고체역학 (Gere) — Axially Loaded Members: Problem 2.3-17

2.3-17 A flat bar of rectangular cross section, length \(L\), and constant thickness \(t\) is subjected to tension by forces \(P\) (see figure). The width of the bar varies linearly from \(b_1\) at the smaller end to \(b_2\) at the larger end. Assume that the angle of taper is small. (a) Derive the following formula for the elongation of the bar: \[ \delta = \frac{PL}{Et(b_2 - b_1)} \ln \frac{b_2}{b_1} \] (b) Calculate the elongation, assuming \(L = 1.5\text{ m}\), \(t = 25\text{ mm}\), \(P = 125\text{ kN}\), \(b_1 = 100\text{ mm}\), \(b_2 = 150\text{ mm}\), and \(E = 200\text{ GPa}\).