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Civil Engineering QUESTION #2117
Question 1
According to Euler's theory, the critical buckling load for a column with both ends pinned (hinged) is \(P_{cr} = \dfrac{\pi^2 EI}{L^2}\). For the same column with one end fixed and other end free, the critical load becomes:
  • The same \(\dfrac{\pi^2 EI}{L^2}\)
  • \(\dfrac{2\pi^2 EI}{L^2}\)
  • \(\dfrac{\pi^2 EI}{4L^2}\)✔️
  • \(\dfrac{4\pi^2 EI}{L^2}\)
Correct Answer Explanation
Effective length \(L_e\) for different end conditions: both pinned \(= L\); one fixed one free \(= 2L\). Euler's formula \(P_{cr} = \dfrac{\pi^2 EI}{L_e^2}\). For fixed-free: \(P_{cr} = \dfrac{\pi^2 EI}{(2L)^2} = \dfrac{\pi^2 EI}{4L^2}\). This is the minimum possible buckling load — the fixed-free condition is the least stable of all standard end conditions.