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### Partially Post-TensionedPrecast Concrete Walls

Yahya C. (Gino) Kurama

Assistant Professor

University of Notre Dame

Notre Dame, Indiana, USA

American Concrete Institute Spring 2003 Convention

Vancouver, Canada

April 2, 2003

POST-TENSIONED PRECAST CONCRETE WALL

anchorage

wall panel

horizontal

joint

unbonded

PT bars

spiral

reinforcement

foundation

spiral

bonded

unbonded

reinforcement

wire mesh

PT bar

precast wall with full PT

BEHAVIOR UNDER LATERAL LOADS

gap opening

friction or metallic-yield damper

Priestley et al.

Perez et al.

Kurama

Pall et al.

WALLS WITH PARTIAL POST-TENSIONING

unbonded

PT bar

bonded

mild

bar

unbonded

bonded

mild bar

PT bar

precast wall with partial PT

PARTIALLY POST-TENSIONED PRECAST FRAME

column

fiber reinforced grout

trough

mild steel bar

beam

PT tendon

beam-to-column joint

Cheok et al.

Priestley et al.

Stanton et al.

Nakaki et al.

OBJECTIVES

- Investigate precast wall systems with PT steel and mild steel
- Develop seismic design approach
- Evaluate seismic response

- Prototype walls and expected behavior
- Seismic design approach and evaluation
- Summary and conclusions

- Four fully post-tensioned walls
- Four walls with only mild steel (emulative walls)
- Four partially post-tensioned walls

PLAN LAYOUT OF PROTOTYPE BUILDINGS

8 x 24 ft = 192 ft (58.5 m)

hollow-

lateral load

gravity load

core

frame

frame

panels

40 + 30 + 40 = 110 ft

(33.5 m)

wall

inverted

column

L-beam

T-beam

N

4 story building, high seismicity

6 story building, high seismicity

10 story building, high seismicity

6 story building, medium seismicity

FULLY POST-TENSIONED WALLS

133 ft

(41 ft)

81 ft

81 ft

(25 ft)

(25 ft)

55 ft

(17 ft)

26 ft (8 m)

20 ft (6 m)

20 ft (6 m)

20 ft (6 m)

4 story

high seismicity

6 story

high seismicity

10 story

high seismicity

6 story

medium seismicity

FULLY POST-TENSIONED WALLS

C

C

L

L

#3 spirals

#3 spirals

Ap=1.49in2 (961mm2)

Ap=1.49in2 (961mm2)

fpi=0.60-0.65fpu

rsp=7.3%

fpi=0.60-0.65fpu

rsp=7.3%

12in.

12in.

(305mm)

(305mm)

10 ft (3 m)

10 ft (3 m)

Wall PH4

Wall PH6

C

C

L

L

#3 spirals

#3 spirals

Ap=1.49in2 (961mm2)

Ap=1.49in2 (961mm2)

fpi=0.60-0.65fpu

rsp=7.3%

fpi=0.625fpu

rsp=1.8%

12in.

12in.

(305mm)

(305mm)

13 ft (4 m)

10 ft (3 m)

Wall PH10

Wall PM6

EMULATIVE WALLS

No. 8 bars

No. 5 bars

No. 8 bars

No. 5 bars

16 pairs

5 pairs

15 pairs

5 pairs

C

C

L

L

@ 18 in.

@ 2.5 in.

@ 2.25 in.

@ 18 in.

(@ 57 mm)

(@ 457 mm)

(@ 63 mm)

(@ 457 mm)

12in.

12in.

(305mm)

(305mm)

10 ft (3 m)

10 ft (3 m)

Wall EH4

Wall EH6

No. 6 bars

No. 5 bars

No. 8 bars

No. 5 bars

7 pairs

5 pairs

20 pairs

6 pairs

C

C

L

L

@ 5.25 in.

@ 18 in.

@ 2.25 in.

@ 18 in.

(@ 57 mm)

(@ 457 mm)

(@ 133 mm)

(@ 457 mm)

12in.

12in.

(305mm)

(305mm)

10 ft (3 m)

13 ft (4 m)

Wall EM6

Wall EH10

PARTIALLY POST-TENSIONED WALLS

No. 5 bars

No. 5 bars

No. 8 bars

No. 5 bars

C

7 pairs

5 pairs

C

7 pairs

5 pairs

L

L

@ 5.5 in.

@ 18 in.

@ 5.5 in.

@ 18 in.

(@ 140 mm)

(@ 457 mm)

(@ 140 mm)

(@ 457 mm)

12in.

12in.

(305mm)

(305mm)

10 ft (3 m)

10 ft (3 m)

Wall HH6-25

Wall HH6-50

No. 8 bars

No. 5 bars

No. 5 bars

11 pairs

5 pairs

C

8 pairs

C

L

L

@ 3.5 in.

@ 18 in.

@ 17 in.

(@ 89 mm)

(@ 457 mm)

(@ 432 mm)

12in.

12in.

