Question

A column $ABCD(2y_1\times 2y_2)$ of rectangular section carries a load $P$ at $Z$ having the coordinates $(x,y)$ as show in the given figure.


If the compressive stresses are taken as positive and area $A=2y_1\times 2y_2=4y_1{y}_2$ and the moment of inertia about $X$ and $Y$ axis being $I_{xx}$ and $I_{yy}$ respectively, then the stress at the corner $D$ is

• A. $\frac{P}{A}+\frac{Py}{I_{xx}}{y}_1+\frac{Px}{I_{yy}}{y}_2$
• B. $\frac{P}{A}-\frac{Py}{I_{xx}}{y}_1-\frac{Px}{I_{yy}}{y}_2$
• C. $\frac{P}{A}+\frac{Py}{I_{yy}}{y}_1+\frac{Px}{I_{xx}}{y}_2$
• D. $\frac{P}{A}-\frac{Py}{I_{yy}}{y}_1-\frac{Px}{I_{xx}}{y}_2$

Answer 1

The correct option is B $\frac{P}{A}-\frac{Py}{I_{xx}}{y}_1-\frac{Px}{I_{yy}}{y}_2$

Moment about $X-X$ axis $=Py$
Moment about $Y-Y$ axis $=Px$
$\therefore$ $StressatA=\frac{P}{A}+\frac{Py}{I_{xx}}{y}_1-\frac{Px}{I_{yy}}{y}_2$
$StressatB=\frac{P}{A}+\frac{Py}{I_{xx}}{y}_1+\frac{Px}{I_{yy}}{y}_2$
$StressatC=\frac{P}{A}-\frac{Py}{I_{xx}}{y}_1+\frac{Px}{I_{yy}}{y}_2$
$StressatD=\frac{P}{A}-\frac{Py}{I_{xx}}{y}_1-\frac{Px}{I_{yy}}{y}_2$