Journal of Traffic and Transportation ~ngineeringCEnglish Edition)

2014,1(1) :62-71

Behavior of composite rigid frame bridge underbi-directional seismic excitations

Xiaogang Liu, Jiansheng Fan *, Jianguo Nie, Guo Li

Department of Civil Engineering, Tsinghua University, Beijing, China

Abstract: Pushover analysis and time history analysis are conducted to explore the bi-directional

seismic behavior of composite steel-concrete rigid frame bridge, which is composed of RC piers

and steel-concrete composite girders. Both longitudinal and transverse directions excitations are

investigated using OpenSees. Firstly, the applicability of pushover analysis based on the funda­

mental mode is discussed. Secondly, an improved pushover analysis method considering the

contribution of higher modes is proposed, and the applicability on composite rigid frame bridg­

es under bi-directional earthquake is verified. Based on this method, an approach to predict the

displacement responses of composite rigid frame bridge under random bi-directional seismic ex­

citations by revising the elasto-plastic demand curve is also proposed. It is observed that the de­

veloped method yield a good estimate on the responses of composite rigid frame bridges under

bi-directional seismic excitations.

Key words: composite rigid frame bridge; bi-directional seismic excitation; pushover analysis;

time history analysis

1 Introduction

Continuous rigid frame bridge has a rigid connec­

tion between the girders and piers, making them

work together under lateral loads. Meanwhile,

the piers are subjected to both axial force and

flexural moment, especially, generate negative

flexural moment in the end of girders. For this

benefit, the positive flexural moment at mid-span

will decrease. This will reduce the cross-sectional

• Corresponding author: Jiansheng Fan, PhD, Professor.E-mail: fanjsh@tsinghua.edu.cn.

height of girders correspondingly. Composite rig­

id frame bridge comprises of steel-concrete girder

and RC piers or composite piers. The advantages

of such structural solution include better seismic

performance and convenience in constructionCNie

2011). Rigid frame bridges are widely used in

highway overpasses, viaducts and railway bridg­

es, especially in Chinese western areas. As these

bridges are usually used in the areas with great re­

quirement for seismic resistance, their seismic

?1994-2014 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net

(1)

Journal of Traffic and Transportation EngineeringCEnglish Edition)

performances need further research.

Although the direction of seismic excitation is

randomly varied. most of investigations only fo­

cused on uni-directional responses along bridge

longi tudinal or transverse direction. Previous

studies have confirmed that bi-directional seismic

excitations have significant influence on structure

responses. especially when the bridge structures

are under elasto-plastic stage CDe Stefano et al.

1998; Heredia-Zavoni and Machicao-Borrniuevo

2004). Furthermore. the influence of bi-direction

seismic excitations is also relative to seismic inten­

sity and bridge structural features CLopez and

Torres 2000; Wang et al. 2004). The responses of

bridge structures are dependent on the variation

of seismic excitation input direction. Usually, the

most unfavorable input direction does not coin­

cide with the bridge longitudinal or transverse di­

rectionC Li et al. 2010; Lopez and Torres 1997;

Wilson et al. 1995). Therefore. it is necessary to

conduct further analysis on the seismic behavior

of composite rigid frame bridge under bi-direc­

tional seismic excitations.

Some methods can be used for bridge seismic

behavior analysis. Time history analysis has the

best accuracy, but the computational cost is also

the greatest. Relatively. pushover analysis has

lower computational cost as well as acceptable ac­

curacyCYang et al. 2000). Pushover analysis was

first proposed in 1970s. With great previous re­

search in past years. it has become a good instru­

ment for seismic analysis. Saiidi and Sozen(1981)

proposed an approach to replace the multi degree

of freedom system (MDOF) by single degree of

freedom system CSDOF). Fajfar and Gaspersic

(1996) improved the application of capacity spec­

trum in pushover analysis. On these bases. Gupta

and Kunnath (2000) proposed a better applicable

pushover analysis approach. To account for the

influence of higher modes. Chopra and Goel

( 1999) proposed model combination pushover

analysis approach. Vidic et al. (1994) and Cho­

pra and Goel ( 1')9') also improved the capacity

spectrum to account for the elasto-plastic behav­

ior. making pushover analysis applicable in elas-

63

to-plastic seismiC response. Besides. Krawinkler

and Seneviratna ( 1998 ). Mwafy and Elnashai

(2001) and Yang et al. (2000) also conducted

much work on pushover analysis. including load

patterns. determination of target displacement.

accuracy evaluation and applicable conditions.

