GATE 2024 AE – Question 54

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

The cross section of a thin-walled beam with uniform wall thickness t, shown in the figure, is subjected to a bending moment $M_x$ = 10 Nm. If h = 1 m and t = 0.001 m, the magnitude of maximum normal stress in the cross section is _________N/m$^2$ (answer in integer).

A channel section. A vertical web of height $h$ and thickness $t$, with a horizontal flange of length $h/2$ at the top and bottom, both pointing to the right. The x axis is horizontal through the middle of the web.

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Correct answer: 15000

Explanation

The section is symmetric about the $x$ axis, so $x$ is a principal axis. $I_{xx} = \frac{th^3}{12} + 2\left(t\frac{h}{2}\right)\left(\frac{h}{2}\right)^2 = \frac{th^3}{12} + \frac{th^3}{4} = \frac{th^3}{3} = 3.33 \times 10^{-4}$ m$^4$. The maximum stress is at the flanges, $y = \frac{h}{2}$: $\sigma = \frac{M_xy}{I_{xx}} = \frac{10 \times 0.5}{3.33 \times 10^{-4}} = 15000$ N/m$^2$.