Sensitivity Analysis of the Influence of Structural Parameters on Dynamic Behaviour of Highly Redundant Cable-Stayed Bridges

7/28/2019 Sensitivity Analysis of the Influence of Structural Parameters on Dynamic Behaviour of Highly Redundant Cable-Stayed Bridges

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Hndw Pshn CopotonAdvncs n Cv EnnnVom 2013, Atc ID 426932, 11 pshttp://dx.do.o/10.1155/2013/426932

Research ArticleSensitivity Analysis of the Influence of Structural Parameters onDynamic Behaviour of Highly Redundant Cable-Stayed Bridges

B. Asgari,1 S. A. Osman,1 and A. Adnan2

1 Department o Civil & Structural Engineering, Faculty o Engineering & Built Environment, National University o Malaysia (UKM),43600 Bangi, Selangor, Malaysia

2 Department o Civil & Structural Engineering, Faculty o Engineering & Built Environment, UM University o Malaysia,81310 Skudai, Johor, Malaysia

Cospondnc shod ddssd to B. As; [email protected]

Rcvd 14 Fy 2013; Accptd 10 Ap 2013

Acdmc Edto: John Mnd

Copyht 2013 B. As t . Ts s n opn ccss tc dsttd nd th Ctv Commons Attton Lcns, whchpmts nstctd s, dstton, nd podcton n ny mdm, povdd th on wok s popy ctd.

T modtnn thoh snstvty nyss s pomnnt pocd to ssss th stcthvond dynmc chctstcso c-styd ds. Most o th pvos snstvty-sd mod tnn mthods tomtc ttv pocsss; howv,th sts o cnt stds show tht th most son sts chv y ppyn th mn mthods to pdt thnytc mod o c-styd ds. Ts pp psnts mod pdtn othm o hhy dndnt c-styd dstht cn sd s n ttv mn pocd. T pdtn pmts sctd thoh thsnstvtynysswhch hpsto tt ndstnd th stct hvo o th d. T fnt mnt mod o tBd s consdd o th nmcstds. T sts o th smtons ndct th cncy nd ppcty o th psntd mn tnn mthod o pdtnth fnt mnt mod o c-styd ds. T nw spcts dn ctv mt nd stct pmts ndmodtnn pocd psntd n ths pp w s o nyzn nd mod pdtn o c-styd ds.

1. Introduction

In th pst dcd th constcton o c-styd dshs ncsd nd th spn nths own d tompovmnts n dsn nd nyss tchnoos. How-v, th compx stct chctstcs o on-spnc-styd ds cs dcts n ndstndn thdynmc hvo nd mk thm vn to dynmcodns om phnomn sch s wnd o thqks. Incnt ys, mny xpmnt nd nytc nvsttonshv stdd ctv ctos on th dynmc hvo oc-styd ds, sch s nt pods, mod shps,nd dmpn popts [15]. T snstvty nyss s pomsn wy to povd tnd nytc mod nd ssssth ct dynmc chctstcs o spstcts sch sc-styd ds.

Snstvty nyss s tchnq to dtmn thnnc o dnt popts, sch s ondy cond-tons, dmpn popts, mt constnts, nd omt-c pmts, on th stct sponss. A nm

o snstvty mthods o mod pdtn pposs hvn poposd o dnt stcts [612]; th hvn sccss ppctons o snstvty-sd pdtntchnooy o ds n cnt ys. Cntn [13] ndPvc t . [14] w mon th fst to nvstt th modpdtn o ds sn th snstvty mthod. Mck ndStojdnovc [15] condctd snstvty stdy to dnty thct o tmnt mss nd stnss on ssmc dmnd oshot- nd mdm-nth ds. Fo compx stctwth hh ds o ndtmncy, sch s c-sppotdds, mod pdtn coms dct cs t mynvty nvov nctnts n mny pmts, oxmp, mt nd omtc popts, nd ond-y condtons. Most o th cnt stds hv ppdttv sotons o snstvty-sd mod pdtn oc-styd ds. Zhn t . [16] mpmntd fntmnt (FE) mod pdtn o 430 m mn spn c-styd d n Hon Kon. T pdtn mthod ws nttv nv snstvty-sd ppoch wth ownd pp onds o th pmt vs nd th ds


