고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.3-16

6.3-16 A reinforced concrete slab (see figure) is reinforced with 13-mm bars spaced 160 mm apart at \( d = 105 \text{ mm} \) from the top of the slab. The modulus of elasticity for the concrete is \( E_c = 25 \text{ GPa} \), while that of the steel is \( E_s = 200 \text{ GPa} \). Assume that allowable stresses for concrete and steel are \( \sigma_{ac} = 9.2 \text{ MPa} \) and \( \sigma_{as} = 135 \text{ MPa} \). (a) Find the maximum permissible positive bending moment for a 1-m wide strip of the slab. (b) 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.)