For the composite bar of Prob. 2.111, determine the residual stresses in the tempered-steel bars if P is gradually increased from zero to 98 kips and then decreased back to zero.

Prob. 2.111

Two tempered-steel bars, each 3/16 in. thick, are bonded to a 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 X 10⁶ 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 = 0.04 in. 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