1. 1 Design of Concrete Structure I Dr. Ali Tayeh First Semester 2009 Dr. Ali Tayeh First Semester 2009

2. 2 Lecture 8 DESIGN OF T-Section BEAMS FOR MOMENTS

3. 3 Analysis of Flanged Section Floor systems with slabs and beams are placed in monolithic pour. Slab acts as a top flange to the beam; T-beams, and Inverted L(Spandrel) Beams.

4. 4 Analysis of Flanged Sections Positive and Negative Moment Regions in a T-beam

5. 5 Analysis of Flanged Sections If the neutral axis falls within the slab depth analyze the beam as a rectangular beam, otherwise as a T-beam.

6. 6 Analysis of Flanged Sections Effective Flange Width Portions near the webs are more highly stressed than areas away from the web.

7. 7 Analysis of Flanged Sections Effective width (b eff ) b eff is width that is stressed uniformly to give the same compression force actually developed in compression zone of width b (actual)

8. 8 ACI Code Provisions for Estimating b eff From ACI 318, Section 8.10.2 T Beam Flange:

9. 9 ACI Code Provisions for Estimating b eff From ACI 318, Section 8.10.3 Inverted L Shape Flange

10. 10 ACI Code Provisions for Estimating b eff From ACI 318, Section 8.10 Isolated T-Beams

11. 11 Various Possible Geometries of T-Beams Single Tee Twin Tee Box

12. 12 Analysis of T-Beam Case 1: Equilibrium

13. 13 Analysis of T-Beam Case 1: Confirm

14. 14 Analysis of T-Beam Case 1: Calculate M n

15. 15 Analysis of T-Beam Case 2:Assume steel yields

16. 16 Analysis of T-Beam Case 2: Equilibrium Assume steel yields The flanges are considered to be equivalent compression steel.

17. 17 Analysis of T-Beam Case 2: Confirm

18. 18 Analysis of T-Beam Case 2: Calculate nominal moments

19. 19 Analysis of T-Beams The definition of M n1 and M n2 for the T-Beam are given as:

20. 20 Limitations on Reinforcement for Flange Beams Lower Limits –Positive Reinforcement

21. 21 Limitations on Reinforcement for Flange Beams Lower Limits –For negative reinforcement and T sections with flanges in tension

22. 22 Example - T-Beam Find M n and M u for T-Beam. h f = 15 cm d = 40cm A s = 50cm 2 f y = 420Mpa f c = 25Mpa b w = 30cm L = 5.5m S=2.15m

23. 23 Example of T-Beam Confirm b eff

24. 24 Compute the equivalent c value and check the strain in the steel,  s Steel will yield in the tension zone. Assume a<t.

25. 25 Compute the reinforcement  and check to make sure it is greater than  min Section works for minimum reinforcement.

26. 26 Compute nominal moment components