Pushover analysis was originally used in seismic

analysis for building structures. After Northridge

and Kobe earthquakes. this approach was also de­

veloped in seismic analysis for bridge structures.

Paraskeva et al. C2(04) first evaluated the appli­

cability of modal pushover analysis in seismic be­

havior evaluation for bridges. and Lu et al.

C2004) evaluated the applicability of pushover

analysis in steel arch bridges. In China. pushover

analysis was also used in seismic behavior evalua­

tion of bridge piers( Qian et al. 2006; Wang et al.

2000; Qin 20(8). However. little research re­

garding pushover analysis of composite rigid

frame bridge can be referred to. Furthermore.

the influence of higher modes and bi-directional

seismic excitations on the seismic behavior of

composite rigid frame bridge is also unclear. In

this study. pushover analysis in both longitudinal

and transverse directions on composite rigid frame

bridge will be conducted. and a new seismic re­

sponses prediction approach under bi-directional

seismic excitations will be proposed using push­

over analysis.

2 Pushover analysis method

Based on site condition and structure damping ra­

tio. the corresponding elastic response spectrum

for specific seismic wave can be obtained. The

S.e-Sde demand curve can be derived by Eq. (1 )

using elastic response spectrum.

{

Sae=filxolmax

T1

Sde = 4--,Sac1(-

Applying specific load pattern on structures. an

overall load-displacement curve can be obtained

when conducting pushover analysis using FEA

method. The Sa-Sd capacity curve can be obtained

by Eq. (2) using load-displacement curve.

?1994-2014 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net

64 Xiaogang Liu et al.

established using OpenSees (Open System for

Earthquake Engineering Simulation) to conduct

elasto-plastic time history analysis and pushover

analysis( Mazzoni et al. 2(06). Piers and girders

were all defined as nonlinear beam element based

on cross-sectional fibers. This nonlinear beam el­

ement has 5 integration points along axial direc­

tion with good accuracy and computational effi­

ciency. Mass of piers, girders and vehicle loads

were simplified as lumped mass. Rayleigh damp­

ing was used in FE analysis and material damping

ratio was 5%.

Constitutive model of concrete was selected as

Kent-Scott-Park modelCMazzoni et al. 20(6), and

the uniaxial stress-strain relationship is illustrated

in Fig. 1 (a). The compressive segment of the

curve is defined by Eqs. (7)-(12), where: K is

the concrete strength enhancement factor ac­

counting for the confinement effect; t: =O. Hfeu is

the concrete cylinder compressive strength; feu is

the concrete cubic compressive strength; Z is the

softening modulus in compressive softening seg­

ment; fYh is the yielding strength of hoops; Ps is

the volume stirrup ratio; h I is the width of core

concrete measuring from outer edge of stirrups;

Sh is the spacing of stirrups; f, is the concrete axi­

al tensile strength and is defined as ft = O. 26f~~J;

tensile stiffness is E e = 2{1E,,; tensile softening

modulus is selected as E, = O. 1E e for easier con­

vergence. The corresponding concrete material in

OpenSees is Concrete D2. Constitutive models of

rebar and steel are selected as Mene-Gotto-Pinto

model(Mazzoni et al. 20(6), and the stress-strain

relationship is illustrated in Fig. 1 (b), where E =

2.06 X 105 MPa, E p = O. 01 E. The corresponding

material in OpenSees is Steel 01.

