Question

LECTURE # 1) beft 36 " Determine the design moment strength of the section shown. Use fc' = 4 ksi and fy = 60 ksi. (10 | Also check the minimum reinforcement 32 requirement and the ductility of the beam. 8-# 9 bars 14in Asyrin Pin= 200 156 As OK TAs fy =480 Ksi OXS f 4.3530

Answer 1

GIVEN DATA h = Slab thickness 3 in Breadth of web, bw= 14 in Effective depth of beam, 32 in Effective width of flange, b = 36 in (double layer) Reinforcement No. 9 4000 psi fe'= Strength of concrete, fy 60000 psi Yield Strength of steel, CALCULATIONS STEP-1: Computation of a the depth of equivalent rectangular compressive stress block 7,96 in Area of steel, A= Assuming that the stress in steel, f =fy the depth a the equivalent stress blcok is obtained as: А,f, 0.85f b 7.96 x 60000 0.85 4000 х 36 > hf 3.9 in 3 in Since a is greater than hf, compression stress block must be treated as T section STEP-2: Dividing beam into "beam F" and "beam W a) Beam F The compressive force, C, in the overhanging flanges is Cf = (0.85f)(b-b)h, 4000 x 0.85 x 22 x 3 224400 Area of steel i beam F is obtained as; A f Clfy 224400 60000 in 3 3.74 c, (d -h,/2) Therefore M= 6844200 b.in kip.ft 570.4 b) Вeam W A S A,-Asf in 2 4.22 0.85 fb 4.22 x 60000 0.85 4000 x 14 5.32 in Mnw Aw (d - a/2) Therefore, 5.32 /2) 60000 x 32 4.22 7428888 b.in

kip.ft 619.1 Therefore, total moment capacity of the beam is: M, Мnt 570.4 619.1 1190 kip.ft STEP-3: Check if A, = A min 200bd bd Asmin= f 1.49 1.417 2 A, Amin OK STEP-4: Check whether f, = f, a 0.122 d Note: i) For f <= 4000 psi, B-0.85 0.85 ii) For 4000<fc' < 8000 psi, B 1.05-0.05f /1000 iii) For f'>8000 psi, B-0.65 87,000 B, 87,000f d 0 a/d 0.503> Therefore, fs = fy Check if the section is tension-controlled or not For single layer of reinforcement, d,= d Note: i) For double layer, d, d-clear cover-stirrup dia - half of bar dia Since the tension reinforcement is in double layer dt = 33 in a d, 0.118 0.375B ad, [ a/d =0.319 > 0.118 Therefore, the section is tension-controlled and 0.90 Note: i0.9 for tension-controlled sections ii) = 0.7 for compress ion-controlled sections i 0.204/(a/(B d,) for transition sections 0.356 STEP-3: Computation nominal moment capcaity of beam, M jd (d-a/2) Lever arm, 30.05 in Nominal moment capacity, М,3 А/,(d -а12) 30.05 1.44E+07 in.lb 7.96 60000 x X 1196.0 ft-kips The design moment capacity of the beam is obtained as 1196 0 1076.4 ft-kips M= 0.90