Question

1. Use ρ-p0.004 and choose (you decide) the number (3 to 5) and size of steel bars from the attached table. Then proceed to determine (a) the size of the cross-sectional area, (b) the moment capacity of the RC section that you design, and (c) show where is the neutral axis on the diagram (or sketch a new one). 2.5" Given: fe 3,000 psi, fy -60,000 psi Concrete cracking strain 0.003 Initial yielding strain of steel 0.002 The cross-sectional area has h 1.5 b ratio

Please answer in numerical order.

Answer 1

"Given fc' = 3000 psi = 3k psi f_y = 60 ksi sigma_u = 0.003 sigma_f = 0.002 rho = rho_0.004 = 0.0155 phi rho f_y (1 - rho f_y/ 17 f_i) greater than or equal to mu here rho = delta st/bd rightarrow D, a = ASf_y/0.85 fc' fb phi m_u greater than or equal to m_u & a_s dy (d - a/2) greater than or equal to mu bd^2 mu/phi rho f_y (1 - rho f_y/1.7 f'c) ----(2) bar area = 0.31 in^2 dio = 0.625 area of sheet = 2 times 0.31 = 0.62 in^2 d = h - phi/2 - cc = 1.5 b - 0.625/2 - 2.5 = 1.5 b - 2.8 rho = Ast/bd = Ast/b (1.5 b - 2.8) b (1.5 b - 2.8) = 0.625/0.0155 = 40 1.5b^2 - 2.8 b - 40 = 0 b = b"" d = 1.5 times 6 - 2.8 = 5.85"" h = 1.5 times 6 = 9"" bd^2 = mu/phi rho f_y (1 - ff_y/1. 7 fc') \r\n"