(2)

(6)

C Rc,Damping ratio

Proportional to mass 1.00 1.00 0.65 O..,0

Structure

JS.P = SRe

1SdP = f1 S~e = f :;: S.e

Tall. 1 J>'lrameters of Vidic model (damping ratio 5 %)

Q style

Hysterical loop

15• = ;~

5 - 0d - r t CPt.,oof

The target displacement is defined as the inter­

section point of demand curve and capacity curve

in pushover analysis. If the structure is still under

elastic status, the target displacement can be de­

termined by the intersection point of S.e-Sde de­

mand curve and S,-Sd capacity curve.

When structure is under elasto-plastic status,

the elastic response spectrum needs to be revised

to account for the influence of elasto-plastic be­

havior. Vidic et al. (1994) proposed that the

elastic response spectrum could be reduced using

strength reduction coefficient R and displacement

reduction coefficient f1. The elasto-plastic S"P-Sdp

demand curve can be obtained by Eqs. (3)-(6),

where c\' C" CR and Cr are determined by the

hysterical behavior and damping ratio of struc­

tures, as shown in Tab. 1; T g is the characteristic

period of structures. The target displacement can

be determined by the intersection point of S"p -SdP

demand curve and S. -Sd capacity curve if struc­

ture is under elasto-plastic status.

R=c\(/l-l)'RT/Tn +l T~Tn 0)

R = C\ (/l - 1 )'R + 1 T> T" (4)

Tn = C'/l'T T g (5)

Q styleProportional to

instantaneous stiffness0.75 1.000.650.30

(J, = Kr[2€e - (~)'J€o €o

(7)

3 Finite element model

The composite rigid frame bridge FE model was

( 10)

(9)

(Je = Kf[l - Z(€, -€n)]~O. 2K!, €"<€"<€u

(Je = D. 2Kf~ €e~€u

K = 1 + PsfYhf.

Z = O. 5( 3 +0. 29f + 0 75. W - 0 O()? K ) - \ (10145f, - 1000 . p, '\j s;: .-

1.35 0.95 0.75 0.20

1. 1() 0.95 0.75 0.20

Proportional to mass

Proportional to

instantaneous stiffnessBilinear

Bilinear

?1994-2014 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net

..IoJrnal ot Traffic and Transportation EngineeringCEllglish Edition) 65

E

o •

"""_-0.JS7g

20 30 40

n·)(b) EICUlro

"

0,2

,.,:;; , IIi'I'i~v"•

-0.1,,_-o.179.r

-0.2," " 30 " "n.)

(.) T.ft...0.2

:;; ,•

-0.2

( 12)(', =O.U02K

= O. 00" + 0. 9p./•• ]l)()

Fig. I Conslllluhc laws of n!;llcri:t1,

•

•

.... I.

f, .... E.

"". E

(b) Mene-lIo11o,P,nlo $leel model

_.. -,_ ... f.

Fi&.2 Ro:ord of ~Ism".· ""a\CS

4.1 Pushover analysis in transverse direction

""

---Tin.•.. III Centro- Norlhridlle

20 30 40n·)

(e) Norlhndgc

,:' '1.j ':O.j ." .,', ";'..

,N':~_ ~, '" . ..,-~':"'';'''': ..... '.

~ -- - - _..: ::::.: ::..: '-= :....,'----,---t,===~,=""'~.n.)

(d) Response lpeclmms

'.6

",.,:;;• ,

-0.2

-0.4,

I'

..,

Pushover all<lIysis in tTllllSVCrSC direction is can­

dueted on all bridges using the I" modal load.

Transverse displacement at the lOp of the middle

in Tab.2. Similar results call be obtained for

Bridges 2001 .5" .

4 Composite rigid frame bridge pushover

analysis

Composite rigid frame bridges usually have large

span and relatively long natural vibration period.

making them located at the decay segment of the

response spectrum curve. Therefore. three typical

seismic waves with different intensities lire select­

ed for an<llysis. Seismic records and response

spectrums for the waves arc illustrated in Fig.2.