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2 Advncs n Cv Ennn

o nctnty. Bownjohn nd X [17] sccssy ppdttv snstvty-sd mod pdtn to th dynmcssssmnt o cvd c-styd d n Snpo.T sts o pvos stds dmonstt tht dn nttv pocd, t s mposs to otn dsst ony on o two ttons, nd t s ncssy

to qnty djst th tnn stts o sccsspdtn. Athoh most o th poposd tnn mthods tomtc pocsss, th sonppoxmtons otndy mn mthods (.., nnn jdmnt) qdto otn th st sts. Dn nd Mcdond [18]sccssy ppd mn tnn to 3D FE mod o onncd cntv scton o th Scond Svn Cossn(SSC) c-styd d, sndtmsd om mnt

vton tsts dn ts constcton. Bndttn nd Gn-t [19] nvsttd th snstvty o th nt qncsto chns n nctn pmts o c-styd dn Ity wth 70 m mn spn thoh mn snstvtynyss. Howv, th ppcton o th mn snstvty-sd mod pdtn tchnooy to on-spn c-stydds s st chn to th cv nnn commnty.

Ts pp psnts mn ttv mod tnn o-thm o pdtn th nytc mod o on-spn c-styd ds. T snstvty nyss s ppd to dntyth ct o dnt pmts on dynmc chctstcso th d, whch povds tt ndstndn o thnt o th stct hvo o hhy dndnt c-styd ds. T FE mod o t c-styd d nJpn s ntd n ANSYS 12 [20], nd th snstvty o thd to stct nd mt pmts s nvsttdto ndstnd th ct on th dynmc hvo o thstct. T nw nd mpotnt spcts o ths stdy cn s s d o th nyss nd mod pdtn oon-spn c-styd ds.

2. Model Updating Procedure Based onSensitivity Analysis

Snstvty nyss s common wy to fnd ctv pm-ts o stct sponss o c-styd ds, schs sttc dspcmnts, mod shps, nt qncs, ocoton vs sch s mod ssnc cton (MAC)

vs. Condctn snstvty stdy hps to pdt thFE mod o xstn ds nd ndstnd th stc-t hvo o t dsn o c-styd ds. In

cnt ys, dnt mthods hv n poposd to ppysnstvty-sd mod pdtn to ds. Most o th po-posd mthods tomtc sotons tht ttvy pdtsctd stct nd mt popts to mpov thcoton o mod sponss nd tst sts o th d.Howv, nw nvsttons show tht dn th pocss, ts ncssy to djst th tnn stts qnty sdon nnn jdmnt o sccss pdtn. Ttomtc snstvty-sd pdtn othm o c-styd ds ws dscd pvosy y Zhn t . [16].Ts pp nvstts mn mod pdtn othmsd on snstvty stdy to ssss th dynmc hvo oth on-spn c-styd ds. T nt qncs

o sctd mods consdd to comp th sts. Tpnc o th poposd mthod ov oth mod pdt-n mthods sts om th possty o sn mntnn to otn th most son sts. Howv, thtomtc mod pdtn s so poss sn thpsntdothm y ppyn th tton oops n ANSYS.

T od nd th mn ts o th pdtn poc-d psntd s oows.T tnn pocd qs coct scton o pdt-

n pmts nd nc sponss to otn th stmtch twn FE nd msd sts. T oownpmts (, = 1, . . . , ) sctd o snstvty n-yss:

() mt popts: Yons mods, Possons to,nd mss dnsty o th dck, tows, nd cs;

() omtc mnt popts: spn stnss ndm coss-scton popts;

() mpd popts: mpd stnss (ondy con-

dtons) nd mpd msss.T choc o snstv pmts om th mntond

pdtn pmts s th most mpotnt spct o th po-css, whch qs ws nnn nshts. T nctnpmts mst sctd to pvnt mnnss stsn th FE smton. Fthmo, th nm o pdtnpmts shod kpt sm, nd sch pmts shod chosn wth th m o coctn conzd nctntyn th mod nd nsn th dt snstvty to thm.

