고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.3-15

6.3-15 A reinforced concrete T-beam (see figure) is acted on by a positive bending moment of \( M = 240 \text{ kN}\cdot\text{m} \). Steel reinforcement consists of four bars of 40 mm diameter. The modulus of elasticity for the concrete is \( E_c = 20 \text{ GPa} \) while that of the steel is \( E_s = 210 \text{ GPa} \). Let \( b = 1200 \text{ mm} \), \( t_f = 100 \text{ mm} \), \( b_w = 380 \text{ mm} \), and \( d = 610 \text{ mm} \). (a) Find the maximum stresses in steel and concrete. (b) If allowable stresses for concrete and steel are \( \sigma_{ac} = 9.5 \text{ MPa} \) and \( \sigma_{as} = 125 \text{ MPa} \), respectively, what is the maximum permissible positive bending moment?