_B = 9.571 + 2 = 11.571$ cm$^2$. The ratio is $\frac{11.571}{9.571} = 1.21$.