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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