Question

The rectangular column shown in the figure below carries a load $P$ having eccentricities ${}^{\prime }{e}_x^{\prime }$ and ${}^{\prime }{e}_y^{\prime }$ along the X-axis and Y-axis respectively. The stress at any point $(x,y)$ is given by

• A. $\frac{P}{bd}[1+\frac{12e_y\times y}{d^2}+\frac{12e_x\times x}{d^2}]$
• B. $\frac{P}{bd}[1+\frac{12e_y\times y}{b^2}+\frac{12e_x\times x}{d^2}]$
• C. $\frac{P}{bd}[1+\frac{6e_y\times y}{d^2}+\frac{6e_x\times x}{b^2}]$
• D. $\frac{P}{bd}[1+\frac{6e_y\times y}{b^2}+\frac{6e_x\times x}{d^2}]$

Answer 1

The correct option is A $\frac{P}{bd}[1+\frac{12e_y\times y}{d^2}+\frac{12e_x\times x}{d^2}]$

Stress at any point
$=\frac{P}{bd}+\frac{P{e}_y\times y}{1_{xx}}+\frac{P{e}_x\times x}{I_{yy}}$
$=\frac{P}{bd}[1+\frac{12e_y\times y}{d^2}+\frac{12e_x\times x}{d^2}]$