Question

For the case of a slender column of length $l$, and flexural rigidity $EI$ built in at its base and free at the top, the Euler's critical buckling load is

• A. $\frac{4{\pi }^{2}EI}{l^2}$
• B. $\frac{2{\pi }^{2}EI}{l^2}$
• C. $\frac{{\pi }^{2}EI}{l^2}$
• D. $\frac{{\pi }^{2}EI}{4l^2}$

Answer 1

The correct option is D $\frac{{\pi }^{2}EI}{4l^2}$

In this case, effective length $=2l$
$P=\frac{{\pi }^{2}EI}{(2l{)}^2}=\frac{{\pi }^{2}EI}{4l^2}$