1. PEER 2002 PEER Annual Meeting PEER 2002 Annual Meeting Ian Robertson University of Hawaii

2. Objective Development of a load-deformation hysteretic model for slab-column connections of varying dimensions, reinforcement arrangements, gravity loads, and lateral loading routines. Specific reference to non-ductile specimens with discontinuous slab reinforcement.

3. RC Floor Systems

4. Punching Shear Failure No Continuity Reinforcement

5. Approach Task 1: Assemble Web Database Task 2: Fabricate and test 6 non-ductile interior connections Task 3: Develop backbone curve parameters Task 4: Develop hysteretic model Task 5: Validate hysteretic model

6. Non-Ductile Specimen tests Six specimens fabricated Three tested with varying gravity load levels V g /V o = 0.2, 0.28, 0.47 Three with varying slab reinforcement ratios = 0.3, 0.5 & 0.8% top reinforcement One specimen with bent-up bars

7. Test Setup

8. Varying gravity shear ratio TOP BOTTOM

9. ND1: Non-ductile V g /V o = 0.2 SLAB PUNCH

10. ND1: V g /V o = 0.2 SLAB PUNCH

11. ND4: Non-ductile, V g /V o = 0.28 ZERO RESIDUAL STRENGTH PUNCHING FAILURE

12. ND4: V g /V o = 0.28

14. ND5: Non-ductile, V g /V o =0.47 PUNCHING FAILURE ZERO RESIDUAL STRENGTH

15. ND5: V g /V o =0.47 TRANSVERSE BOTTOM REINF.

16. Varying Gravity Shear Ratio

18. Low reinforcement ratio BOTTOMTOP

19. Low reinforcement ratio PUNCHING FAILURE ZERO RESIDUAL STRENGTH

20. High reinforcement ratio TOPBOTTOM

21. High reinforcement ratio PUNCHING FAILURE

22. Reinforcement ratio comparison

23. Bent-up bars TOP BOTTOM

24. Bent-up bars PUNCHING FAILURE RESIDUAL STRENGTH

25. Comparison

26. Bent-up Bars

27. Critical Limit States for Flat Slab Response

28. FEMA 273 Backbone Curve

29. Limit States Significant Cracking No Repair Required Repairable Cracking Major Reconstruction Punching Failure

30. FEMA 273 Backbone

32. Typical Interior Connection

33. Backbone Curve Parameters

34. Initial Stiffness

35. FEMA 273: –Based on gross section modulus of one third slab width (uncracked). Proposed: –Based on cracked section modulus of one third slab width. for width

36. Peak Lateral Load Capacity

37. FEMA 273: –Based on flexural capacity, M n, of c 2 +5h slab width, divided by f where c 2 is the column width perpendicular to the applied lateral load h is the overall slab thickness f is the portion of unbalanced moment transferred by flexure according to the ACI 318 design approach.

38. Peak Lateral Load Capacity Proposed: –Based on flexural capacity of c 2 +5h slab width using 1.25f y, divided by f –Overestimated for heavily reinforced slabs –Neglect reinforcement in excess of = 0.0065 –Discontinuous bottom reinforcement included proportional to development length beyond face of column.

39. FEMA 356 Modification

40. Peak Lateral Load Capacity

41. Stiffness Degradation

42. Stiffness Model

43. Stiffness Degradation

44. Drift Capacity FEMA 273: –Specify Plastic Rotation Angle beyond Yield point, a

45. Drift Capacity FEMA 273: –Plastic Rotation Angle, a, depends on V g /V o V g = Gravity shear acting on slab critical section as defined by ACI 318 V o = direct punching shear strength as defined by ACI 318

46. Maximum Drift Level Proposed Model: –Based on proposal by Hueste and Wight –Maximum drift level related to V g /V o –Based on prior test results for connections failing in punching shear Slab Shear Reinforcement –Connections with adequate shear reinforcement will not experience shear failure –Gradual strength decay after peak lateral load

47. Prior test data

48. Drift < 0.5%

49. Pan and Moehle

50. Maximum Drift Level

51. Hueste and Wight

52. Recent data points

53. Proposed Model

54. Residual Strength FEMA: –20% of peak lateral load strength Proposed: –20% of peak lateral load strength for connections with continuity reinforcement –0 for connections without continuity reinforcement

55. Example Backbone Output

56. Example Hysteretic Output

57. Model Verification Comparison with data from tests performed at other universities Comparison with data from PEER non- ductile tests Verification of the models predicted energy dissipation to the measured energy dissipation

58. Robertson and Durrani Specimen

59. Test Setup

60. Backbone Comparison

61. Hysteretic Comparison

62. Hwang-Moehle Specimen

63. Hwang-Moehle Specimen - Plan N-S E-W

64. Hwang-Moehle Specimen - Elev.

65. Typical Interior Connection

67. Summary Pre-1970 non-ductile specimens more appropriately referred to as non-continuity connections. Propose conservatism in estimating drift limit for punching shear of such connections. High gravity shear ratio produces non-ductile response. Develop backbone and hysteretic model for interior and exterior connections, both perpendicular and parallel to edge, including various connection parameters. Propose revised limit states for FEMA 273 (356) slab- column connection response.