design of large openings in unbonded post-tensioned precast concrete walls michael g. allen yahya c....

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)