Analysis of Self Centering Bridges

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29 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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1



Manisha
Rai

Chair: Prof.
ElGawady



Time Domain Probabilistic Seismic Demand
Analysis of Self Centering Bridges

under near
-
fault ground

motions

Manisha Rai


2

Introduction




Probabilistic Seismic Demand Analysis (PSDA)



Near
-
fault ground motion




Self centering Bridges






Manisha Rai


3

Outline


PSDA Overview



Bridge Model



-

Material Models





-

Moment Curvature Analysis




-

P
-
M interaction




-

Model calibration




-

SAP 2000 model assembly




PSDA methodologies



Results and Conclusion






Manisha Rai


4

Probabilistic Seismic Demand Analysis


Probabilistic seismic demand analysis is an important step in PBEE





PSHA is used to estimate
l
IM




PSDA builds upon PSHA and links IM to EDP



Result of PSDA is used to estimate DM which in turn is used to get DV
(decision variables)














|
]
[
|
]
|
[
]
|
[
]
|
[
)
(
IM
d
IM
EDP
dP
EDP
DM
dP
DM
DV
P
DV
l
l
Manisha Rai


5

PSDA






A predictive model for EDP is used to get



PSHA is used to estimate term

)
|
(
y
IM
x
EDP
P


IM
l



dMdR
R
M
f
R
M
y
Sa
P
y
IM
)
,
(
)
,
|
(
)
(

l




|
)
(
|
)
|
(
)
(
y
d
y
IM
x
EDP
P
x
IM
EDP
l
l
Manisha Rai


6

PSDA for near fault ground motion



Near fault ground motions may
be affected by directivity effects.



Directivity effects produce a
“pulse” in the velocity time
history.



Need to account for this effect in
PSDA

Manisha Rai


7

Near fault PSDA




Directivity effects amplify the Sa(IM) at near fault site so we need to
account for it during PSHA



The pulse in the ground motion may also have an effect on the response.



Need to account for near fault effects in EDP


IM predictive relationships
too

Manisha Rai


8

Different approaches for near fault PSDA



Traditional approach


Do nothing.



Broadband approach


Amplify Sa prediction during PSHA (using Abrahamson 2000)


No modification in EDP
-
IM relationship



Enhanced Broadband


Amplify Sa prediction during PSHA


Modify EDP
-
IM relationship to account for pulses



Time domain approach (
Sehhati

2008)


Amplify Sa prediction during PSHA


Elaborate modification in EDP
-
IM relationship.


Manisha Rai


9

Enhanced Broadband PSDA


The earthquake events are divided into two parts:


Near source


Non
-
near source



A ground motion model which accounts for near fault effects is used
(Abrahamson 2000)



Two EDP
-
IM relationships are needed to predict the response for near
source and non near source cases.


Manisha Rai


10

Time domain PSDA


More elaborate than enhanced broadband



The near source case is divided into three parts


When no pulse is observed at the site.


When pulse has an effect on the structure (pulse is dominant).


When pulse doesn’t have a significant effect.



Idealized pulses are used to find the relationship between EDP and pulse
period and amplitude.



Manisha Rai


11

Results needed to complete the PSDA



Relationship between EDP
-
IM for near source ground motion



Relationship between EDP
-
IM for non
-
near source ground motion



Relationship between EDP and pulse period(
Tp
) and amplitude (
Ap
)

Manisha Rai


12

Bridge Model

Zhu et. al( 2006)

Manisha Rai


13

Bridge Model

Zhu et. al ( 2006)

Manisha Rai


14

Results needed for bridge analysis


Plastic Hinge Properties


Moment Curvature Analysis


Behavior of column


Material Model for Confined Concrete


Material model for Steel


Initial Loading condition


Post tension Force





PM interaction Diagram



Manisha Rai


15

Moment Curvature Analysis


Column Behavior



Manisha Rai


16

Moment Curvature Analysis


Column Behavior



Manisha Rai


17

Moment Curvature Analysis


Material Model for confined concrete



0
10
20
30
40
50
60
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Stress ( MPa)

strain

Samaan’s

Model

Manisha Rai


18

Moment Curvature Analysis


Post Tension Bar


Dywidag

Bar (Grade 160 )



Initial Loading condition


Dead Load = 3118
kN


Initial compressive strength = 45 %
f’c


Initial Post tension Force = 60%
fyield


Manisha Rai


19

Moment Curvature Analysis

0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Moment (kN
-
m)

Curvature (1/m)

Zhu et. al (2006) (
RC column)
Zhu et. al (2006)(
FRP column)
45% of f'c
Manisha Rai


20

Moment Curvature Analysis

0
1000
2000
3000
4000
5000
6000
0
0.02
0.04
0.06
0.08
Moment (kN
-
m)

Curvature (1/m)

45% of f'c
Bilinear
Manisha Rai


21

PM interaction Diagram

-20000
-10000
0
10000
20000
30000
40000
50000
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Axial Load (
kN
)

Moment (
kN
-
m)

Manisha Rai


22

Code Verification

Manisha Rai


23

Pushover and Calibration

Manisha Rai


24

Probabilistic Seismic Demand Analysis


Predictive Equations required for PSHA


Rupture Length ,
f (Magnitude(Mw

))


Ground Motion Attenuation Relationship ,
f( Mw
,
Rjb
, site conditions etc.)


For Pulse period (
f(Mw)
)


For Pulse amplitude (
f (Mw,
Rjb
)
)


Pulse
occurance

(f(S,

)
)



Predictive Equations required for Time Domain PSDA


EDP
vs

Sa relationship for Forward Directivity ( FD ) Ground Motions


EDP
vs

Sa relationship for Non
-

Forward Directivity Ground Motions


EDP
vs

Sa relationship for Simple Gabor Pulses










Manisha Rai


25

Bridge Response to FD and NFD ground motions



For Pulse like GM:

For non
-
pulse like GM:

Manisha Rai


26

Fitting a relationship between EDP and
Ap,Tp



Finding a functional form to fit 3D
data is difficult.



Genetic programming was used
to find the appropriate functional
form



Genetic Programming is a search
algorithm which searches the
space of computer programs.

Manisha Rai


27

Genetic Programming


Functional forms are represented
as trees.



Random functional trees are
generated to initialize the
population.



Genetic operation like crossover
and mutation are applied to
generate new



Fittest individual are selected for
reproduction and the space is
searched through natural
selection

Manisha Rai


28

Crossover operation

Manisha Rai


29

Bridge Response

For Simple Gabor Pulses

Manisha Rai


30

Results of PSDA analysis









Manisha Rai


31

Results of PSDA analysis









Manisha Rai


32

Results of PSDA analysis









Manisha Rai


33

Results of PSDA analysis









Manisha Rai


34

Results of PSDA analysis









Manisha Rai


35

Results of PSDA analysis









Manisha Rai


36

Results









Manisha Rai


37

Results









Manisha Rai


38

Results of PSDA analysis









Manisha Rai


39

Results of PSDA analysis









Manisha Rai


40

Results of PSDA analysis









Manisha Rai


41

Results of PSDA analysis









Manisha Rai


42

Results of PSDA analysis









Manisha Rai


43

Results of PSDA analysis









Manisha Rai


44

Results of PSDA analysis









Manisha Rai


45

Results of PSDA analysis









Manisha Rai


46

Acknowledgements




Prof.
ElGawady
, Prof. Rodriguez
-
Marek


Prof.
Cofer
, Prof. Dolan


Roommate


Friends


Parents