With the variation of peak ground acceleration

(PGA). piers will be subjected to different de­

grees of plastic deformation.

Five composite rigid frame bridges. as illustra­

ted in Fig.3. are selected to conduct time history

anal)si~ and pusho\'cr anal)si~ u~ing the ~i~mic

\\a\cs illustrated in Fig.2. All bridge piers com­

prise of RC piers and steel-concrele composile

girder~. All RC piers ha\c the same rectangular

cross-section of 2.6 m x 3.5 m. The reinforce·

ment rallO of piers is (J. H6°o. and the \olume sllr­

rup ratio is O.H2°o . Material slTcngths of concrete

/ .... steel plate /. and rebar {.. arc ~ll MPa. 3~5

MP,I and JJ5 MPa. rcspccti\cl}. In FE model.

lumped milSS model is used and mass of girders

and picrs arc simplified as lumped m,ISS in FE ele­

ments. Modal analysis result of Bridge 1" is shown

71994-2014 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net

66

" " ,

If] I I(.) Bridlf ,"

" " "

Xiaogang Liu el al

mic wave can be obtained by procedures detailed

in Section 2. Pusho\'er analysis and time history

analysis are conducted using each seismic wave.

and the comparison of target displacements by

pushover analysis and the maximum displaccmcni

by lime history analysis are shown in Tab.3.

·hb.) Mesult tomparl_ or pllliho.ft" analysis and II..,., hlstor,

analysis in bridJ:" tno'I!i"~ dindi9n

Fig.] ijridge mo<Jcls(Unit, m)

o•

" '1'

(b) Dridll~ 2"

" "

I

Middle pier topBridge Seismic displacement( 10m) Dc"iation( <v.)No. wa,·c

l'ushover Time histroy

Taft 20J \(,0 "IJridgcEl Cemro '" J55 "'" Nonhridgc ,.. .., 25

Taft 30' 2201 J5

,. E1 Cenlro -lS'} ", "Northridge 823 '" 25

Tafl 26J '" J5

J. E1 (;(cntro ." J77 JJ

Nonhridgc "0 .., 16

Taf! 101 ,W ," El Centro 272 2111 J

Northridge -150 "0 ,Taft 212 '" J2,. El Centro m '" 29

Northridge '"' '" "Tab. '1 Vihrati"" l)('riuoJ~ "nd "willes

Mode No. Vibration pcriod(sl Vibration mode

4.2Sfl.g Transverse

, 2.1!175 Transverse

J I.H7J Trans'·crsc

, 1.7JJJ Longitudinal

5 0.%75 Tr~nsn"sc

• O.72'}2 Trlns\'crsc

, O.70H Trallli'"enc

, 0.558l Longitudinal

9 0.45UO Longitudinal

'" O.41{>.l Longitudinal

pier and transverse bottom shear force of the mid­

dle pier are selected as the [oad-displacement­

curve. The larget displllCClTlCnl for specific seis-

If piers are not quite high. the target displace­

ment by pushover analysis using the ,. modal load

will fit well with the maximum displacement by

time history analysis. The deviations of pushover

anal)'sis and time history analysis for Bridge -I'~ do

not exceed 10010 for all seismic waves. Besides.

the increase of span number will have linle influ­

ence on the deviations if lhe maximum span is un­

changed. However. Wilh the increase of pier

height and maximum span. the analysis resull by

pushover analysis becomes significantly gre,lter

than that by time history analysis. The devialions

of Bridges 1". 2.... 31<1 and 5'~ ,Ill exceeds 20% for

all seismic waves. which indicates thai the influ­

ence of higher modes of vibration cannOI be ncg­

lected.

