고체역학 (Gere) — Axially Loaded Members: Problem 2.5-30

2.5-30 Prestressed concrete beams are sometimes manufactured in the following manner. High-strength steel wires are stretched by a jacking mechanism that applies a force \(Q\), as represented schematically in part a of the figure. Concrete is then poured around the wires to form a beam, as shown in the figure part b. After the concrete sets properly, the jacks are released, and the force \(Q\) is removed (see part c of the figure). Thus, the beam is left in a prestressed condition with the wires in tension and the concrete in compression. Assume that the prestressing force \(Q\) produces in the steel wires an initial stress \(\sigma_0 = 620\) MPa. If the moduli of elasticity of the steel and concrete are in the ratio 12:1 and the cross-sectional areas are in the ratio 1:50, what are the final stresses \(\sigma_s\) and \(\sigma_c\) in the two materials?