Practice Question: Column Buckling

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Solution

Answer: C) 1.0

 

Refer to PE Civil Reference Handbook Section 1.6.8
 
Euler formula for critical axial load for long column subjected to buckling:

\[P_{cr}=\frac{\pi^2EI}{(Kl)^2}\\\]

Both columns have the same \(E\), \(I\)

Accordingly, the ratio of critical buckling can be simplified as follows:

\[P_{cr1} / P_{cr2} = (K_{2}L_{2})^2/(K_{1}L_{1})^2 \\\]

Effective Length Factor for Column 1 (Pin-Pin):
\[K_{1}\ =\ 1.0 \qquad    (L_1 = 2L) \\\]

Effective Length Factor for Column 2 (Fixed-Free):
\[K_{2}\ = 2.0 \qquad    (L_2 = L) \\\]

So, the ratio is:
\[P_{cr1} / P_{cr2} = \frac{(2L)^2}{(1\times 2L)^2}=1.0\\\]

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