Serway & Jewett — Static Equilibrium and Elasticity: Problem 27

The lintel of prestressed reinforced concrete in Figure P12.27 is \( 1.50 \text{ m} \) long. The concrete encloses one steel reinforcing rod with cross-sectional area \( 1.50 \text{ cm}^2 \). The rod joins two strong end plates. The cross-sectional area of the concrete perpendicular to the rod is \( 50.0 \text{ cm}^2 \). Young’s modulus for the concrete is \( 30.0 \times 10^9 \text{ N/m}^2 \). After the concrete cures and the original tension \( T_1 \) in the rod is released, the concrete is to be under compressive stress \( 8.00 \times 10^6 \text{ N/m}^2 \). (a) By what distance will the rod compress the concrete when the original tension in the rod is released? (b) What is the new tension \( T_2 \) in the rod? (c) The rod will then be how much longer than its unstressed length? (d) When the concrete was poured, the rod should have been stretched by what extension distance from its unstressed length? (e) Find the required original tension \( T_1 \) in the rod.