PCI 6 th Edition

1. PCI 6th Edition Flexural Component Design

2. Presentation Outline • What’s new to ACI 318 • Gravity Loads • Load Effects • Concrete Stress Distribution • Nominal Flexural Strength • Flexural Strength Reduction Factors • Shear Strength • Torsion • Serviceability Requirements

3. New to ACI 318 – 02 • Load Combinations • Stress limits • Member Classification • Strength Reduction factor is a function of reinforcement strain • Minimum shear reinforcement requirements • Torsion Design Method

4. Load Combinations • U = 1.4 (D + F) • U = 1.2 (D + F + T) + 1.6 (L + H) + 0.5 (Lr or S or R) • U = 1.2D + 1.6 (Lr or S or R) + (1.0L or 0.8W) • U = 1.2D + 1.6W + 1.0L + 0.5(Lr or S or R) • U = 1.2D + 1.0E + 1.0L + 0.2S • U= 0.9D + 1.6W + 1.6H • U= 0.9D + 1.0E + 1.6H

5. Comparison of Load Combinations • U=1.2D + 1.6 L 2002 • U= 1.4D + 1.7L 1999 If L=.75D i.e. a 10% reduction in required strength

6. Classifications • No Bottom Tensile Stress Limits • Classify Members Strength Reduction Factor • Tension-Controlled • Transition • Compression Controlled • Three Tensile Stress Classifications • Class U – Un-cracked • Class T – Transition • Class C – Cracked

7. Copied from ACI 318 2002, ACI 318-02 table R18.3.3

8. Class C Members • Stress Analysis Based on Cracked Section Properties • No Compression Stress limit • No Tension Stress limit • Increase awareness on serviceability • Crack Control • Displacements • Side Skin Reinforcement

9. Minimum Shear Reinforcing 1999 2002

10. System Loads • Gravity Load Systems • Beams • Columns • Floor Member – Double Tees, Hollow Core • Spandrels • Tributary Area • Floor members, actual top area • Beams and spandrels • Load distribution • Load path • Floor members  spandrels or beams  Columns

11. Live Load Reduction • Live Loads can be reduced based on: Where: KLL = 1 Lo = Unreduced live load and At = tributary area

12. Live Load Reduction • Or the alternative floor reduction shall not exceed or Where: R = % reduction ≤ 40% r = .08

13. Member Shear and Moment • Shear and moments on members can be found using statics methods and beam tables from Chapter 11

14. Strength Design • Strength design is based using the rectangular stress block • The stress in the prestressing steel at nominal strength, fps, can be determined by strain compatibility or by an approximate empirical equation • For elements with compression reinforcement, the nominal strength can be calculated by assuming that the compression reinforcement yields. Then verified. • The designer will normally choose a section and reinforcement and then determine if it meets the basic design strength requirement:

15. Concrete Stress Distribution • Parabolic distribution • Equivalent rectangular distribution

16. Stress-Strain relationship is not constant Stress Block Theory f’c=6,000 psi f’c=3,000 psi

17. Stress Block Theory • Stress-Strain relationship • Stress-strain can be modeled by: Where :strain at max. stress and :max stress

18. Stress Block Theory • The Whitney stress block is a simplified stress distribution that shares the same centroid and total force as the real stress distribution =

19. Equivalent Stress Block – b1 Definition b1 = 0.85 when f’c < 3,000 psi b1 = 0.65 when f’c > 8,000 psi

20. Design Strength • Mild Reinforcement – Non - Prestressed • Prestress Reinforcement

21. Strength Design Flowchart • Figure 4.2.1.2 page 4-9 • Non-Prestressed Path • Prestressed Path

22. Non-Prestressed Members • Find depth of compression block

23. Depth of Compression Block Where: As is the area of tension steel A’s is the area of compression steel fy is the mild steel yield strength Assumes compression steel yields

24. Flanged Sections • Checked to verify that the compression block is truly rectangular

25. Compression Block Area • If compression block is rectangular, the flanged section can be designed as a rectangular beam = =

26. Compression Block Area • If the compression block is not rectangular (a> hf), = To find “a”

27. Determine Neutral Axis • From statics and strain compatibility

28. Check Compression Steel • Verify that compression steel has reached yield using strain compatibility

29. Compression Comments • By strain compatibility, compression steel yields if: • If compression steel has not yielded, calculation for “a” must be revised by substituting actual stress for yield stress • Non prestressed members should always be tension controlled, therefore c / dt < 0.375 • Add compression reinforcement to create tesnion controlled secions

30. Moment Capacity • 2 equations • rectangular stress block in the flange section • rectangular stress block in flange and stem section

31. Strength Design Flowchart Figure 4.2.1.2page 4-9 Non- Prestressed Path Prestressed Path

32. This portion of the flowchart is dedicated to determining the stress in the prestress reinforcement

33. Stress in Strand fse - stress in the strand after losses fpu - is the ultimate strength of the strand fps - stress in the strand at nominal strength

34. Stress in Strand • Typically the jacking force is 65% or greater • The short term losses at midspan are about 10% or less • The long term losses at midspan are about 20% or less

35. Stress in Strand • Nearly all prestressed concrete is bonded

36. Stress in Strand • Prestressed Bonded reinforcement gp = factor for type of prestressing strand, see ACI 18.0 = .55 for fpy/fpu not less than .80 = .45 for fpy/fpu not less than .85 = .28 for fpy/fpu not less than .90 (Low Relaxation Strand) rp = prestressing reinforcement ratio

37. Determine Compression Block

38. Compression Block Height Assumes compression steel yields Prestress component Where Aps - area of prestressing steel fps - prestressing steel strength

39. Flange Sections Check

40. Compression Steel Check • Verify that compression steel has reached yield using strain compatibility

41. Moment Capacity • 2 Equations • rectangular stress block in flange section • rectangular stress block in flange and stem section

42. Flexural Strength Reduction Factor • Based on primary reinforcement strain • Strain is an indication of failure mechanism • Three Regions

43. Member Classification • On figure 4.2.1.2

44. e < 0.002 at extreme steel tension fiber or c/dt > 0.600 = 0.70 with spiral ties = 0.65 with stirrups Compression Controlled

45. e > 0.005 at extreme steel tension fiber, or c/dt < 0.375 f= 0.90 with spiral ties or stirrups Tension Controlled

46. 0.002 < e < 0.005 at extreme steel tension fiber, or 0.375 < c/dt < 0.6 f = 0.57 + 67(e) or f = 0.48 + 83(e) with spiral ties f = 0.37 + 0.20/(c/dt) or f = 0.23 + 0.25/(c/dt) with stirrups Transition Zone

47. Strand Slip Regions • ACI Section 9.3.2.7 ‘where the strand embedment length is less than the development length’ f =0.75

48. Limits of Reinforcement • To prevent failure immediately upon cracking, Minimum As is determined by: • As,min is allowed to be waived if tensile reinforcement is 1/3 greater than required by analysis

49. Limits of Reinforcement • The flexural member must also have adequate reinforcement to resist the cracking moment • Where Correction for initial stresses on non-composite, prior to topping placement Section after composite has been applied, including prestress forces

50. Critical Sections