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
1998 PCI Daniel P. Jenny Research Fellowship University of Notre Dame
ELEVATION wall panel horizontal joint unbonded PT steel spiral reinforcement foundation anchorage
GAP OPENING BEHAVIOR gap
BASE PANEL compression stresses shear stresses
CRACKING
RESEARCH OBJECTIVES Develop analytical model Conduct parametric investigation Develop design approach
FINITE ELEMENT MODEL truss elements contact elements nonlinear plane stress elements
ABAQUS MODEL
GAP OPENING
ABAQUS VERSUS DRAIN base shear (kips) roof drift (%) DRAIN yielding state gap opening state ABAQUS
ABAQUS VERSUS DRAIN roof drift (%) contact length / wall length ABAQUS DRAIN
CLOSED FORM VERIFICATION (Savin 1961) (INFINITE PANEL) f tx T C
ABAQUS VERSUS CLOSED FORM SOLUTION f tx (ksi) closed form (Savin 1961) ABAQUS h o /l o lolo hoho
PARAMETRIC INVESTIGATION Wall length Initial concrete stress Opening size
WALL LENGTH 10 feet x 16 feet 15 feet x 16 feet 20 feet x 16 feet
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)
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 )
STAGES OF RESPONSE Gravity and post-tensioning only Gap opening PT steel yielding Concrete crushing
UNDER GRAVITY AND POST-TENSIONING ONLY A sf or A sc
EFFECT OF f ci (l p =20 feet) A sf (in 2 ) 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
EFFECT OF f ci (l p =20 feet) A sf (in 2 ) 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
A sf (in 2 ) h o /h p 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
A sf (in 2 ) l o /l p 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
EFFECT OF f ci (l p =20 feet) A sc (in 2 /ft) 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
EFFECT OF f ci (l p =20 feet) A sc (in 2 /ft) 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
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 l o /l p =0.3 lolo lplp hphp hoho
A sc (in 2 /ft) l o /l p 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
DESIGN PREDICTION T C C
PREDICTED VERSUS ABAQUS (l p =20 feet) A sf (in 2 ) f ci predicted ABAQUS l o /l p =0.3 h o /h p =0.25 lolo lplp hphp hoho
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
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
PREDICTED VERSUS ABAQUS (l p =20 feet) predicted ABAQUS f ci l o /l p =0.3 h o /h p =0.25 A sc (in 2 /ft) lolo lplp hphp hoho
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
l o /l p A sc (in 2 /ft) l p =20 feet PREDICTED VERSUS ABAQUS (f ci =0.68 ksi) h o /h p =0.25 predicted ABAQUS lolo lplp hphp hoho
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
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
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
REMAINING WORK Design for lateral loads Experimental verification (Lehigh Tests)