Discussion
A simply supported plate \( 2 \) mm thick and \( 100 \) mm wide, with \( k = 4 \), \( E = 70 \) GPa and \( \nu = 0.33 \), buckles at nearest to
Answer: A
Correct answer: 103 MPa
\[ \sigma_{cr} = \frac{k\pi^2 E}{12(1-\nu^2)}\left(\frac{t}{b}\right)^2 = \frac{4 \times 9.87 \times 70{,}000}{12(1 - 0.33^2)} \times \left(\frac{2}{100}\right)^2 \] \[ = \frac{2{,}763{,}000}{10.69} \times 0.0004 = 103\ \mathrm{MPa}. \] The factor \( (t/b)^2 \) dominates: halving the panel width would quadruple this figure.
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