고체역학 (Gere) — Axially Loaded Members: Problem 2.3-15

2.3-15 The nonprismatic cantilever circular bar shown has an internal cylindrical hole of diameter \(d/2\) from 0 to \(x\), so the net area of the cross section for segment 1 is \((3/4)A\). Load \(P\) is applied at \(x\), and load \(P/2\) is applied at \(x = L\). Assume that \(E\) is constant. (a) Find reaction force \(R_1\). (b) Find internal axial forces \(N_i\) in segments 1 and 2. (c) Find \(x\) required to obtain axial displacement at joint 3 of \(\delta_3 = PL/EA\). (d) In part (c), what is the displacement at joint 2, \(\delta_2\)? (e) If \(P\) acts at \(x = 2L/3\) and \(P/2\) at joint 3 is replaced by \(\beta P\), find \(\beta\) so that \(\delta_3 = PL/EA\). (f) Draw the axial force (AFD: \(N(x), 0 \le x \le L\)) and axial displacement diagrams (ADD: \(\delta(x), 0 \le x \le L\)) using results from parts (b) through (d).