고체역학 (Gere) — Axially Loaded Members: Problem 2.7-1

2.7-1 A prismatic bar \(AD\) of length \(L\), cross-sectional area \(A\), and modulus of elasticity \(E\) is subjected to loads \(5P\), \(3P\), and \(P\) acting at points \(B\), \(C\), and \(D\), respectively (see figure). Segments \(AB\), \(BC\), and \(CD\) have lengths \(L/6\), \(L/2\), and \(L/3\), respectively. (a) Obtain a formula for the strain energy \(U\) of the bar. (b) Calculate the strain energy if \(P = 27\text{ kN}\), \(L = 130\text{ cm}\), \(A = 18\text{ cm}^2\), and the material is aluminum with \(72\text{ GPa}\).