Question

A steel column, pinned at both ends, has a buckling load of 200 kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be

• A. 200 kN
• B. 283 kN
• C. 400 kN
• D. 800 kN

Answer 1

The correct option is D 800 kN

Both ends are pinned, $l_{eff}=l$
Buckling load, $P_1=\frac{{\pi }^{2}EI}{l^2}=200kN$
When column is restrained against lateral movement at its mid height,
$l_{ef}=\frac{l}{2}$
Buckling load,
$P_2=\frac{{\pi }^{2}EI}{{\left(\frac{l}{2}\right)}^2}$
$=4\left(\frac{{\pi }^{2}EI}{l^2}\right)$
$=4\times 200$
$=800kN$