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Journal of Traffic and Transportation EngineeringCEnglish Edition) 67

To account for the influence of higher vibration

modes, an adaptive pushover analysis method was

proposed( Gupta et al. 20(0) and a modal push­

over analysis method was also proposed (Chopra

et al. 2(02). The procedures of the former meth­

od are very complex, making it difficult to be ap­

plied. The latter method usually overestimates

structural response. Therefore, a new pushover

method similar with modal pushover analysis

method is proposed. The influences of the target

displacements for major vibration modals are con­

sidered, and the final target displacement is ob­

tained by the combination of target displacements

for major vibration modals according to the con­

tribution of each modal (equivalent mass coeffi­

cient). The calculation procedure is detailed in

Eqs. (13)-(15).

Tab. 4 Result comparison of pushover analysis considering

contribution of higher vibration modals and time history

analysis in bridge transverse direction

Obviously, the result of this new pushover meth­

od accounting for the influence of higher vibra­

tion modals fits well with that of time history

analysis.

Middle pier top

displacement( mm) Deviation

(%)

Pushover Timehistroy

175 160 9.0

390 355 10.0

654 607 8.0

251 224 12.0

38<) 384 1.0

6'>7 65') 6.0

226 1')5 16.D

423 377 12.D

771 665 16.0

118 110 7.0

312 281 11.0

485 440 10.0

183 161 14.0

375 368 0.2

688 643 7.0

wave

Taft

SeismicBridge

No.

El Centro

Northridge

El Centro

Taft

Taft

lSI El Centro

Northridge

Northridge

yd El Centro

Northridge

Northridge

2nd El Centro

Taft

Taft

( 14)

(15)

( 13)N

2..: m i!P]ij= 1

N

(2..:mj!pji)2j=1

; = 1

Mt-N--

2..: mi

d = ..:..i-_-1,--_II

~rii = 1

where Mt is the modal mass for the i lb vibration

modal; m; is the lumped mass; !pj; is the standard

vibration model coefficient; r; is the contribution

coefficient for the i Ib vibration modal (equivalent

mass coefficient); d; is the target displacement

by pushover analysis for major vibration modal;

d is the final target displacement by pushover

analysis method.

It should be noted that the contribution coeffi­

cient of transverse vibrations should be zero for

longitudinal vibration, and the contribution coef­

ficient of longitudinal vibrations should be zero

for transverse vibration.

New pushover analysis by the proposed method

using the transverse vibration modals in the first

10 vibra tion modals is conducted for each bridge.

The final target displacements for all bridges by

this new pushover method are shown in Tab.4.

4.2 Pushover analysis in longitudinal direction

Pushover analysis in longitudinal direction is con­

ducted on all bridges using the 151 modal load. As pier

top displacements along longitudinal direction are al­

most the same for all piers in one bridge, longitudinal

displacement at the top of middle pier and the sum of

longitudinal bottom shear force of all the piers are se­

lected as the load-displacement for capacity curve.

The target displacement for specific seismic wave

can be the obtained by procedures detailed in Sec­

tion 2. Pushover analysis and time history analysis

are conducted using each seismic wave, and the

comparison of target displacement by pushover

analysis and the maximum displacement by time

history analysis are illustrated in Fig. 4. As can be

seen, the target displacement of the pushover

?1994-2014 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net

68 Xiaogaog Uti el at

Norlhridge

NClrlhridgcEl CentroSeismiewue

(e) Bridge)"

£1 CentroSd,micwlvc

(M) Il'idgc I"

£1 Cntn!~;,mlcwlvc

(b) Brid,e 2"

ToO

Tlfi

EI CnitO!kismie ..·.ve

(d) Brodie'·

T.n

(5;SS!Pushovcr_ Time: hiltory

~Pusbo"cr

_Time ~'5tOry

&SSJ Pusbovcr..Timc ~1510ry

em Pushoverm:ra Time ~i510ry

•

'00

•

-.~c )00

•~ 200•'"r. 100

•

fiB.:; Comparison of pu~ho,cr lInal)'Sl$ conSidering contribuuon

or h'Bhcr vibn'lllon modals lind liD><' h,story analysis in

bridge lon&l1udc dm~cllon

5 Pushover analysis under bi-directional

seismic excitations

There is significant difference between seismic

Fig. 5. Obviously. the result of this new pushover

method considering the influence of higher vibra­

lion modals fits better wilh that of time history

analysis.

