Question

P9.032 The internal shear force V at a certain section of a steel beam is 65 kips. If the beam has the cross section shown (assume a 2.9 in., b1-4.7 in., b2-7.7 in., tw-1n., d- 12.3 in.), determine: (a) the value of Q associated with point H, which is located 2.9 in. below the top surface of the flanged shape. (b) the maximum horizontal shear stress Tmax in the flanged shape. Answers: in ksi max

Answer 1

Centroid location in y direction shape Area, Ai yi yiAi Top flange 3.51 15.35 54.8 Web 10.01 7.5 75.075 bottom 6.58 0.35 2.303 flange sigma Ai = 20.16cn^2 sigma yiAi = 132.178cn^3 y = sigma Ai/sigma Ai = 132.178/20.16 y = 6.556 in (from bottom of shape centroid) y = 9.1435m (from bottom of shape centroid) \r\n Moment of inertia about the Z - axis shape I_c(in^4) d = y - i - J d^2 (in^4) Ic + d^2 A Top flange 0.1457 8.794 276.08 276.23 Web 170.578 0.944 8.92 179.49 bottom flange 0.2687 - 6.206 253.425 253.69I_z = 709.41in^4 theta at point M theta = (5.1)(0.7)(8.794) + (1.5)(0.7)(8.274) Maximum horizontal share stress theta_max = (5.1)(0.7)(8.794) + (0.7)(8.4435)(4.22175) theta_max = 56.347in^3 Z_max = V theta/I t = (65)(56.347)/(709.41 times 0.7) z_max = 7.3ksi