design of large openings in unbonded post-tensioned precast concrete walls
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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
1998 PCI Daniel P. Jenny Research Fellowship
University of Notre Dame
ELEVATION
wall panel
horizontaljoint
unbondedPT steel
spiralreinforcement
foundation
anchorage
GAP OPENING BEHAVIOR
gap
UNDER LATERAL LOADS AT FAILURE
compression stresses
shearstresses
CRACKING
1
2
2
3
3
4
5
5
3
RESEARCH OBJECTIVES
• Develop analytical model
• Conduct parametric investigation
• Develop design approach
FINITE ELEMENT MODEL
truss elements
contact elements
nonlinearplane stress elements
GAP OPENING
STAGES OF RESPONSE
• Gravity and post-tensioning only
• Lateral loads
UNDER GRAVITY AND POST-TENSIONING ONLY
Asf
DESIGN PREDICTION
T
C
C
0 2.0 4.0
ho/lo
1.0
lp=10 feet (fci=0.68 ksi)lp=15 feet (fci=0.44 ksi)lp=15 feet (fci=0.68 ksi)lp=20 feet (fci=0.68 ksi)
lp=20 feet (fci=1.48 ksi)lp=20 feet (fci=0.67 ksi)
lp=20 feet (fci=0.34 ksi)
1.5
Asf (predicted/ABAQUS)ALL CASES
0.5
UNDER LATERAL LOADS AT FAILURE
compression stresses
shearstressesTmax
xcr
CRITICAL SECTION
xcr
LARGE OPENING VERSUS SMALL OPENINING
small opening large opening
xcr xcr
PANEL REGION TO BE ANALYZED
xcr
FREE BODY DIAGRAM
V1
Ncr
Nlc
Mcr
Mlc
Vtop
Vlc
NtopNgrav
FREE BODY DIAGRAM
MOMENT AT CRITICAL SECTION, Mcr
ho/hp = 0.125
-8
0
8
0.25 0.50lo/lp
V1Vtop
Vlc
Mlc
Nlc
Ngrav
Ntop
M / Mcr
MOMENT AT CRITICAL SECTION
V1Vtop
Vlc
Mlc
Nlc
Ngrav
Ntop
-8
0
8
0.25 0.50lo/lp
M / Mcr
ho/hp = 0.375
MOMENT AT CRITICAL SECTION
-8
0
8
0.25 0.50ho/hp
M / Mcr
lo/lp = 0.1
V1Vtop
Vlc
Mlc
Nlc
Ngrav
Ntop
MOMENT AT CRITICAL SECTION
V1Vtop
Vlc
Mlc
Nlc
Ngravity
Ntop
-8
0
8
0.25 0.50ho/hp
M / Mcr lo/lp = 0.4
PREDICTED VERSUS ACTUAL MOMENT
-3
-2
-1
0
Mcr (104 kip-in)
ABAQUS (Vtop)predicted (Vtop)ABAQUS (Vlc)predicted (Vlc)
lo/lp = 0.3
0.25 0.50ho/hp
Ncr
Mcr
Vtop
Vlc
ABAQUS (Vlc)
PREDICTED VERSUS ACTUAL MOMENT
-3
-2
-1
0
Mcr (104 kip-in)
ABAQUS (Vtop)predicted (Vtop)
predicted (Vlc)
ho/hp = 0.25
0.25 0.50lo/lp
PREDICTED VERSUS ACTUAL MOMENT
ABAQUS (Ntop)
1
2
3
Mcr (104 kip-in)
ABAQUS (Mlc)predicted (Mlc)
predicted (Ntop)
ho/hp = 0.25
0.25 0.5lo/lp
0
PREDICTED VERSUS ACTUAL MOMENT
ABAQUS (Ntop)
1
2
3
Mcr (104 kip-in)
ABAQUS (Mlc)predicted (Mlc)
predicted (Ntop)
lo/lp = 0.3
0.25 0.5ho/hp
0
TOTAL Mcr
1
2
3
Mcr (104 kip-in) ho/hp = 0.375
0.25 0.50lo/lp
ABAQUSpredicted
TOTAL Mcr
1
2
3
Mcr (104 kip-in) lo/lp = 0.3
0.25 0.50
ho/hp
ABAQUSpredicted
TOTAL Ncr
ho/hp = 0.25
0.25 0.50lo/lp
ABAQUSpredicted
-400
0
400
Ncr (kip)
TOTAL Ncr
lo/lp = 0.3
0.25 0.50ho/hp
ABAQUSpredicted
-400
0
400
Ncr (kip)
Asf IN TOP CHORD
3
6
0.25 0.50
lo/lp
ABAQUSpredicted
ho/hp = 0.25Asf (in2)
Asf IN TOP CHORD
lo/lp = 0.3
ABAQUSpredicted
3
6
0.25 0.50
ho/hp
Asf (in2)
Asf (predicted/ABAQUS)TOP CHORD
0
1
3
1.5 3 ho/lo
2
Asf IN LEFT CHORD
3
6
0.25 0.50
Asf (in2)
ABAQUSpredicted
lo/lp
ho/hp = 0.25
Asf IN LEFT CHORD
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5
ABAQUS
predicted
lo/lp=.3
Asf IN MIDDLE CHORD
3
6
0.25 0.50
ho/hp
Asf (in2)
lo/lp = 0.3
ABAQUSpredicted
Asf (predicted/ABAQUS)LEFT CHORD
0
1.5
3
1.5 3 ho/lo
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 fci increases, steel requirement increases significantly
• As ho increases, steel requirement decreases, especially for longer walls
• As lo 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
– Asc to prevent cracking
– Asf to minimize crack widths
REMAINING WORK
• Finish design for lateral loads
• Experimental verification (Lehigh Tests)
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