고체역학 (Gere) — Axially Loaded Members: Problem 2.2-19

2.2-19 Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (\(L_1\) or \(L_2\)) and outer diameters (\(d_1\) or \(d_2\)) are different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load \(q = 2P/L\) is applied over a distance of 3L/4 along BC, and concentrated load P/4 is applied downward at D. (a) Derive a formula for the displacement \(\delta_D\) at point D in terms of P and column flexibilities \(f_1\) and \(f_2\). (b) If \(d_1 = (9/8)d_2\), find the \(L_1/L_2\) ratio so that beam BCD displaces downward to a horizontal position under the load system in part (a). (c) If \(L_1 = 2L_2\), find the \(d_1/d_2\) ratio so that beam BCD displaces downward to a horizontal position under the load system in part (a). (d) If \(d_1 = (9/8)d_2\) and \(L_1/L_2 = 1.5\), at what horizontal distance x from B should load P/4 be placed so that beam BCD displaces downward to a horizontal position under the load system in part (a)?