1

UH-Contribution

Ravi MullapudiParnak Charkhchi

Ashraf Ayoub

NEES - Jan 23, 2008

2

OUTLINE Combined Bending/Shear

Modified Compression Field Theory (MCFT) Rotating Angle Softened Truss Model (RA-STM) Fixed Angle Softened Truss Model (FA-STM) Soften Membrane Model (SMM) Comparison between Models Seismic Analysis – Numerical Results

Combined Torsion/Bending/Shear Discretization of Section in 2D/3D Regions 3D Constitutive Models Section Analysis Numerical Results

On-Going Work Beam Element under Combined Torsion/Bending/Shear Seismic Analysis OpenSees

3

Modified Compression Field Model

1

0

10.34

0.8

2 p cf

Rotating Angle- Softened Truss Model

1 1 2 3cf f f f

25.8

0.9cc

f ff

3 124

f

1 1

1

1

1 400f

4

SOFTEN TRUSS MODEL -Principle

Shear stress along crack ≠ 0 Vc

Biaxial Stress & Strain

Smeared Approach

Concrete Element

SOFTEN Membrane MODEL

Hsu/Zhu Poisson Ratio

5

NUMERICAL RESULTS – USC Shear-Critical Column

'cf = 86 MPa

Longitudinal yield stress = 510 MPaTransverse yield stress = 449 MPa

Xiao and Martirossyan

6

NUMERICAL RESULTS Effect of Different Models

HC4-8L16-T6-0.1P Column Monotonic Analysis with different Elements

-300

-200

-100

0

100

200

300

400

-40 -30 -20 -10 0 10 20 30 40

Displacement(mm)

Sh

ear

Fo

rce(

KN

) SMM

RA-STM

TEST

FA-STM

Vecchio

7

NUMERICAL RESULTS

HC4-8L16-T6-0.1P Column

Hoop Strain Distributions

0

200

400

600

800

1000

1200

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Hoop Strain

Co

lum

n H

eig

ht

Duct 5

Duct 4

Duct 3

Duct 2

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NUMERICAL RESULTS – Cyclic Load DisplacementAxial Load = 1068 kNUSC Column

-500

-400

-300

-200

-100

0

100

200

300

400

500

-40 -30 -20 -10 0 10 20 30 40Lateral Displacement (mm)

Sh

ear

forc

e (k

N)

.

Analytical Solution

Experiment

Flexure Element

Flexure element is unable to predict the correct behavior

9

NUMERICAL RESULTS – Cyclic Load DisplacementAxial Load = 1068 kNUSC Column

Shear Element

-500

-400

-300

-200

-100

0

100

200

300

400

500

-40 -30 -20 -10 0 10 20 30 40Lateral Displacement (mm)

Sh

ear

force

(k

N)

.

Analytical Solution

Experiment

Shear element is able to predict the correct behavior

0

50

100

150

200

250

300

350

400

450

500

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045

Stirrup Strain (mm/mm)

Sti

rru

p S

tres

s (M

Pa)

.

Analytical SolutionExperimental Strain at ductility 6

HC4-8L16-T6-0.2P Column

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NUMERICAL RESULTS Shear Element Load Displacement

HC4-8L16-T6-0.1P Column Dynamic Shear Analysis

-20

-15

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14 16

Time(Sec)

Dis

pla

cem

ent(

mm

)

11

NUMERICAL RESULTS – Earthquake Analysis – Load vs. Deformation

HC4-8L16-T6-0.1P Column

-100

-80

-60

-40

-20

0

20

40

60

80

100

-10 -8 -6 -4 -2 0 2 4 6 8 10

Displacement (mm)

Sh

ear

Fo

rce

(KN

)

El Centro Record

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NUMERICAL RESULTS – Shear-Critical Column

Aboutaha et al.

'cf = 22 MPa

Longitudinal yield stress = 434 MPaTransverse yield stress = 400 MPa

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Syracuse,NY - SC3 Column

-500

-400

-300

-200

-100

0

100

200

300

400

500

-40 -30 -20 -10 0 10 20 30 40

Displacement (mm)

Loa

d (k

N)

SC3 - Shear Element Monotonic

SC3- Experiment

SC3 - Shear Element

NUMERICAL RESULTS – Shear Element Load Displacement

48” ColumnSyracuse ColumnAxial Load = 0 kN

Due to weak axis loading, Pinching is high

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Syracuse,NY - SC3 Column

-800

-600

-400

-200

0

200

400

600

800

-40 -30 -20 -10 0 10 20 30 40

Displacement (mm)

Loa

d (

kN

)

