Discussion
Doubling the thickness of a plate at constant width changes its buckling stress by a factor of
Answer: C
Plate buckling stress varies as the square of the thickness-to-width ratio: \[ \sigma_{cr} = k \frac{\pi^{2} E}{12(1-\nu^{2})} \left(\frac{t}{b}\right)^{2} \] With \( b \) held constant, doubling \( t \) gives \[ \frac{\sigma_{2}}{\sigma_{1}} = \left(\frac{2t}{t}\right)^{2} = 2^{2} = 4 \] so the buckling stress quadruples. Compare the column case, where doubling a cross-sectional dimension raises the second moment of area far more sharply still.
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