고체역학 (Gere) — Axially Loaded Members: Problem 2.5-29

2.5-29 A polyethylene tube (length L) has a cap that when installed compresses a spring (with undeformed length \(L_1 > L\)) by an amount \(\delta = (L_1 - L)\). Ignore deformations of the cap and base. Use the force at the base of the spring as the redundant. Use numerical properties given in the boxes. (a) What is the resulting force in the spring, \(F_k\)? (b) What is the resulting force in the tube, \(F_t\)? (c) What is the final length of the tube, \(L_f\)? (d) What temperature change \(\Delta T\) inside the tube will result in zero force in the spring? Numerical Properties (from Problem 2.5-29 image): Modulus of elasticity: Polyethylene tube (\(E_t = 0.7\) GPa) Coefficients of thermal expansion: \(\alpha_t = 140 \times 10^{-6}/^{\circ}\text{C}\), \(\alpha_k = 12 \times 10^{-6}/^{\circ}\text{C}\) Properties and dimensions: \(d_0 = 150\) mm, \(t = 3\) mm, \(L_1 = 308\) mm, \(L = 305\) mm, \(k = 262.5\) kN/m