Lecture 16 – Design(T-Beams)

1. Lecture 16 – Design(T-Beams) February 21, 2003 CVEN 444

2. Lecture Goals • Design of T-Beams • Known section dimensions

3. Design Procedure for section dimensions are unknown (T- Reinforced Beams) Assume that the material properties, loads, and span length are all known. Estimate the dimensions of self-weight using the following rules of thumb: a. The depth, h, may be taken as approximate 8 to 10 % of the span (1in deep per foot of span) and estimate the width, b, as about one-half of h. b. The weight of a rectangular beam will be about 15 % of the superimposed loads (dead, live, etc.). Assume b is about one-half of h. Immediate values of h and b from these two procedures should be selected. Calculate self-weight and Mu.

4. Design Procedure for Singly Reinforced Flange Beams when flange is in compression Known dimensions • Calculate controlling value for the design moment, Mu. • Assume that resulting section will be tension controlled, et 0.005 so that can take f = 0.9.

5. Design Procedure for Singly Reinforced Flange Beams when flange is in compression Known dimensions • Calculate d, since h is known For one layer of reinforcement. For two layers of reinforcement.

6. Design Procedure for Singly Reinforced Flange Beams when flange is in compression Known dimensions • Determine the effective width of the flange, beff • Check whether the required nominal moment capacity can be provided with compression in the flange alone. and

7. Design Procedure for Singly Reinforced Flange Beams when flange is in compression Known dimensions If Need to utilize web below flanges. Go to step 4. If Use design procedure for rectangular beams with b = beff , (d -a/2) = 0.95d Note:f = 0.9 for flexure without axial load (ACI 318-02 Sec. 9.3)

8. Singly Reinforced Beams where flange is in compression Design Procedure when section dimensions are known Find nominal moment capacity provided by overhanging flanges alone (not including web width) For a T shaped section: and

9. Singly Reinforced Beams where flange is in compression Design Procedure when section dimensions are known • Find nominal moment capacity that must be provided by the web.

10. Singly Reinforced Beams where flange is in compression Design Procedure when section dimensions are known • Calculate depth of the compression block, by solving the following equation for a.

11. Singly Reinforced Beams where flange is in compression Design Procedure when section dimensions are known • Find required reinforcement area, As (req’d)

12. Singly Reinforced Beams where flange is in compression Design Procedure when section dimensions are known • Select reinforcing bars so As (provided) As (req’d). Confirm that the bars will fit within the cross-section. It may be necessary to change bar sizes to fit the steel in one layer or even to go to two layers of steel.

13. Singly Reinforced Beams where flange is in compression Design Procedure when section dimensions are known • Calculate the actual Mn for the section dimensions and reinforcement selected. Check strength f Mn Mu (keep over-design within 10 %)

14. Singly Reinforced Beams where flange is in compression Design Procedure when section dimensions are known • Check whether As provided is within allowable limits. As (provided) As (min)

15. Minimum Area Calculate the minimum amount of steel

16. Additional Requirements for flanged sections when flange is in tension ACI 318 Section 10.6.6 Must distribute flexural tension steel over effective flange width, be (tension)

17. Additional Requirements for flanged sections when flange is in tension ACI 318 Section 10.6.6 When be (comp) > l/10 some longitudinal reinforcement shall be provided in outer portions of flange.

18. Additional Requirements for flanged sections when flange is in tension ACI 318 Section 10.6.6 For l use centerline dimensions when adjacent spans for - M @ support are not equal, use average l to calculate be (tension) One scenario when be (tension) < be (compression)

19. Design Procedure for SR Beam Unknown Dimension Do a preliminary geometric size based on the following:

20. 1 2 3 4 A reasonable value for k in terms Effective flange width based on ACI guidelines. Desired ration of b and d. b = 0.5 – 0.65 d Depth of the flange based on design of the slab. Design Procedure for SR Beam Unknown Dimension Assume

21. Example Problem T-Beam with unknown dimensions, hf = 6 in.(slab) fc = 4500 psi & fy = 60 ksi. Three spans continuous beam, simply supported on walls. Spans are (25ft, 30 ft. and 25 ft.) The beam spacing is 14 ft center to center

22. Example Problem Using estimated values h = 26 in. , b =16 in. Max + Mu = 300 k-ft Max - Mu = 435 k-ft

23. Example Problem – Negative Moment Calculate the – moment term, where the bottom section is in compression. Max –Mu = 435 k-ft.

24. Example Problem-b Value Determine the b1 term for the concrete

25. Example Problem – k value Calculate a desired k = c/d Determine the Ru term for the concrete

26. Example Problem – Design From the design of the Determine the Ru term for the concrete

27. Example Problem – Design The nominal moment is defined as The bd2 value will for design is

28. Example Problem – Design Assume that the b = 0.65d so that Determine the value for b

29. Example Problem – Design Determine h assuming a single layer of reinforcement Check to see if the estimate will work Over-designed by 10.9 % so it will work but we would need to go back an recalculate the weight

30. Example Problem – Design Calculate the actual value for k Use the quadratic formula

31. Example Problem – Check Calculate the actual value for k’

32. Example Problem – Check Calculate the actual value for k Calculate the As required for the beam

33. Example Problem – Check Calculate the actual value for As

34. Example Problem – Flange The flange is in tension so the reinforcement, the beff in tension must be computed according to ACI 10.6.6

35. Example Problem – Flange The size of the flange in compression is from 8.10.2 of the ACI code, the beff in compression

36. Example Problem – Flange The size of the flange in compression is from 8.10.2 of the ACI code, the beff in compression Use 82 in. for the compression flange.

37. Example Problem – Flange The flange is in tension so the reinforcement, the beff in tension must be computed according to ACI 10.6.6 Use 33 in. for beff in tension.

38. Example Problem – Steel Select the steel for the reinforcement at least 0.5 As needs to be in the beff of the beam. Use 3 #8 bars and 8 # 5 bars, (which will give you 4 on each side.) The As = 4.85 in2 > 4.84 in2 OK!

39. Example Problem – Cover Check to the value for d The d will work.

40. Example Problem – a value Calculate the new a using the equilibrium equations.

41. Example Problem – Strain Check the strain condition for the beam Use f = 0.9

42. Example Problem – Mn Calculate the moment capacity of the beam Ultimate moment capacity of the beam.

43. Example Problem – Amin Calculate the minimum amount of steel Amin = 2.26 in2 < 4.85 in2 OK

44. Example Problem – Summary Summary of the beam with M 435 k-ft.

45. Example Problem – Positive Moment Calculate the + moment term, where the bottom section is in compression. Max +Mu = 300 k-ft.

46. Example Problem – Capacity Calculate the moment capacity of the beam with d= 22.5 in. and hf = 6 in.

47. Example Problem – Amin The minimum amount of steel is Use As = 6.19 in2

48. Example Problem – a value So the beam can be designed as a singly reinforced beam with the minimum amount of steel 5.91 in2.

49. Example Problem – Mn Compute the moment capacity of the beam with the minimum amount of steel 6.19 in2.

50. Example Problem – Summary Use 8 #8 bars As = 6.32 in2. Check to see that the steel will fit. It will not be within 10% of the ultimate moment capacity of the beam. However, the minimum amount steel will preside.