(305mm)

(305mm)

10 ft (3 m)

10 ft (3 m)

Wall HH6-75

Wall HM6-50

ANALYTICAL WALL MODEL

stress, ksi (MPa)

100 (690)

truss

element

0

MILD STEEL

-100 (690)

-0.08

0

0.08

fiber

element

strain

stress, ksi (MPa)

stress, ksi (MPa)

7 (48)

160 (1103)

120 (827)

kinematic

constraint

strain

0

0

0.006

0.0351

strain

PT STEEL

CONCRETE

WALL BEHAVIOR UNDER MONOTONIC LOADS

base shear, kips (kN)

base shear, kips (kN)

1000

1500

(4448)

(6672)

Wall PH6

Wall HH6-25

Wall HH6-50

Wall PH4

Wall HH6-75

Wall EH4

Wall EH6

0

3

0

3

roof drift, %

roof drift, %

base shear, kips (kN)

base shear, kips (kN)

1000

500

(4448)

(2224)

Wall PM6

Wall PH10

Wall HM6-50

Wall EH10

Wall EM6

0

0

3

2

roof drift, %

roof drift, %

Wall HH6-50

SIX STORY WALLS IN HIGH SEISMICITYbase shear, kips (kN)

base shear, kips (kN)

base shear, kips (kN)

1000

Wall PH6

(4448)

0

(-4448)

-1000

0

3

0

3

0

3

-3

-3

-3

roof drift, %

roof drift, %

roof drift, %

base shear, kips (kN)

base shear, kips (kN)

1000

1000

Wall EH6

Wall HH6-75

(4448)

(4448)

0

0

(-4448)

(-4448)

-1000

-1000

0

3

3

0

-3

-3

roof drift, %

roof drift, %

NORMALIZED INELASTIC ENERGY DISSIPATION

base shear, kips (kN)

1000

(4448)

ksec

Dh

-Dc

Dh

0

=

dh

-Dc

Ue

Ue

(-4448)

-1000

-3

0

3

roof drift, %

NORMALIZED INELASTIC ENERGY DISSIPATION

(dh = Dh / Ue)

(dh = Dh / Ue)

2

2

Wall PH6

Wall PH4

Wall HH6-25

Wall EH4

Wall HH6-50

1.5

1.5

Wall HH6-75

Wall EH6

1

1

0.5

0.5

0

0

3

3

cycle roof drift, %

cycle roof drift, %

(dh = Dh / Ue)

(dh = Dh / Ue)

2

2

Wall PH10

Wall PM6

Wall EH10

Wall HM6-50

1.5

1.5

Wall EM6

1

1

0.5

0.5

0

0

2

3

cycle roof drift, %

cycle roof drift, %

DYNAMIC RESPONSE

roof drift, %

roof drift, %

2.5

2.5

NOSY

PH6

PH4

HH6-25

EH4

PGA=0.97g

0

0

HH6-50

NOSY

HH6-75

EH6

PGA=0.97g

-2.5

-2.5

0

15

0

15

time, seconds

time, seconds

roof drift, %

roof drift, %

2.5

1.5

PH10

NOSY

EH10

PGA=0.39g

0

0

PM6

HM6-50

NOSY

EM6

PGA=0.97g

-1.5

-2.5

0

15

0

15

time, seconds

time, seconds

REDUCTION IN MAXIMUM ROOF DRIFT

normalized maximum roof drift

1.0

0.8

0.6

0.4

PH6

HH6-25

HH6-50

HH6-75

EH6

0.2

average

0

0

0.2

0.4

0.6

0.8

1

normalized mild steel ratio

REDUCTION IN NUMBER OF DRIFT PEAKS

average number of drift peaks

average number of drift peaks

8

8

WALL PH6

WALL PH4

WALL HH6-25

WALL EH4

6

6

WALL HH6-50

WALL HH6-75

4

4

WALL EH6

2

2

0

0

0.5

1

0.5

1

normalized amplitude of drift peak

normalized amplitude of drift peak

average number of drift peaks

average number of drift peaks

8

8

WALL PH10

WALL PM6

6

6

WALL EH10

WALL HM6-50

WALL EM6

4

4

2

2

0

0

0.5

1

0.5

1

normalized amplitude of drift peak

normalized amplitude of drift peak

- Prototype walls
- Expected behavior
- Seismic design approach and evaluation
- Summary and conclusions

MDOF MODEL

SDOF MODEL

base shear, kips (kN)

base shear, kips (kN)

2000

2000

(8896)

(8896)

0

0

(8896)

(8896)

-2000

-2000

-3

0

3

-3

0

3

roof drift, %

roof drift, %

F

akbe

F

F

akbe

[(1+br)Fbe,Dbe]

(brFbe,Dbe)

(Fbe,Dbe)

D

D

D

=

+

kbe

(1+bs)kbe

bskbe

Bilinear-Elastic/

Bilinear-Elastic (BE)

Elasto-Plastic (EP)

