Question

Instructions: 1. Carefully read each problem and understand the question. 2. Use ENGINEERING PAPER for all your workings and graphs. 3. Answer ALL Questions. portant Knowing that the allowable normal stress for the steel used is 24 ksi, select the most economical S-shape beam to support the loading shown 1. IS kips S kips ?? 6 It 2 ft 2 ft

Answer 1

Given data is * as per the equilibrium condition of the given beam sigma F_y = 0 R_B + R_E = (48 + 48 * 48) kips here, R_B + R_e = 144 kips equation 1 * Now sigma H_B = 0 R_E times 10 - (48 times 48) - (48 times 2) + (48 times 2) = 0 implies R_E times 10 = 384 therefore R_E = 384/10 therefore R_E - 38.4 kips here shear force diagram: - * representing the above calculations with a diagram as above, Now, bending moment diagram is, Here, the maximum bending moment M_max = 96 kips.ft so, sigma = M/2 = 96 times 12/24 inch^3 therefore z = 48 inch^3 so, the section modulus of 's' shape beam is 12 times 50 = 50.8 in^3 so, it is the most economical section for the required beam for supporting the loading.