고체역학 (Gere) — Axially Loaded Members: Problem 2.3-3

2.3-3 An aluminum bar \(AD\) (see figure) has a cross-sectional area of \(250 \text{ mm}^2\) and is loaded by forces \(P_1 = 7560 \text{ N}\), \(P_2 = 5340 \text{ N}\), and \(P_3 = 5780 \text{ N}\). The lengths of the segments of the bar are \(a = 1525 \text{ mm}\), \(b = 610 \text{ mm}\), and \(c = 910 \text{ mm}\). (a) Assuming that the modulus of elasticity is \(E = 72 \text{ GPa}\), calculate the change in length of the bar. Does the bar elongate or shorten? (b) By what amount \(\Delta P\) should the load \(P_3\) be increased so that the bar does not change in length when the three loads are applied? (c) If \(P_3\) remains at \(5780 \text{ N}\), what revised cross-sectional area for segment \(AB\) will result in no change of length when all three loads are applied?