고체역학 (Gere) — Axially Loaded Members: Problem 2.5-22

2.5-22 A nonprismatic bar \(ABC\) made up of segments \(AB\) (length \(L_1\), cross-sectional area \(A_1\)) and \(BC\) (length \(L_2\), cross-sectional area \(A_2\)) is fixed at end \(A\) and free at end \(C\) (see figure). The modulus of elasticity of the bar is \(E\). A small gap of dimension \(s\) exists between the end of the bar and an elastic spring of length \(L_3\) and spring constant \(k_3\). If bar \(ABC\) only (not the spring) is subjected to temperature increase \(\Delta T\), determine the following. (a) Write an expression for reaction forces \(R_A\) and \(R_D\) if the elongation of \(ABC\) exceeds gap length \(s\). (b) Find expressions for the displacements of points \(B\) and \(C\) if the elongation of \(ABC\) exceeds gap length \(s\).