Question

4.2 (a) Design the reinforcement for the beam shown in the figure for Problem 4.2, if the

Answer 1

SOLUTION :-

n b = = GIVEN DATA Slab thickness Breadth of web, Effective depth, Effective width, Strength of concrete, Yield Strength of steel, Bending Moments 4 in 15 in 24 in 48 in 4000 60000 fe's fy= psi psi (assumed; not specified in problem) (assumed; not specified in problem) M M = = 90 140 kip.ft kip.ft CALCULATIONS STEP-1: Computation of factored bending moment Therefore, design moment, M, = 1.2 Mo + 1.6 M = 332 kip.ft STEP-2: Computation of area of reinforcement, As Assuming j = 0.95, jd = 22.800 м As = fjd 332 3.24 /(0.9 X 60000 X = = 22.80 ) x 12000 in? Provide 3 # 10 bars and these will fit into the web in a double layer. Area of steel provided, As = 3.68 in STEP-3: Check if A, >= As,mi 3 Asmin = , 2005 d deb d > 1.2 = 1.14 As > Asmin OK CAPACITY CHECK STEP-4: Computation of a = 0.85fb 3.68 x 60000 0.85 X 4000 x 1.35 in < 48 4 = in Since a is less than hf, the beam has rectangular beam action STEP-5: Check whether for fy a = 0.05625 B = 0.85 Note: i) Forf' <= 4000 psi, B1=0.85

ii) For 4000<fc' < 8000 psi, B. = 1.05-0.05f/1000 i) For fc' >= 8000 psi, B=0.65 87,000 Pi87,000+ f, 0.056 = a/d] = 0.50306 > Therefore, fs = fy Check if the section is tension-controlled or not Note: i) For single layer of reinforcement, d = d ii) For double layer, d, = d-clear cover-stirrup dia - half of bar dia Since the tension reinforcement is in single layer di = 24 in ald, = 0.05625 al/d, = 0.375 Bi = 0.31875 > 0.056 = a/d+] Therefore, the section is tension-controlled and Note: i) = 0.9 for tension-controlled sections ii) = 0.7 for compression-controlled sections iii) = 0.356 + 0.204/(a / dt) for transition sections STEP-6: Computation of nominal moment capcaity of beam, M, Lever arm, jd = (d-a/2) = 23.325 in Nominal moment capacity, M = 4./, (d-a/2) = 3.68 X 60000 X 23.3 = = 5.15E+06 429.2 in.lb ft-kips The design moment capacity of the beam is obtained as: OM, = 0.90 X 429.2 = > 386.27 ft-kips 332 ft-kips Hence, it is SAFE 4 in 24 in 3# 10 15 in
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