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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 Convention, Palm Springs, California, October 17-20, 1999
1998 PCI Daniel P. Jenny Research Fellowship
University of Notre Dame
ELEVATION
wall panel
horizontaljoint
unbondedPT steel
spiralreinforcement
foundation
anchorage
GAP OPENING BEHAVIOR
gap
BASE PANEL
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
ABAQUS MODEL
GAP OPENING
ABAQUS VERSUS DRAIN
base shear (kips)
0 0.5 1 1.5 2 2.5
500
1000
roof drift (%)
DRAIN
yielding state
gap openingstate ABAQUS
ABAQUS VERSUS DRAIN
roof drift (%)
contact length / wall length
0 0.5 1 1.5 2 2.5
0.5
1.0
ABAQUS
DRAIN
CLOSED FORM VERIFICATION (Savin 1961)(INFINITE PANEL)
ftx
T
C
ABAQUS VERSUS CLOSED FORM SOLUTIONftx (ksi)
closed form (Savin 1961)ABAQUS
6.00 3.0
1.2
0.6
ho/lo
loho
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 STRESSlp=20 feet CL
fci=1.48 ksi (high seismicity)
fci=0.67 ksi (medium seismicity)
fci=0.34 ksi (no seismicity)
OPENING SIZE
lo
ho hp=16 feet
lp=20 feet
ho
2 feet (0.13 hp)
4 feet (0.25 hp)
6 feet (0.38 hp)
8 feet (0.50 hp)
lo 2 feet (0.10 lp)
4 feet (0.20 lp)
8 feet (0.40 lp)
6 feet (0.30 lp)
10 feet (0.50 lp)
STAGES OF RESPONSE
• Gravity and post-tensioning only
• Gap opening
• PT steel yielding
• Concrete crushing
UNDER GRAVITY AND POST-TENSIONING ONLY
Asf or Asc
EFFECT OF fci
(lp=20 feet)Asf (in2)
0
1.0
2.0
0.5 1.0 1.5fci
ho/hp=0.125ho/hp=0.25ho/hp=0.375
lo/lp=0.3
lo
lp
hpho
EFFECT OF fci
(lp=20 feet)Asf (in2)
0
1.0
2.0
0.5 1.0 1.5fci
lo/lp=0.1lo/lp=0.2
lo/lp=0.4lo/lp=0.3
ho/hp=0.25
lo
lp
hpho
Asf (in2)
ho/hp
0 0.25 0.5
1.0
2.0lp=20 feetlp=15 feetlp=10 feet
EFFECT OF ho
(fci=0.68 ksi)
lo/lp=0.3lo
lp
hpho
Asf (in2)
lo/lp
0 0.25 0.5
1.0
2.0lp=20 feetlp=15 feetlp=10 feet
EFFECT OF lo
(fci=0.68 ksi)
ho/hp=0.25
lo
lp
hpho
EFFECT OF fci
(lp=20 feet)
0
10
20
30
Asc (in2/ft)
0.5 1.0 1.5fci
ho/hp=0.125ho/hp=0.25ho/hp=0.375
lo/lp=0.3
lo
lp
hpho
EFFECT OF fci
(lp=20 feet)
0
10
20
30
Asc (in2/ft)
0.5 1.0 1.5fci
lo/lp=0.1lo/lp=0.2
lo/lp=0.4lo/lp=0.3 ho/hp=0.25
lo
lp
hpho
EFFECT OF ho
(fci=0.68 ksi)
0.5ho/hp
0.25
Asc (in2/ft)
0
lp=20 feetlp=15 feetlp=10 feet
15
10
5
lo/lp=0.3
lo
lp
hpho
Asc (in2/ft)
lo/lp
0.25 0.50
5
10
15
ho/hp=0.25lp=20 feetlp=15 feetlp=10 feet
EFFECT OF lo
(fci=0.68 ksi)
lo
lp
hpho
DESIGN PREDICTION
T
C
C
PREDICTED VERSUS ABAQUS(lp=20 feet)Asf (in2)
0.5 1.0 1.50
1.0
2.0
fci
predictedABAQUS
lo/lp=0.3ho/hp=0.25
lo
lp
hpho
0 0.25 0.5
1.0
2.0Asf (in2)
ho/hp
lp=20 feet
PREDICTED VERSUS ABAQUS (fci=0.68 ksi)
lo/lp=0.3
predictedABAQUS
lo
lp
hpho
0 0.25 0.5
1.0
2.0Asf (in2)
lo/lp
lp=20 feet
PREDICTED VERSUS ABAQUS (fci=0.68 ksi)
ho/hp=0.25
predictedABAQUS
lo
lp
hpho
0
10
20
30
PREDICTED VERSUS ABAQUS (lp=20 feet)
predictedABAQUS
0.5 1.0 1.5fci
lo/lp=0.3ho/hp=0.25
Asc (in2/ft)
lo
lp
hpho
Asc (in2/ft)
15
0 0.25 0.5
5
10
ho/hp
lp=20 feet
PREDICTED VERSUS ABAQUS (fci=0.68 ksi)
lo/lp=0.3
predictedABAQUS
lo
lp
hpho
lo/lp
Asc (in2/ft)
0.25 0.50
5
10
15
lp=20 feet
PREDICTED VERSUS ABAQUS (fci=0.68 ksi)
ho/hp=0.25
predictedABAQUS
lo
lp
hpho
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
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
• Design for lateral loads
• Experimental verification (Lehigh Tests)
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