Question

Problem 5. Determine the nominal or theoretical moment capacity Mn of beam iffy = 60,000 psi and fc' = 4000 psi. 3 in 3 in... 3 in.3 in. inli 18 in

Answer 1

3 6 Ea 0.003 GIVEN DATA 3 Breadth of beam, 18 in b = 3 Effective depth of beam d = 27 in single layer ) Reinforcement 4 No. 9 4000 psi Strength of concrete, N.A fy 60000 psi Yield Strength of steel, h 21 d-c STEP-1: Computation of tension force in2 Area of steel, As 3.98 Assuming that the stress in steel, f =f, the tension force in steel reinforcement can be calculated as T fyA 60000 3.98 238800 lb = STEP-2: Ccomputation of area of compression stress block From equilibrium,we have C T 238800 lb Let a be the depth of equivalent rectangular compression stress block. Therefore, compressive force can be written as: 4000 x 6 x 3 12 x 6) x 18 C 3(a 0.85 X Hence in 6 in 6.9 > a= STEP-3: Check whet her f =fy This check is done using strain compatibility. The ultimate compressive strain in concrete at its extreme fiber is: 0.003

Note: 0.85 i) For f4000 psi, p10.85 ii) For 4000<fc' < 8000 psi, B 1.05-0.05 f, /1000 Therefore c alB ili) For f8000 psi, p-0.65 8.12 in From similar triangles of the strain diagram, we can write, d-c C 8.12 8.12 ] Therefore, 27 0.003 &, = 0.00698 The yield strain in reinforcement for the given grade of steel is: 60000 2.9E+07 0.00207 E, > E,, Since fs = fy and thus the assumption in step-1 is justified Since fs fy, the section is tension-controlled and hence, 0.90 0.9 for tension-controlled sections Note: i)0.7 for compression-controlled sections i)0.356 0.204/(a /B dfor transition sections + STEP-4: Computation of nominal moment capcaity of beam, M, The compressive stress block can be divided into three areas Compressive area, Ac= 6 x 3 in 2 18 Lever arm LA= - 3 /2 27 in 25.5 Compressive area A c2= 12 X 3 2 in 36 32 Lever arm, LA 2 = 27 3 22,5 in

A 3= - 6) x 18 Compressive area, 6.9 in 2 16.2 Lever arm L.A 3 6)/2 27 6 6.9 20.55 psi M,0.85f (A4 x L4)(A, *LA,)+(A Nominal moment capacity, xLA,)] 5446494.0 in.lb 5446494.0 12000 453.9 ft-kips