.,.-.f ),. _ r".hovc.

• _ Time hillory, ,,.•~•~

'00

• •

...-. _Pusbov~.

i _Timehislory

• ...,i.;; ,,.

f •(.)...-. IilliilI Pushover

~ tim Time hinory,• .,.,•.!0

c6 ".~• •

(b)...-. I'lI::3 r ...boo"c,~ _ Ti_ hillOry,•...•,•.;; ,,.••• •

analysis is obviously lower Ihan the lime history

analysis result. ovcreslimating Siructural seismic

perrorm,tOce.

Similar 10 pushover analysis accounting for Ihe

influence of higher vibration modals. pushover

analysis using the proposed method in Section -I. I

is conducted. The longilUdinal vibration rnodals

in the firsl 10 vibration madals arc conducted for

bridges. The final target displacement considering

high vibration influence modal is illustrated in

Fig. 4 Comparison of pushO"cr anal)"sjSllnd time hislor}'

analysis in bridge lon&"IlGe di.oxlion

11994-2014 China Academic Journal Electronic Publi5hing House. All rights reserved. http://www.cnki.nct

(16)

(17)

(18)

Journal of Traffic and Transportation Engineering( English Edition)

performances of longitudinal direction and trans­

verse direction. Thus, bridge structural response

may vary with the input direction of seismic exci­

tations. As input direction of actual seismic waves

is random, the influence of bi-directional seismic

excitations may be significant (De Stefano et al.

1998; Heredia-Zavoni and Machicao-Borrniuevo

2004). Previous research has confirmed that the

maximum seismic response of bridges may not oc­

cur when seismic input in the longitudinal or

transverse direction alone and the maximum seis­

mic responses may be 30% larger when seismic in­

put direction is random. The results of SRSS com­

bination, EuroCode-8 and Code for seismic design

of buildings may be un-conservative (Li et al.

2011) .

The influence of bi-directional seismic excita­

tions on the reduction coefficient of elasto-plastic

response spectrum has the statistical laws for vari­

ous vibration periods, structural displacement

ductility coefficients and damping ratios. There­

fore, the demand curve can be revised to account

for bi-directional seismic excitations, and SRSS

combination of the final longitudinal and trans­

verse target displacements can be selected as the

prediction of the maximum displacement re­

sponse. The Sapb-Sdpb demand curve considering

bi-directional seismic excitations can be derived

from Vidic model in Section 2, revising strength

reduction coefficient R and displacement ductility

reduction coefficient p., as shown in Eqs. (16)­(19) .

R b =1.4[cl (p.-1)CR T/Tll +1] T~Tll

R b =1.4[c, (p.-1)c R +1] T>T"

i5ae

Sapb =If(19)

_ Sde _ l!:... 41C2

SdPb - p. If - R T2 5 ae

Pushover analysis is conducted on composite

rigid frame bridges in Tab. 5 following the procedures

detailed in Section 2. All parameters of piers and

composite girders are same as detailed in Section 3.

The Sapb-Sdpb demand curve considering bi-directional

seismic excitations is adopted and seismic waves in

Tab. 6 are used for analysis. Pushover analysis

69

considering high vibration modal is conducted for

all bridges in Tab.5 using the first 10 vibration

modes following the procedures detailed in Sec­

tions 4. 1 and 4. 2, and the final target displace­

ments E xl and E yl for longitudinal and transverse

direction respectively can be obtained. The target

displacement E maxl considering bi-directional seis­

mic excitations is defined as SRSS combination of

E x, and Ey! , namely Emax1 = I E~, + E;1 . The com­

parison of bi-directional pushover analysis and

time history analysis is illustrated in Fig. 6, where

E max is the maximum displacement response by

time history. As can be seen, the prediction re­

sults of maximum displacement response by bi-di­

rectional pushover analysis are conservative

enough. As the results of bi-directional pushover

analysis are the biggest displacement response

considering the random input of seismic excita­

tions, it is a bit conservative in comparison with

time history analysis when input direction of seis­

mic waves<Tab. 6) is not the most unfavorable.

