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. Determine the residual stresses in the tempered$-$steel bars if the load $P$ is gradually

increased from zero until the deformation of the bar reaches a maximum value ${}_m=0\mathrm{.}04in.$ and is then decreased back to zero. Take

$L=13\mathrm{.}5$ in$.$