Question

Problem 1: A reinforced concrete beam having the cross section shown is on a simple span of 26.5ft. It has already been estimated that the applied factored moment, Mu, is 700 k-ft. Assume 60ksi. interior exposure, #3 stirrups, f'e 3ksi, fy Required: 1) Analyze if the beam is adequate for moment only. (3 points) Solution: 91 34.4" d 38" 6u-7 4.#9 (4)

Answer 1

GIVEN DATA Breadth of beam Overall depth of beam 16 in 38 in h = Effective depth beam, 34.4 in No. 9 double Reinforcement layer) Strength of concrete, 3000 psi 60000 psi Yield Strength of steel, f= CALCULATIONS STEP-1: Computation of a, the depth of equivalent rectangular compressive stress block 5.96 in Area of steel, As Assuming that the stress in steel, f, =fy the depth a of the equivalent stress blcok is obtained as: A,f a = 0.85fb 5.96 x 60000 0.85 x 3000 x 16 8.76 in STEP-2: Check whether f. f a 0 255 d Note: ) For f 4000 psi, B 0.85 085 ii) For 4000<fc' < 8000 psi, B 1.05-0.05 f/1000 iii) For f 8000 psi, B1-0.65 87,000 b 87,000 d 0.503 0.255 [ a/d] 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 d 35.56 in ald, = ad 0.246 0.375B 0.246 a/dJ. 0.319> Therefore, the section tension-controlled and 0.90 Note: i)0.9 for tension-controlled sections i) = 0.7 for compression-controlled sections iii 0.356 0.204/(a/(B d) for transition sections

STEP-3: Computation of nominal moment capcaity of beam, M. jd (d-a/2) Lever arm, 30.020 in 4f, (d-a/2) Nominal moment capacity 10735152.0 in.lb 5,96 x 60000 30.020 10735152.0/12000 894.6 ft-kips The design moment capacity of the beam is obtained as: ft-kips 0.90 X M,= 894.6 805.1 ft-kips Mu] 700 Hence, O.K Thus, the beam is adequate to resist the moment.