PROBLEM $2\mathrm{.}111$

Two tempered$-$steel bars, each $\frac{3}{16}$ in$.$ thick, are bonded to a $\frac{1}{2}-$in$.$ mild$-$steel

bar. This composite bar is subjected as shown to a centric axial load of

magnitude $P.$ Both steels are elastoplastic with $E=29{10}^6$ psi and with

yield strengths equal to $100$ ksi and $50$ ksi $,$ respectively, for the tempered

and mild steel. The load $P$ is gradually increased from zero until the

deformation of the bar reaches a maximum value ${}_m=0\mathrm{.}04in.$ and then

decreased back to zero. Determine $($a$)$ the maximum value of $P,($b$)$ the

maximum stress in the tempered$-$steel bars, $($c$)$ the permanent set after the

load is removed.