Question $5$

A composite bar of square cross$-$section with dimensions $2b2b$ is constructed of two different materials

having moduli of elasticity $E_1$ and $E_2($see the figure below$).$ Both parts of the bar have the same cross$-$sectional

dimensions. $($a$)$ Assuming that the end plates are rigid, derive a formula for the eccentricity $e$ of the load P so

that each part of the bar is stressed uniformly in compression. $($b$)$ Under these conditions, what axial forces $P_1$

and $P_2$ are carried by materials $1$ and $2,$ respectively?

$[$Ans$.($a$)e=\frac{b(E_2-E_1)}{2(E_2+E_1)},$

$($b$)\{$:$P_1=\frac{P{E}_1}{E_1+E_2},P_2=\frac{P{E}_2}{E_1+E_2}]$