Question

Q.1. The 6x12 in timber beam has been strengthened by bolting to it the steel reinforcement shown. The modulus of elasticity, E for wood is 1.8x10 psi and for steel, 29x10 psi. The beam is bent by a moment M 450 kip in. (a) determine the maximum stress in the wood; (b) determine the maximum stress in the steel. 12 in

Answer 1

Given data, compute the ratio required to convert the steel portion of the section in to a transformed section of entire wood n = E_s/Ew Here, E_s + E_w are the moduli of elasticity of steel and wood respectively substitute E_s = 29 times 10^6 psi & E_w = 1.8 times 10^6 psi n = 29 times 10^6/ 1.8 times 10^6 = 16.11 = 16 Now, multiply the width of the steel section with the obtained ratio, to get the equivalent wooden section. Draw the transformed cross section. Compute the distance of the neutral axis from the Bottom base v^bar = sigma A_V/ sigma A = A_1y_1 + A_2 Y_2/ A_1 + A_2 . Here A is the area of the cross section and y is the distance of the centroid . from the Bottom Base. Substitute the values of areas and distance, v^bar = (6 times 12)