Question

Design a rectangular simple supported beam to carry service loads of 1.05 kips/ft of dead load (DL) (self-weight included) and 2.47kip/ft live load (LL) on a span length of 18 ft. The beam is limited to be (due to architectural reasons) 10” wide with an overall depth of 20”. Use f’c= 3,000 psi and fy=40,000psi. Design the longitudinal reinforcement (flexure design) and the web reinforcement (Stirrups).

Answer 1

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10" 2#8 4# 10 ACI CODE GIVEN DATA:- bxh = 10 x 20 in, Wd= 1.05 kips/ft , WI= 2.47 kips/ft, = 18 ft f'c=3000 psi, fy=40000 psi Mpa , Wu=1.2 x Wd+ 1.6 x W= 1.2 x 1.05 +1.6 x 2.47 =5.212 kips/ft Mu= Wux 2/8 = 5.212 x 18 12 /8 = 211.09 ft-k Mnr Mu/0.9 = 211.09/0.9 = 234.54 ft-k Assume d= 20 -3 = 17 in, d'= 2.5 in pmax if singly reinforced = 0.0203 As1 = 0.0203 x 10 x 17 = 3.451 sqin Mu phi x 5 x dx 2 =682.3 psi Mu1 = 682.3 x 0.9 x 10 x 17^2 = 1774662.3 in -Ib = 1775 in - k = 147.9 ft-k Mn1 = Mu1/0.9 = 147.9/0.9 = 164.33 ft-k < Mn = 234.54 ft-k Hence Doubly Reinforced Required. Mn2 = Mn - Mn1 = 234.54 - 164.33= 70.21 ft-kips Checking to See if compression Steel yields a= 3.451 x 60000/(0.85 x 3000 x 10) = 8.12 in C= 8.12/ 0.85 = 9.55 in E's = (9.55 -2.5) <0.003/ 9.55=0.0022 > 40000 / 29000000 = 0.0014 Hence compression steel yields A's reqd = Mn21 / f (d-d') = 70.21 x 1000 x 12/{40000 x( 17 -2.5}} = 1.45 sq in (Use 2 #8 =1.57 sqin ) = As = As 1 + As2 = 3.451+ 1.57 = 5.021 sqin ( Use 4 # 10 = 5.06 sqin ) Max S.F( Vu ) = Wux 1/2 = 5.212 x 18/2 = 46.91 kips Vu at a distance d from the face of support = 46.91 - 17 x 5.212/12 = 39.53 kips phi x Vc = phi x 2x lemda x sqrt (fc) x 5 xd = 0.75 x 2 x 1 x sqrt ( 3000 ) x 10 x 17 = 13967 |b=13.97 kips Vu = phi x Vc + Phi x Vs phi x Vs = Vu - phi x Vc = 39.53 - 13.97= 25.56 lips Vs = 25.56 / 0.75 = 34.08 kips Taking #3 Stirrups (Av = 0.11 sqin ) S= Av xfyxd/Vs = 2 x0.11x40000 x 17 / (34.08 x 10^3 )= 4.39 in Maximum spacing to provide minimum Av stirrups S= Av x fy/{0.75 x sqrt (fc) x b }= 2 x0.11 x 40000/{0.75 x sqrt ( 3000 ) x 10}= 21.42 in S= Av x fy / (50 xb) = 2 x 0.11x 4000 / ( 50 x 10 ) = 17.6 in Use #3 @ 4 in spacing center to center