Question

Urgent help !

Problem 2 Analysis of T-Beams (15 pts.) Compute the design strength for the T-beam shown in Figure 2.1, in whichfc-4000 psi and f 60,000 psi. The overall depth is 33.5 in. The slab thickness is 4 in. The effective width be is 30 in. E IS effective width 30 in 4 in. 26 in. 8 W10 (10.12 in.2) 14 in. Figure 2.1 T-Beam Section

Answer 1

GIVEN DATA 4 in 14 in 30 in 30 in 8 No. 10 double layer Slab thickness Breadth of web Effective depth of beam, Effective width of flange Reinforcement Strength of concrete Yield Strength of steel, fc4000 psi fy60000 psi CULATIONS STEP-1: Computation of a, the depth of equivalent rectangular compressive stress block A9.82 in Area of steel, Assuming that the stress in steel, fs -fy the depth a of the equivaestress blcok is obtained as 0.85f,b 9.82 60000 0.85 x 4000x 30 5.78 in>h4 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: 0.85 x4000 x 16 x4 217600 lb Area of steel in beam F is obtained as; 21760060000 3.63 in Therefore 6092800 Ib.in 507.7 kip.ft bl Beam W 6.19 in 0.85 fb 6.19 x 60000 0.85 x 4000 x14 7.8 in Therefore 6.19 x 60000 x( 30-7.80/2) 9693540 lb.in

807.8 kip.ft Therefore, total moment capacity of the beam is: 507.7807.8 - 1316 kip.ft STEP-3: Check if A,An 200b, d - 1.328 21.40 A >A, min OK STEP-4: Check whether f f a0.193 Note i) For f' <= 4000 psi, β 1-0.85 ii) For 4000<fc8000 psi, 10.85 P, 1.05-0.05s,/1000 ii) For fc' > 8000 psi, P,-0.65 87,000 87,000 j 0.503 0 E a/d Therefore, fs fy Check if the section is tension-controlled or not Note: i) For single layer of reinforcement, dtd i) For double layer, dtd-clear cover-stirrup dia - half of bar dia Since the tension reinforcement is in double layer 31 in ald, 0.186 ald, 0.375 B 0.319>0.186 a/d Therefore, the section is tension-controlled and Note: i) ф-0.9 for tension-controlled sections ii) ф-0.7 for compression-controlled sections iii) ф: 0.356 + 0.204/(a /(8 d.) for transition sections STEP-3: Computation of nominal moment capcaity of beam, M jd(d-a/2) Lever arm, 27.11 in Nominal moment capacity 9.82 x 60000 x 27.11 1.6OE+07 in.lb 1331.1 ft-kips The design moment capacity of the beam is obtained as: фМп- 0.90 x 1331.1-1198.0 ft-kips