Dynamic/Seismic analysis of RC Element including shear effect
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![Page 1: Dynamic/Seismic analysis of RC Element including shear effect](https://reader035.fdocuments.us/reader035/viewer/2022062221/56812cee550346895d91b55a/html5/thumbnails/1.jpg)
1
Dynamic/Seismic analysis of RC Element including shear effect
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2
ys
yc
Concrete BeamStirrups
0yc c ys sA A
From Lateral Equilibrium:
Fiber model with Stirrups
x xy y
xxy
y
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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
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• 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
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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
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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
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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
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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
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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
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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
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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
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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
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13
Dynamic/Seismic Analysis of Shear-Critical Elements
• Newmark Method
– Constant Average Acceleration Method– Lumped Mass– Rayleigh Damping– Ground Acceleration/Dynamic Load
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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
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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
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6.5”
20.25”5”
10 kips6.5”
5”
Loading
2%S # 3 Longitudinal Bars
Low - Moehle Beam
Weak Axis
Strong Axis
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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
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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
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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
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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
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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’
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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
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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
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-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
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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%
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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.
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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%
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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