For a column of length L with both ends pinned, the Euler critical buckling load Pcr is:
Choose the correct answer
Pcr = pi x E x I / L^2
Pcr = pi^2 x E x I / L^2
Pcr = pi^2 x E x A / L^2
Pcr = E x I / L
Correct Answer
B. Pcr = pi^2 x E x I / L^2
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Euler (1744): Pcr = pi^2 EI / (KL)^2, where KL = effective length (K = 1.0 for both ends pinned, 0.5 for both ends fixed, 0.7 for fixed-pinned, 2.0 for fixed-free/cantilever). Slenderness ratio lambda = KL/r (r = sqrt(I/A)). Euler formula valid only for slender columns (lambda > 100 for steel). Critical stress sigma_cr = pi^2 E / lambda^2.
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