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9. Determine the design moment strength, M, of the section shown below. Use fe 4,000 psi and fy 60,000 psi. 4 i 33 i Figure for Question 9

Answer 1

Please note that some of the values could not be read properly as the given image is too dull to distinguish numbers. If in case, the numbers are different, please let know. GIVEN DATA Breadth of beam, h. 9 in Overall depth of beam 33 in beam Effective depth 30 in compression reinf. Reinforcements-tension Depth in 4 No. 11 single layer 2 No. 9 single layer -compression fe' Strength of concrete, 4000 psi 60000 psi f Yield Strength of steel, CALCULATIONS STEP-1: The beam is divided into beam-1 and beam-2. Both compression and tension steel are assumed to yield, i.e., f, f, and f, f, in: 6.00 A, = Area of tension steel, in2 Area of compression steel, As in2 A A, Area of steel in Beam-1 2 in2 A A-A,l Area of steel in Beam-2 4 STEP-2: Compute a for beam-2 a 0.85 fb 60000 4 X 4000 x 9 1 x 7.85 in STEP-3: Check if compression steel yields or not that is whether f,' f d= 2.5 in d 0.32 Note: ) For f' < 4000 psi, B0.85 a В, 3 ii) For 4000<fc' < 8000 psi, 0.85 B1.05-0.05/1000 iii For f8000 psi, B-0.65 f. a a 87000 1 (1 60000/ 87000) 0.85 0.32 d'/a 0.366 Therefore, compression steel yields and fs' fy STEP-4: Reevaluate value of a (0.85/-b)a? + (0.003E, А, - А,J,)a - (0.003E, А, Bа) %3D0 30600 a -186000 a = 0 369750 Solving the quadratic equation in a , we get 7.66 in a =

STEP-5: Check whether f, = fy 0.256 a d 87,000 87,000f d 0.26 a/d Therefore, fs fy that is tension steel yields 0.504 = Check if the section is tension-controlled or not For single layer of reinforcement, d For double layer, d= d-clear cover-stirrup dia half of bar dia d Note: Since the tension reinforcement is in single l: layer d 3о in ald, = ad, 0.256 0.375 0.26 a/d 0.319 Therefore, the section tension-controlled and 0.90 0.9 for tension-controlled sections Note: ) - 0.7 for compression-controlled sections ii0.356+ 0.204/(a/(B d,) for transition sections STEP-5: Check if minimum reinforcement is satisfied 3 - b d 200bd A min 0.86 0.9 > Since As>As, min о.к STEP-6: Computation nominal moment capcaity of beam, M Beam-1 jd (d-d) Lever arm 27.5 in х0.003x (d -d') фМ 3 Design moment capacity, 259.3 ft-kips Beam-2 jd = (d-a/2) 26.170 in Lever arm, Design moment capacity, M n2 x0.85fba (d -a/2) 460.1 ft-kips The total design moment capacity f the beam is obtained as: фм, фМ, + фм ,, 719.4 ft-kips