Question

Determine if the beam shown in the figure is adequate as governed by the ACI

Code (318-11). The loads shown are service loads. The uniformly distributed load is DL =

0.65 + 0.F = _________ kip/ft, LL = 0.55 + 0.E = ________ kip/ft. The dead load excludes

the beam weight. The point load is a live load. f’c = 3,000 psi, fy = 40,000 psi.

Assume that all variables A,B,C,D,E,F,G are 3.5

kips (LL) 20A"= 20 + D= - 23.A" Uniform load L0.55+O.Ekip/ft. 3-#9 bars 10 + C= ft. ft ft. 202C-

Answer 1

GIVEN DATA Beam Dimensions Span of beam Breadth of beam, Overall depth of beam Effective depth of beam Reinforcements 27 ft 14.5 in h26.5 in d23.5 in 3# 9 UDL 1 kip/ft 0.9 kip/ft Dead load Live load Concentrated Load P23.5 kips Live load Grades of materials Strength of concrete ус._ 3000 psi y40000 psi Yield Strength of steel CALCULATIONS STEP-1: Estimation of the dead load of the beam Self weight of beam 0.15 x 14.5 26.5 12 12 0.40 kip/ft STEP-2: Computation of factored moment Factored udl Wu1.2 x 1+.41.6x 0.9 3.12 kip/ft Factored concentarted load, 1.6 x 23.5 37.6 kips Factored design moment, Mu- 3.12 x 27" /8 + 37.6 x #/4 538.1 ft.kips STEP-3: Computation of area of reinforcement As2.98 in 3 200b, d 1.704 A, 1.704 in OK STEP-4: Computation of a, the depth of equivalent rectangular compressive stress block Assuming that the stress in steel, fs fy the depth a of the equivalent stress blcok is obtained as A,f 0.85f,b

2.98 x 40000 0.85 x 3000 x15 3.22 in STEP-5: Check whether f f a0.137 Note: |i) For fe"c 4000 psi, β נ0.85- ii) For 4000<fc8000 psi B 0.85 : ,1.05-0.05f /1000 ii) For fc> 8000 psi, p1-0.65 87,000 87,000 +j 0.5820.137a/d] Therefore, fs-fy Check if the section is tension-controlled or not Note: i) For single layer of reinforcement, dd ii) For double layer, dtd-clear cover-stirrup dia half of bar dia Since the tension reinforcement is in single layer dt23.5 in ald,0.137 0.3190.1 a/d O0.90 Therefore, the section is tension-controlled and i) ф-0.9 for tension-controlled sections ii) φ: 0.7 for compression-controlled sections iii) ф:0.356 + 0.204/(a/(J dt) for transition sections Vote: STEP-6: Computation of nominal moment capcaity of beam, M d(d-a/2) Lever arm, 21.890 in Nominal moment capacity - 2.98 x 21.890 2609288.0 in.lb x 40000 - 2609288.0 12000 217.4 ft-kips The design moment capacity of the beam is obtained as: Mn0.90 2174195.7 ft-kips <538.1 -Mu] Hence, the beam is NOT SAFE