Question

A steel column pinned at both ends has a buckling load of 300 kN. If the column is restrained against lateral movement and rotation at its mid-height, its buckling load will be_____kN.
$\text{[Adopt}{l}_{eff}=0.707l,\text{for one end fixed}\text{and one end hinged]}$

Answer 1

The buckling load of a steel column pinned at both ends is
$P_1=\frac{{\pi }^{2}EI}{l_{eff}^2}=\frac{{\pi }^{2}EI}{l^2}=300kN$

When the column is restrained against lateral movement and rotation at its mid-height

$l_{eff}=0.707\left(\frac{l}{2}\right)=0.3535l$

$\therefore P_2=\frac{{\pi }^{2}EI}{(0.3535l{)}^2}=\frac{100}{12.5}\frac{{\pi }^{2}EI}{l^2}$

$=\frac{100}{12.5}\times 300=2400kN$