GATE 2023 AE – Question 52

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

The shear flow distribution in a single cell, thin-walled beam under the action of an arbitrary shear load ys applied at the shear centre S is shown in the figure. The cell has horizontal symmetry with booms marked by 1 to 4 that carry direct stresses. The shear modulus G is the same for all the walls, and the area of the cell is 135000 mm2. With respect to the point O marked in the figure, the distance to the shear centre S is ______ mm. (round off to the nearest integer)

source diagram and its labels are reproduced in the attached image.

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Correct answer: 196 to 198

Explanation

Taking moments of the shear-flow distribution about O, with the straight-wall span 500 mm, gives $e=2(135000)(-2.14\times10^{-3})+2(500)(100)(2.75\times10^{-3})+(500)(200)(5\times10^{-3})=197.2$ mm.

Official GATE 2023 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2023/AE_ANS_GATE2023.pdf