Question

Consider two axially loaded columns namely 1 and 2, made of linear elastic material with Young's modulus $2\times {10}^5$MPa, square cross-section with side 10 mm and length 1 m. For column 1, one end is fixed and the other end is free. For column 2, one end is fixed and the other end is pinned. Based on the Euler's theory the ratio (up to one decimal place) of the buckling load of column 2 to the buckling load of column 1 is .

• A. 8

Answer 1

The correct option is A 8
$Eule{r}^{\prime }sBucklingload=\frac{{\pi }^{2}EI}{l_e^2}$
$l_{effective}$ for column $1=2l$
$l_{effective}forcolumn2=\frac{l}{\sqrt{2}}$
$\frac{P_2}{P_1}={\left(\frac{l_1}{l_2}\right)}_{effective}={\left(\frac{2l}{\frac{l}{\sqrt{2}}}\right)}^2$

$=(2\sqrt{2}{)}^2=8$