Elasto-Plastic (BP)

pseudo-acceleration, g

4

Los Ang., SD soil, survival-level

(SAC LA21-40)

AVG spectrum

2

5% damping

0

0.5

1

1.5

2

2.5

3

3.5

period, seconds

SDOF/MDOF PEAK DISPLACEMENT

SDOF/MDOF maximum displacement ratio

1.2

1.0

mean

0.8

0.6

0.4

Wall HW1

SAC LA21- 40

0.2

0

50

100

(381) 150

maximum incremental velocity, in/sec (cm/sec)

DUCTILITY DEMAND

F

F

F

akbe

akbe

[(1+br)Fbe,Dbe]

(brFbe,Dbe)

(Fbe,Dbe)

D

D

D

+

=

kbe

(1+bs)kbe

bskbe

Bilinear-Elastic/

Bilinear-Elastic (BE)

Elasto-Plastic (EP)

Elasto-Plastic (BP)

- bs = br = 1/4, 1/3, 1/2
- a = 0.02, 0.10
- Moderate and High Seismicity
- Design-Level and Survival-Level
- Stiff Soil and Medium Soil Profiles

R=[c(m-1)+1]1/c

Tab

c= +

Ta+1 T

(Nassar & Krawinkler, 1991)

(Farrow and Kurama, 2001)

DUCTILITY DEMAND SPECTRA (Farrow and Kurama, 2001)

br = bs = 1/3, a=0.10, High Seismicity, Stiff (Sd) Soil, R=1, 2, 4, 6, 8 (thin thick)

Design EQ (SAC): a=3.83, b=0.87

Survival EQ (SAC): a=1.08, b=0.89

ductility demand, m

ductility demand, m

14

14

BP, mean

regression

0

0

3.5

3.5

period, seconds

period, seconds

Survival EQ (SAC): BP versus EP

Survival EQ (SAC): BP versus BE

ductility demand, m

ductility demand, m

14

14

BP, mean

EP, mean

BE, mean

0

0

3.5

3.5

period, seconds

period, seconds

NONLINEAR DEMAND SPECTRA

demand acceleration, g

demand acceleration, g

1.5

1.5

T = 0.5 sec.

T = 1.5 sec.

m=1

m=1

a = -0.71

a = -0.71

b = 0.94

b = 0.94

1

1

(linear-elastic)

(linear-elastic)

2

a = 2.3

2

1.5

1.5

T = 0.5 sec.

T = 1.5 sec.

m

=

1

m

=

1

a = 2.3

demand

b = 1.3

b = 1.3

spectrum

1

1

2

2

a

a

S (g)

S (g)

B

4

D

4

0.5

0.5

C

8

8

E

F

capacity curve

4

0

0

20

40

60

80

100

20

40

60

80

100

S (cm)

S (cm)

d

d

(a)

1.5

1.5

T = 0.5 sec.

T = 1.5 sec.

m

=

1

m

=

1

0.5

a = -0.71

a = -0.71

0.5

b = 0.94

b = 0.94

1

1

A

4

2

2

a

a

S (g)

S (g)

B

4

D

0.5

0.5

4

C

8

8

E

F

0

0

20

40

60

80

100

20

40

60

80

100

S (cm)

S (cm)

d

d

8

(b)

8

0

0

(39) 100

(39) 100

demand displacement, cm (in.)

demand displacement, cm (in.)

DESIGN OBJECTIVES – SURVIVAL LEVEL

base

shear

immediate

occupancy

(Dt=1.19%)

collapse

prevention

(Dt=2.17%)

WALL WH1

WALL WH2

roof drift

WALLS HW1 AND HW2

No. 10 bars

No. 5 bars

C

L

8 pairs

7 pairs

@ 2.5 in.

@ 18 in.

(@ 63 mm)

(@ 457 mm)

12in.

(305mm)

11 ft (3.35 m)

Wall WH1

No. 10 bars

No. 5 bars

C

L

7 pairs

6 pairs

@ 2.5 in.

@ 18 in.

(@ 63 mm)

(@ 457 mm)

12in.

(305mm)

10 ft (3 m)

Wall WH2

WALL HW1

maximum roof drift, %

3

2

Dt=1.19%

1

Dmean=1.13%

0

50

100

(381) 150

maximum incremental velocity, in/sec (cm/sec)

WALL WH2

maximum roof drift, %

3.5

3

2.5

Dt=2.17%

2

Dmean=1.85%

1.5

1

0.5

0

50

100

(381) 150

maximum incremental velocity, in/sec (cm/sec)

CONCLUSIONS

- Energy Dissipation
- Mild steel reinforcement yielding in tension and compression

- Design Approach
- MDOF SDOF Nonlinear demand spectra
- Target drift

- Seismic Response Evaluation
- Maximum drift reduced below target drift
- Significant scatter in results

National Science Foundation CAREER-Program CMS 98-74872Program DirectorsDr. S. C. LiuDr. S. MaCabe

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