1

Dynamic/Seismic analysis of RC Element including shear effect

2

ys

yc

Concrete BeamStirrups

0yc c ys sA A

From Lateral Equilibrium:

Fiber model with Stirrups

x xy y

xxy

y

3

Equivalent Uniaxial Stress: Rotating Crack Model

Element in CartesianCoordinate System

Element in PrincipalCoordinate System

cracks

1

1

2

2

PStress/Strain Model In Principal Directions

0

ip ci c

ip ci

K f

K

1

0

11

0.340.8

'2 p cf

1.0

0.6

00

0.8

0.5

0.2

1 2 3 4 5 1

0

• Material and Section Properties– Pier Height: 120 in– Concrete: 5930 psi– Longitudinal bar: 16-#8, Fy = 62 ksi– Spiral: #3, Fy = 75 ksi

• Plastic hinge zone: 2.5 in spacing• Out of plastic hinge zone: 4.25 in spacing

#9@3" cs. for the bottom bar

#9@3" cs. for the Top bar

#4@3" cs. for the Bottom bar

#9@3" cs. for the bottom bar

#4@3" cs. for the top bar

Pipe with 2.5" dia

A'A

B'B

C'C

2.52.5

36

4 6 8 8 6 4

18 18

104010

60

41736114

72

417

2112114

27

2.536

120192

34 - #3 stirrup ties

36 - #3 stirrup ties

3060

30

#3 Spiral @ 2.5" o.c.

#3 Spiral @ 4.25" o.c.

24"

16-#8

#3 Spiral @ 4.25" o.c. at middle of pier 2.5" o.c. at top and bottom of pier

1" Cover

22

21,2

5

UIUCReinforced Concrete Squat Column

UIUC Shear ResponseReinforced Concrete Squat Column (PIER1 )

-250

-200

-150

-100

-50

0

50

100

150

200

250

-3 -2 -1 0 1 2 3 4 5

Displcaement (in)

Sh

ear

forc

e (k

ip)

UIUC- Pier1 Dx, Dy & Rz , No Shear Effect

UIUC- Pier1 Dx, Dy & Rz , Shear Effect

UIUC- Pier1 Dx, Dy & Rz , Experiment Add data

Shear Element is matching with the experimental data

Moment ResponseUIUCUIUC Moment ResponseUIUC Reinforced Concrete Squat Column (PIER1 )UIUC Reinforced Concrete Squat Column (PIER1 ) Moment ResponseUIUC Reinforced Concrete Squat Column (PIER1 )

-15000

-10000

-5000

0

5000

10000

15000

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002

Rotation (rad)

Mom

ent

(kip

-in

)

UIUC- Pier1 Dx,Dy &Rz , No Shear EffectUIUC- Pier1 Dx,Dy &Rz ,ExperimentUIUC- Pier1 Dx,Dy &Rz , Shear Effect

Shear Element is matching with the experimental data

Axial Force ResponseReinforced Concrete Squat Column (PIER1 )UIUC

-800

-700

-600

-500

-400

-300

-200

-100

0

100

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Axial Displcaement (in)

Axi

al f

orce

(k

ip)

Dx, Dy &Rz , No Shear EffectUIUC- Pier1 Dx, D &Rz , ExperimentDx, Dy &Rz , Shear Effect

Shear Element is matching with the experimental data

Shear ResponseUIUC Reinforced Concrete Squat Column (PIER2 )

-250

-200

-150

-100

-50

0

50

100

150

200

250

-3 -2 -1 0 1 2 3 4 5

Displcaement (in)

Sh

ear

forc

e (k

ip)

UIUC- Pier1 Dx, Dy & Rz , No Shear Effect

UIUC- Pier1 Dx, Dy & Rz , Shear Effect

UIUC- Pier1 Dx, Dy & Rz , Experiment Add data

Shear Element is matching with the experimental data

Moment ResponseUIUC Reinforced Concrete Squat Column (PIER2 )

-15000

-10000

-5000

0

5000

10000

15000

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015

Rotation (rad)

Mom

ent

(kip

-in

)

UIUC- Pier1 Dx,Dy &Rz , No Shear EffectUIUC- Pier1 Dx,Dy &Rz ,ExperimentUIUC- Pier1 Dx,Dy &Rz , Shear Effect

Shear Element is matching with the experimental data

Axial Force ResponseReinforced Concrete Squat Column (PIER2 )UIUC

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Axial Displcaement (in)

Axi

al f

orce

(k

ip)

Dx, Dy &Rz , No Shear EffectUIUC- Pier1 Dx, D &Rz , ExperimentDx, Dy &Rz , Shear Effect

Shear Element is matching with the experimental data

RC column by Bousias et al. (1995)

0

10

20

30

40

50

60

0 5 10 15 20 25 30

Displcaement (mm)

Sh

ear

forc

e (

KN

) Bousiasis No Shear Effect

Bousiasis Shear Effect

Bousias Column Cyclic Comparisons

-60

-40

-20

0

20

40

60

-80 -60 -40 -20 0 20 40 60 80

Displcaement (mm)

Sh

ear

forc

e (

KN

)

Bosias Shear Effect

Bosias No Shear Effect

Bosias FEDEASlab

13

Dynamic/Seismic Analysis of Shear-Critical Elements

• Newmark Method

– Constant Average Acceleration Method– Lumped Mass– Rayleigh Damping– Ground Acceleration/Dynamic Load

