1. DESIGN OF LARGE OPENINGS IN UNBONDED POST-TENSIONED PRECAST CONCRETE WALLS Michael G. Allen Yahya C. Kurama University of Notre Dame Notre Dame, IN PCI Committee Days, Chicago, Illinois, April 14-15, 2000

2. 1998 PCI Daniel P. Jenny Research Fellowship University of Notre Dame

3. ELEVATION wall panel horizontal joint unbonded PT steel spiral reinforcement foundation anchorage

4. GAP OPENING BEHAVIOR gap

5. UNDER LATERAL LOADS AT FAILURE compression stresses shear stresses

6. CRACKING 1 2 2 3 3 4 5 5 3

7. RESEARCH OBJECTIVES Develop analytical model Conduct parametric investigation Develop design approach

8. FINITE ELEMENT MODEL truss elements contact elements nonlinear plane stress elements

9. GAP OPENING

10. STAGES OF RESPONSE Gravity and post-tensioning only Lateral loads

11. UNDER GRAVITY AND POST-TENSIONING ONLY A sf

12. DESIGN PREDICTION T C C

13. 02.04.0 h o /l o 1.0 l p =10 feet (f ci =0.68 ksi) l p =15 feet (f ci =0.44 ksi) l p =15 feet (f ci =0.68 ksi) l p =20 feet (f ci =0.68 ksi) l p =20 feet (f ci =1.48 ksi) l p =20 feet (f ci =0.67 ksi) l p =20 feet (f ci =0.34 ksi) 1.5 A sf (predicted/ABAQUS) ALL CASES 0.5

14. UNDER LATERAL LOADS AT FAILURE compression stresses shear stresses T max x cr

15. CRITICAL SECTION x cr

16. LARGE OPENING VERSUS SMALL OPENINING small opening large opening x cr

17. PANEL REGION TO BE ANALYZED x cr

18. FREE BODY DIAGRAM V1V1 N cr N lc M cr M lc V top V lc N top N grav

19. FREE BODY DIAGRAM

20. MOMENT AT CRITICAL SECTION, M cr h o /h p = 0.125 -8 0 8 0.25 0.5 0 l o /l p V1V1 V top V lc M lc N lc N grav N top M / M cr

21. MOMENT AT CRITICAL SECTION V1V1 V top V lc M lc N lc N grav N top -8 0 8 0.25 0.5 0 l o /l p M / M cr h o /h p = 0.375

22. MOMENT AT CRITICAL SECTION -8 0 8 0.25 0.5 0 h o /h p M / M cr l o /l p = 0.1 V1V1 V top V lc M lc N lc N grav N top

23. MOMENT AT CRITICAL SECTION V1V1 V top V lc MlcMlc N lc N gravity N top -8 0 8 0.25 0.5 0 h o /h p M / M cr l o /l p = 0.4

24. PREDICTED VERSUS ACTUAL MOMENT -3 -2 0 M cr (10 4 kip-in) ABAQUS (V top ) predicted (V top ) ABAQUS (V lc ) predicted (V lc ) l o /l p = 0.3 0.25 0.5 0 h o /h p N cr M cr V top V lc

25. ABAQUS (V lc ) PREDICTED VERSUS ACTUAL MOMENT -3 -2 0 M cr (10 4 kip-in) ABAQUS (V top ) predicted (V top ) predicted (V lc ) h o /h p = 0.25 0.25 0.5 0 l o /l p

26. PREDICTED VERSUS ACTUAL MOMENT ABAQUS (N top ) 1 2 3 M cr (10 4 kip-in) ABAQUS (M lc ) predicted (M lc ) predicted (N top ) h o /h p = 0.25 0.25 0.5 l o /l p 0

27. PREDICTED VERSUS ACTUAL MOMENT ABAQUS (N top ) 1 2 3 M cr (10 4 kip-in) ABAQUS (M lc ) predicted (M lc ) predicted (N top ) l o /l p = 0.3 0.25 0.5 h o /h p 0

28. TOTAL M cr 1 2 3 M cr (10 4 kip-in) h o /h p = 0.375 0.25 0.5 0 l o /l p ABAQUS predicted

29. TOTAL M cr 1 2 3 M cr (10 4 kip-in) l o /l p = 0.3 0.25 0.5 0 h o /h p ABAQUS predicted

30. TOTAL N cr h o /h p = 0.25 0.25 0.5 0 l o /l p ABAQUS predicted -400 0 400 N cr (kip)

31. TOTAL N cr l o /l p = 0.3 0.25 0.5 0 h o /h p ABAQUS predicted -400 0 400 N cr (kip)

32. A sf IN TOP CHORD 3 6 0.25 0.5 0 l o /l p ABAQUS predicted h o /h p = 0.25 A sf (in 2 )

33. A sf IN TOP CHORD l o /l p = 0.3 ABAQUS predicted 3 6 0.25 0.5 0 h o /h p A sf (in 2 )

34. A sf (predicted/ABAQUS) TOP CHORD 0 1 3 1.53 h o /l o 2

35. A sf IN LEFT CHORD 3 6 0.25 0.5 0 A sf (in 2 ) ABAQUS predicted l o /l p h o /h p = 0.25

36. A sf IN LEFT CHORD

37. Asf IN MIDDLE CHORD 3 6 0.25 0.5 0 h o /h p A sf (in 2 ) l o /l p = 0.3 ABAQUS predicted

38. A sf (predicted/ABAQUS) LEFT CHORD 0 1.5 3 3 h o /l o

39. CONCLUSIONS Analytical Model ABAQUS model developed for walls with openings ABAQUS results compare well with DRAIN-2DX results and closed form results Parametric Investigation Gravity and post-tensioning loads only As f ci increases, steel requirement increases significantly As h o increases, steel requirement decreases, especially for longer walls As l o increases, steel requirement increases, especially for shorter walls

40. CONCLUSIONS Design Approach Utilizes a strut-and-tie model Can be used to predict the ABAQUS results; and To design the reinforcement above the openings –A sc to prevent cracking –A sf to minimize crack widths

41. REMAINING WORK Finish design for lateral loads Experimental verification (Lehigh Tests)