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 Convention, Palm Springs, California, October 17-20, 1999

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. BASE PANEL 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. ABAQUS MODEL

10. GAP OPENING

11. ABAQUS VERSUS DRAIN base shear (kips) 0 0.511.522.5 500 1000 roof drift (%) DRAIN yielding state gap opening state ABAQUS

12. ABAQUS VERSUS DRAIN roof drift (%) contact length / wall length 0 0.511.5 2 2.5 0.5 1.0 ABAQUS DRAIN

13. CLOSED FORM VERIFICATION (Savin 1961) (INFINITE PANEL) f tx T C

14. ABAQUS VERSUS CLOSED FORM SOLUTION f tx (ksi) closed form (Savin 1961) ABAQUS 6.0 0 3.0 1.2 0.6 h o /l o lolo hoho

15. PARAMETRIC INVESTIGATION Wall length Initial concrete stress Opening size

16. WALL LENGTH 10 feet x 16 feet 15 feet x 16 feet 20 feet x 16 feet

17. INITIAL CONCRETE STRESS l p =20 feet C L f ci =1.48 ksi (high seismicity) f ci =0.67 ksi (medium seismicity) f ci =0.34 ksi (no seismicity)

18. OPENING SIZE lolo hoho h p =16 feet l p =20 feet hoho 2 feet (0.13 h p ) 4 feet (0.25 h p ) 6 feet (0.38 h p ) 8 feet (0.50 h p ) lolo 2 feet (0.10 l p ) 4 feet (0.20 l p ) 8 feet (0.40 l p ) 6 feet (0.30 l p ) 10 feet (0.50 l p )

19. STAGES OF RESPONSE Gravity and post-tensioning only Gap opening PT steel yielding Concrete crushing

20. UNDER GRAVITY AND POST-TENSIONING ONLY A sf or A sc

21. EFFECT OF f ci (l p =20 feet) A sf (in 2 ) 0 1.0 2.0 0.51.0 1.5 f ci h o /h p =0.125 h o /h p =0.25 h o /h p =0.375 l o /l p =0.3 lolo lplp hphp hoho

22. EFFECT OF f ci (l p =20 feet) A sf (in 2 ) 0 1.0 2.0 0.51.0 1.5 f ci l o /l p =0.1 l o /l p =0.2 l o /l p =0.4 l o /l p =0.3 h o /h p =0.25 lolo lplp hphp hoho

23. A sf (in 2 ) h o /h p 0 0.25 0.5 1.0 2.0 l p =20 feet l p =15 feet l p =10 feet EFFECT OF h o (f ci =0.68 ksi) l o /l p =0.3 lolo lplp hphp hoho

24. A sf (in 2 ) l o /l p 0 0.25 0.5 1.0 2.0 l p =20 feet l p =15 feet l p =10 feet EFFECT OF l o (f ci =0.68 ksi) h o /h p =0.25 lolo lplp hphp hoho

25. EFFECT OF f ci (l p =20 feet) 0 10 20 30 A sc (in 2 /ft) 0.51.0 1.5 f ci h o /h p =0.125 h o /h p =0.25 h o /h p =0.375 l o /l p =0.3 lolo lplp hphp hoho

26. EFFECT OF f ci (l p =20 feet) 0 10 20 30 A sc (in 2 /ft) 0.51.0 1.5 f ci l o /l p =0.1 l o /l p =0.2 l o /l p =0.4 l o /l p =0.3 h o /h p =0.25 lolo lplp hphp hoho

27. EFFECT OF h o (f ci =0.68 ksi) 0.5 h o /h p 0.25 A sc (in 2 /ft) 0 l p =20 feet l p =15 feet l p =10 feet 15 10 5 l o /l p =0.3 lolo lplp hphp hoho

28. A sc (in 2 /ft) l o /l p 0.25 0.5 0 5 10 15 h o /h p =0.25 l p =20 feet l p =15 feet l p =10 feet EFFECT OF l o (f ci =0.68 ksi) lolo lplp hphp hoho

29. DESIGN PREDICTION T C C

30. PREDICTED VERSUS ABAQUS (l p =20 feet) A sf (in 2 ) 0.51.0 1.5 0 1.0 2.0 f ci predicted ABAQUS l o /l p =0.3 h o /h p =0.25 lolo lplp hphp hoho

31. 0 0.250.5 1.0 2.0 A sf (in 2 ) h o /h p l p =20 feet PREDICTED VERSUS ABAQUS (f ci =0.68 ksi) l o /l p =0.3 predicted ABAQUS lolo lplp hphp hoho

32. 0 0.25 0.5 1.0 2.0 A sf (in 2 ) l o /l p l p =20 feet PREDICTED VERSUS ABAQUS (f ci =0.68 ksi) h o /h p =0.25 predicted ABAQUS lolo lplp hphp hoho

33. 0 10 20 30 PREDICTED VERSUS ABAQUS (l p =20 feet) predicted ABAQUS 0.51.0 1.5 f ci l o /l p =0.3 h o /h p =0.25 A sc (in 2 /ft) lolo lplp hphp hoho

34. 15 0 0.25 0.5 5 10 h o /h p l p =20 feet PREDICTED VERSUS ABAQUS (f ci =0.68 ksi) l o /l p =0.3 predicted ABAQUS lolo lplp hphp hoho

35. l o /l p A sc (in 2 /ft) 0.25 0.50 5 10 15 l p =20 feet PREDICTED VERSUS ABAQUS (f ci =0.68 ksi) h o /h p =0.25 predicted ABAQUS lolo lplp hphp hoho

36. 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

37. 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

38. 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

39. REMAINING WORK Design for lateral loads Experimental verification (Lehigh Tests)