고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.120

*2.120 For the composite bar in Prob. 2.111, determine the residual stresses in the tempered-steel bars if \( P \) is gradually increased from zero until the deformation of the bar reaches a maximum value \( \delta_m = 0.04 \text{ in.} \) and is then decreased back to zero. (From Prob. 2.111: Two tempered-steel bars, each \( 3/16 \text{ in.} \) thick, are bonded to a \( 1/2\text{-in.} \) mild steel bar. This composite bar is subjected as shown to a centric axial load of magnitude \( P \). Both steels are elastoplastic with \( E = 29 \times 10^6 \text{ psi} \) and with yield strengths equal to \( 100 \text{ ksi} \) and \( 50 \text{ ksi} \), respectively, for the tempered and mild steel. The bar width is \( 2.0 \text{ in.} \) and the length is \( 14 \text{ in.} \))