고체역학 (Gere) — Axially Loaded Members: Problem 2.4-9

2.4-9 Repeat Problem 2.4-8, but assume that the bar is made of aluminum alloy and that \(BC\) is prismatic. Assume that \(P = 90\text{ kN}\), \(L = 1\text{ m}\), \(t = 6\text{ mm}\), \(b_1 = 50\text{ mm}\), \(b_2 = 60\text{ mm}\), and \(E = 72\text{ GPa}\). From Problem 2.4-8: Bar \(ABC\) is fixed at both ends and has load \(P\) applied at an intermediate point. Find reactions at \(A\) and \(C\) and the horizontal displacement \(\delta_B\) at point \(B\). Figure 2.4-9 Configuration: Total length of the bar is \(L = 1\text{ m}\). Point \(A\) is the left fixed support (\(x = 0\)). Load \(P\) is applied at distance \(L/4\) from \(A\). Let's call this point \(P_{load}\). Point \(B\) is at distance \(L/4\) from the load point \(P_{load}\) (or \(L/2\) from \(A\)). Point \(C\) is the right fixed support (\(x = L = 1\text{ m}\)). Segment \(A\)-\(P_{load}\) is tapered with width varying linearly from \(b_2\) at \(A\) to \(b_1\) at \(P_{load}\). Its length is \(L_1 = L/4 = 0.25\text{ m}\). Segment \(P_{load}\)-\(C\) is prismatic with constant width \(b_1\). Its total length is \(L_2 + L_3 = L/4 + L/2 = 3L/4 = 0.75\text{ m}\).