Question

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Problem 4 (15 points) Reinforced Concrete Composite Design You are designing a reinforced concrete column E-4x106 psi Concrete Steel Steel content ơcompressive- ơcompressive-36,000 psi 3,500 psi E-29 x 106 psi 4% of cross section a. Find the equivalent modulus of elasticity of the reinforced column b. Find the percent of the column load carried by the concrete. c. Assuming that the concrete will reach failure before the steel does, find the minimum cross sectional area for the reinforced column if it will carry a 500 k axial load. 4

Answer 1

a) E_eq = E_cA_c + E_s A_S/ A_c + A_s;: A_s/A_s + A_c = 4/100 &A_c/A_c + A_s = 96/100 rightarrowE_eq = 4/100 times 29 times 10^6 = 5 times 10^6 psi b) for axial load P, strain = p/A /E_eq: strain will be same in steel & concrete & let�s say x fraction of P IS carried by concrete & (1-x) by steel rightarrow (1-x)p/A_s/E_s = xp/A_c/E_c = p/A/E_eqrightarrow x/0.96A /4 times 10^6 = 1/A/5 times 10^6 rightarrow x = 0.768 so 76.8% of load is carried by concrete c) 76.8% of 500k = 384 k rightarrow384^k/0.6A/4 times 10^6 = 3500psi/4 times 10^psi = failure straionrightarrow 384^k/0.96A = 3500 rightarrow A = 384 times 10^3/0.96 times 3500 in^2 or A = 114.29 in^2