고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.3-14

6.3-14 A reinforced concrete beam (see figure) is acted on by a positive bending moment of \( M = 160 \text{ kN}\cdot\text{m} \). Steel reinforcement consists of 4 bars of 28 mm diameter. The modulus of elasticity for the concrete is \( E_c = 25 \text{ GPa} \) while that of the steel is \( E_s = 200 \text{ GPa} \). (a) Find the maximum stresses in steel and concrete. (b) If allowable stresses for concrete and steel are \( \sigma_{ac} = 9.2 \text{ MPa} \) and \( \sigma_{as} = 135 \text{ MPa} \), respectively, what is the maximum permissible positive bending moment? (c) What is the required area of steel reinforcement, \( A_s \), if a balanced condition must be achieved? What is the allowable positive bending moment? (Recall that in a balanced design, both steel and concrete reach allowable stress values simultaneously under the design moment.) Figure data: Beam width \( b = 300 \text{ mm} \) Effective depth to reinforcement \( d = 625 \text{ mm} \)