Discussion
Euler's crippling load formula gives buckling load of long columns that is the ultimate load a column can take. Mathematically Euler's formula can be expressed as ________
Answer: A
Euler's formula is \(P = \frac{\pi^2 EI}{L^2}\).
For a long column with both ends pinned (the basic case), Euler's theory gives the crippling load
\[ P = \frac{\pi^2 EI}{L_e^2}, \quad L_e = L \]
The other forms are the same formula for other end conditions: one end fixed and the other free gives \(\frac{\pi^2EI}{4L^2}\), one fixed and one pinned about \(\frac{2\pi^2EI}{L^2}\), and both ends fixed \(\frac{4\pi^2EI}{L^2}\). The question asks for the basic expression, which is the pinned-pinned one.
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