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)