Tab.S Analysis models of composite rigid frame bridge

Model No. Span(m) Pier height(m)

Basic model 50 + 75 + 50 40 + 60 + 60 + 40

Contrast model 1" 50 + 75 + 50 60 + 60 + 60 + 611

Contrast model 2nd 50 + 75 + 50 40 + 611 + 611 + 611

Contrast model yd 50 + 75 + 75 40 + 60 + 60 + 411

Contrast model 4th 75 + 75 + 75 40 + 60 + 611 + 411

Contrast model 5th 50 + 75 + 50 40 + 60 + 60 + 40

Contrast model 6th 25 + 37.5 + 25 20 + 30 + 311 + 20

Tab. 6 Records of seismic waves

PGA(gJSeismic wave

Direction x Direction y

Hollywood Storage. 1952 0.059 0.042

Taft Lincoln School. 1952 0.105 0.156

San Fernando. 1971 0.134 0.271

Mexico City.1985 0.171 o.1110

Lorna Prieta. 1989 0.220 0.276

Parkfield Cholame. 1966 D.237 0.275

El Centro Site. 1'140 0.357 0.214

James RD.1979 0.478 0.367

Northridge. 1'194 0.604 0.344

Bonds Corner El Centro. 197,} 0.778 0.5'15

?1994-2014 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net

70

• Buio;:model _Coot'ltllDodtl.-.Conlr.1Imodell- ~ Conlrut model S·,., "ConuUI model 2" +ContNlIl model 6-",eOIlUlSl model)"

•• • •0., • • t •

• • • •~

• • • • II • •• • • •0., • t 1 •J • • •• • ••• •... • • •• • •••

" " • ~ • u " 0= ~ ,,; , -' • u " "" • z

!k'JlDle ....,·es

MS.6 ComparISOn of pusho\er anal)sis and l,rot history

anal)"§Is under bi-dm:cllonal Kism".. UClIations

6 Conclusions

Pushover analysis and time history analysis arc

conducted for composite rigid frame bridge using

OpcnSecs. 'ew pushover analysis method consid­

ering the influence of higher vibration modal b

proposed. and its applicability lind accuracy in

longitudinal and transverse direction arc evalua­

ted. On this basis. the revision of the claslO-plas­

tic demand curve is proposed considering bi-direc­

tional seismic excitations. A bi-directional push­

over analysis prediction approach for target dis­

placement response is also proposed. which is

suiwblc for seismic excitations in random input

directions. Conclusions arc drawn as follows:

(I )The influence of high vibration modals

should be considered for composite rigid framc

bridge with high piers and large sp'lns. The new

pushover amllysis method by the combination of

targct disp!;lcements of major modals according to

equivalent mass coefficiclH can predict the dis­

placement response of rigid frame bridge in longi­

tudinal and transverse direction.

(2)The elasto-plastic demand curc should be rc­

\'iscd to account for the influencc of bi-directional

seismic excitations. The target displacements E J ,

and Ey1 for longitudinal and transverse direction

respcctively can be obtained using the revised Sorb­

Sdfil> demand curve. and the maximum target dis­

placement response considering bi-directional

seismic excitations can be obtained by SRSS com-

Xlaogang liu el at

bination of E J , and E... This bi-directional push­

over analysis method considering the random in­

put of seismic excitations gives the acceptable pre­

diction of target displacement response.

Acknowledgments

The authors gr,lIefully appreciate the financial sup­

{X)rt provided by the National Science and Technolo­

gy Sup{X)rt Program (No. 2011BAJOlJB(2) and the

National Nlltural Scicncc Foundation of China

(No.5113S007.51222810).

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