Question

2. A rectangular beam with b = 12 in., d = 17 in., and h = 20 in. spans 23 feet from simple supports. Each support is 12 inches wide (clear span between face of supports = 22 feet). The unfactored dead load (excluding self-weight) = 0.9 k/ft, and the unfactored live load = 1.25 k/ft. As = 6.0 in.2 . Material strengths are f’c = 3,500, fy = 60,000 psi. Shear reinforcement consists of #3 stirrups at 8 in. c-c spacing along the entire length of the beam. Determine the adequacy of the shear design for: (a) the simple equation for Vc; and (b) the more complicated expressions for Vc.

Answer 1

Given,

b = 12 in

d = 17 in

h = 20 in

Span = 23 ft

unfactored dead load = 0.9 + 0.15 * 12/12 * 20/12 = 1.15 k/ft

unfactored live load = 1.25 k/ft

Factored load = 1.2 D + 1.6 L = 1.2 * 1.15 + 1.6 * 1.25 = 3.38 k/ft

Maximum shear force, V_u = 3.38 * 23/2 = 38.87 kips

Shear reinforcement = # 3 bars @ 8 in C/C

V_s = f_y A_sv d/s = 60 * 2 * 0.11 * 17/8 = 28.05 kips

a) V_n = V_u/0.75 = V_c + V_s

V_c = V_n - V_s = 38.87/0.75 - 28.05 = 23.78 kips

b) V_c = $2\sqrt{f'_{c}}bd$ = = 24137.606 lbs = 24.138 kips

2V3500 1217