SC3- Experiment

SC3 - Shear Element

SC3 - Flexure Element

NUMERICAL RESULTS – Shear and Flexure Element48” ColumnSyracuse ColumnAxial Load = 0 kN

Flexure element is unable to predict the correct behavior

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NUMERICAL RESULTS – Earthquake Analysis – Time History

48” ColumnSyracuse Column Shear AnalysisAssumed Axial Load = 0.1 fc Ag = 205.5 kN

2 * EL Centro (1940) record

-15

-10

-5

0

5

10

15

0 2 4 6 8 10 12 14

Dis

pla

cem

ent (

mm

)

Time (Sec)

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NUMERICAL RESULTS – Earthquake Analysis – Load vs. Deformation

SC3 Column Shear Dynamic 2*El-Centro

-500

-400

-300

-200

-100

0

100

200

300

400

-15 -10 -5 0 5 10 15

Displacement (mm)

Sh

ear

Fo

rce

(KN

)

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NUMERICAL RESULTS – Earthquake Analysis – Time History

Syracuse Column Flexure and Shear AnalysisAssumed Axial Load = 0.1 fc Ag = 205.5 kN

2 * EL Centro (1940) record

-15

-10

-5

0

5

10

15

0 2 4 6 8 10 12 14 16

Time (Sec)

Dis

pla

cem

ent

(mm

)

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Longitudinal Reinforcement 2%

Shell Region

Core Region

406.4 mm Dia.

Transverse Reinforcement 1%

NUMERICAL RESULTS – UNR Column

Vu Phan et al.

1829 mm

EL Centro NS

36.3 N – S2/mm

Axial Load = 355 kN

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NUMERICAL RESULTS – Earthquake Analysis

UNR Column- 9F1 EL Centro (1940) record

Experiment

-7

-5

-3

-1

1

3

5

7

0 5 10 15 20 25 30

Time (sec)

Dis

pla

cem

en

t (in

) .

Analytical Solution

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NUMERICAL RESULTS – Earthquake Analysis

UNR Column EL Centro (1940) record

-40

-30

-20

-10

0

10

20

30

40

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Displacement (in)

Sh

ar

forc

e (

kip

) .

Analytical Solution

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NUMERICAL RESULTS Shear Element Load Displacement

UNR Column 9S1 Deflection for 2.0*El Centro

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

Time(Sec)

Dis

pla

ce

me

nt(

mm

)

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Torsion Basic Equations

2 2

2 2

0

cos sin

sin cos

( )sin cos

(2 )

r r d r

t r r d r t t

t r d r r

t d

f

f

T A t

Equilibrium

Compatibility2 2

2 2

0

0

cos sin

sin cos

( )sin cos2

2

sin(2 )

2

r r d r

t r r d r

tr d r r

t

r

dsd

dsd

P

A

t

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Torsional Section Discretization

2D/3D Regions

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3D Constitutive Model – Vecchio and Selby Approach (1991)

2

2

2

xx

yyxx

zzyy

xyzz

xy

yzyz

zxzx

D

1 1 2 3cf f f f

1 11

1

1 400f

No Complete 3D- Model available

Assuming the same relation ship for intermediate stress calculation

Implemented the 3D procedure to SMM

2 11

1

1 400f

3 3 1( , )f

1 1( ,0)f 2 2 1( , )f

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Torsional Section

xy x

Fiber Section Analysis

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Numerical Results Pure Torsion

0

200

400

600

800

1000

1200

1400

1600

0 0.005 0.01 0.015 0.02 0.025 0.03

Angle of Twist (rad./m)

To

rqu

e (k

N-m

) .

Box Section

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0

1

2

3

4

5

6

7

8

0 0.002 0.004 0.006 0.008 0.01 0.012

Shear Strain (rad)

Sh

ear

Str

ess

(Mp

a)

.Numerical Results

0

50

100

150

200

250

300

350

400

450

0 0.001 0.002 0.003 0.004 0.005 0.006

Transverse Steel Strain (mm/mm)

Tra

nsv

erse

Ste

el S

tres

s (M

pa)

.

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Numerical Results - Combined Torsion/Bending

24”

12”

5, #9 bars

#4 hoops @ 5”

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.001

Curvature (rad/in)

Mom

ent

(kip

-in

) .

0 rad Twist

0.001 rad Twist

0.004 rad Twist

0.007 rad Twist

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Schedule Deadline

Finite element Analysis Development of RC fiber beam-column element including torsion/bending/axial interaction

Calibration of the parameters of the developed element

Development of an OpenSees version of the developed element

• Jan 09- March 09

• March 09-May 09

• June 09-Aug 09

Schedule of On-Going Work