With Erzincan earthquake record

-20

-15

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14 16 18 20

Time (Sec)

Dis

pla

cem

en

t (m

m)

Bousias, No Shear Effect

Bousias Column Earthquake Response

With Erzincan earthquake record

-20

-15

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14 16 18 20

Time (Sec)

Dis

pla

cem

en

t (m

m) Bousias FEDEASlab

With Erzincan earthquake record

-20

-15

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14 16 18 20

Time (Sec)

Dis

pla

cem

ent

(mm

)

Bousias, Shear Effect Bousias, No Shear Effect

Bousias Column Earthquake Response

6.5”

20.25”5”

10 kips6.5”

5”

Loading

2%S # 3 Longitudinal Bars

Low - Moehle Beam

Weak Axis

Strong Axis

0

1

2

3

4

5

6

7

8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Displcaement (in)

Shea

r fo

rce

(kip

)

Low-Moehle Beam, No Shear Effect, Strong Axis

Low-Moehle Beam, Shear Effect

Low-Moehle Beam, No Shear Effect, Weak Axis

Low-Moehle Beam, Shear Effect, Weak Axis

Low - Moehle Beam Monotonic Comparisons

Low - Moehle Beam Analysis by Spacone & Filippou

-8

-6

-4

-2

0

2

4

6

8

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

Displcaement (in)

Sh

ea

r f

orce (

kip

)

Low-Mohele No Shear Effect

Low-Mohele Shear Effect

Low - Moehle Beam Earthquake Response

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 5 10 15 20 25 30 35

Dis

pla

cem

ent

(in

)

Time (Sec)

With EL Centro N-S 1940 earthquake record

Low-Moehle, No Shear Effect

Low - Moehle Beam Earthquake Response

-10

-8

-6

-4

-2

0

2

4

6

8

10

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Sh

ear

For

ce (k

ip)

Time (Sec)

With EL Centro N-S 1940 earthquake record

Low-Moehle, No Shear Effect

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8

Displcaement (in)

Sh

ear

forc

e (k

ip)

UMR 12ft Column No Shear Effect

UMR 12ft Column Shear Effect

UMR Columns Monotonic

Longitudinal Reinforcement

Shell Region

Core Region

2.5” Dia.24” Dia.

Transverse Reinforcement

12’

UMR Columns Monotonic Comparisons

For 6 ft column, increase the ductile behavior by changing the stirrup from #3 bar to #4 bar.

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9 10

Displcaement (in)

Sh

ear

forc

e (k

ip)

UMR 12ft Column No Shear Effect, rhoS=0.73%

UMR 12ft Column Shear Effect, rhoS=0.73%

UMR 6ft Column No Shear Effect, rhoS=0.73%

UMR 6ft Column Shear Effect, NEES 6ft Column Shear Effect, rhoS=0.73%

UMR 6ft Column Shear Effect, rhoS=1.32%

UMR 12ft Column Shear Effect, rhoS=0.73%, Experiment

2323

UMR Column Stirrup Strain

Shear Element

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0 1 2 3 4 5 6 7 8

Column tip Displcaement (in)

Sti

rru

p S

trai

n (

in/in

) .

Stirrup Strain

-150

-100

-50

0

50

100

150

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Displcaement (in)

Sh

ear

forc

e (k

ip)

UMR 6ft Column No Shear Effect, rhoS=0.73%

UMR 6ft Column Shear Effect, rhoS=0.73%

UMR Columns Cyclic Comparisons

Contd..

6’

With 0.73%S Shear element is failing at 1”, whereas Bernoulli element is still continuing..With 0.73%S Shear element is failing at 1”, whereas Bernoulli element is still continuing..With 0.73%S

UMR Columns Cyclic Comparisons 6’ ColumnS

-150

-100

-50

0

50

100

150

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Displcaement (in)

Sh

ear

forc

e (k

ip)

UMR 6ft Column No Shear Effect, rhoS=0.73%UMR 6ft Column Shear Effect, rhoS=0.73%UMR 6ft Column Shear Effect, rhoS=1.32%UMR 6ft Column No Shear Effect, rhoS=1.32%

With EL Centro N-S 1940 earthquake record

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 5 10 15 20 25 30 35

Time (Sec)

Dis

plac

emen

t (in

)

NEES 6ft Column, No Shear Effect, rhoS=1.32% NEES 6ft Column, Shear Effect, rhoS=1.32%NEES 12ft Column, No Shear Effect, rhoS=1.32%NEES 12ft Column, Shear Effect, rhoS=1.32%

UMR Columns Earthquake Response Displacement

6ft column with shear has failed at initial times, where as others continued.

UMR Columns Earthquake Response Resistance

With EL Centro N-S 1940 earthquake record

-150

-100

-50

0

50

100

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

Time (Sec)

Shea

r F

orce

(kip

)

UMR 6ft Column, Shear Effect, , rhoS=1.32%

UMR 12ft Column, Shear Effect, , rhoS=1.32%

Fiber Element Development- Schedule & Deadline

Schedule Deadline

Finite element Analysis Dynamic/Seismic analysis of RC bridge piers including shear effect

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 08-Feb 08

• March 08-May08

• June 08-Aug 08

• Sept 08-Oct 08