Gere & Goodno — Axially Loaded Members: Problem 2.3-14

2.3-14 Consider the copper tubes joined in the figure using a “sweated” joint. Use the properties and dimensions given. (a) Find the total elongation of segment 2-3-4 (\(\delta_{2-4}\)) for an applied tensile force of \(P = 5\text{ kN}\). Use \(E_c = 120\text{ GPa}\). (b) If the yield strength in shear of the tin-lead solder is \(\tau_y = 30\text{ MPa}\) and the tensile yield strength of the copper is \(\sigma_y = 200\text{ MPa}\), what is the maximum load \(P_{\text{max}}\) that can be applied to the joint if the desired factor of safety in shear is \(\text{FS}_\tau = 2\) and in tension is \(\text{FS}_\sigma = 1.7\)? (c) Find the value of \(L_2\) at which tube and solder capacities are equal. Given values from figure: Inner tubes (1 & 5): \(d_0 = 18.9\text{ mm}\), \(t = 1.25\text{ mm}\) Outer sleeve (2-3-4): \(d_0 = 22.2\text{ mm}\), \(t = 1.65\text{ mm}\) Overlap lengths: \(L_2 = L_4 = 18\text{ mm}\) Sleeve-only length: \(L_3 = 40\text{ mm}\)