T snstvty stdy s pomsn wy to fnd th htpmts to pdt. A comphnsv snstvty stdy oth pmts s psntd n ths pp sn snstvtycocnts. T snstvty cocnt () s dfnd s

th t o spons chn wth spct to pmtdjstmnt:

=

, (1)

wh nd psnt stct spons nd pmt,spctvy. T sscpts = 1, 2 , . . . , o pmtsnd = 1, 2, . . . , o sponss. Athoh somschs [19] hv consdd th snstvty cocnt sth chn pcnt n mod qncy p 100% chn nth pmt, th chns n pmts shod sm ndstctd to ow nd hh vs to chv son

sponss nd pvnt physcy mnnss pdtd sts( < < ).T snstvty o th nt qncs to vtons

n dnt pmts o on-spn c-styd d s

nvsttd n ths stdy. T ctv pmts () chosn consdn th snstvty cocnts. As mntondo, th chn n pmts shod stctd to ow

nd hh vs ( < < ). T tonc () s dfnds th dnc twn th nyzd nt qncs

n ch tton ( ) nd th msd qncs ().T othm o th dscd pocd s psntdn F 1. In th mn mod tnn, th dntonds o pmts cn djstd n ch tton,


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Advncs n Cv Ennn 3

Finish

Yes

Set up or selected

parameters

Choose efective

parameters ()

= + 1

No

Select initialparameters ()

<

+1 = +

< < ,

Set , = 0

Figure 1: FE mod tnn othm.

Figure 2: t d.

sd on nnn jdmnt. Moov, choosn thchnn pmts my hv dnt pots sd onth pmt mpotnc. T ty- nd -o pocd cn sd o ttons. In th tomtc pocd, th FE

mod pdtn stts wth n tton oop tht consdsson tonc o th sts to conv. T mnmod tnn sts n tt ndstndn o stcthvo nd consds nnn consdtons n on-spn c-styd ds.

T pdtd nytc mods sn th mntondpocd cn sd n th t o tsks sch s hthmonton o th ds.

3. Numerical Study

3.1. Bridge Description. T nytc FE mod o tBd s consdd o smtons n ths stdy. T t

Bd (F 2) s comptd n 1999 n Jpn, wth mnspn o 890m, nd t s now th 4th onst c-stydd n th wod. T d compss st ox dck2.7 m dp wth pstssd conct (PC) ds svn scontwhts n sd spns (F 3).

T d hs two dmond-shpd st tows wthhhts o 220m. F 4 shows th schmtc vton vw

o th d. A 21 sty cs nd n two-pnmtn shp nd stssd t th ncho ponts o thd dck. T sty cs hv poythyn c cotnto sst n vton. F 5 shows th nmnt o thcs on th tows.

T d s modd n ANSYS sow sd onth dsn nomton o th d. T ct o dntstct nd mt pmts on th dynmc poptso th d s nvsttd om th nyss o th-dmnson FE mod.

3.2. Tree-Dimensional FE Model o the Bridge. T o-

mtc nd nt pmts, connctons, nd ondycondtons o th d smtd n ANSYS sow.T smpfd th-dmnson FE mod o th d sdvopd sn stc m nd nk mnts. T ddck s modd y sn cntspnwth ost d nksto ccommodt c ncho ponts (fshon mod). TBEAM4 mnts sd to mod th dck, tows, hds,nd stts o th tows. T MPC184 mnts ppdto mod th d nks, nd MASS21 mnts sd toncd th mss o nonstct mms. T cs modd y tnson-ony LINK10 mnts tht hv stssstnn cpty. T c ptnsons consdd tons sm domtons nd th dck s-wht. 1


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260260

2 500 2 245295

9 500

30 600

1 000 9 500295

2 245 2 500

2700

1% 2% 2% 1%

6 380 9 040 6 380

4 400 21 800 4 400

Center distance o cable anchor points 23 000

() Coss scton o st d

260260

2700

2959 500

30 600

1 0009 500295

2 245 2 2452 500 2 500

Center distance o cable anchor points 23 000

1% 2% 2% 1%

4 40021 8004 400

() Coss scton o conct d

Figure 3: Mn d sctons [21].

able 1: Popts o stct mms.

Stct mms Emnt typ Mt (MP) (k/m3)

owBEAM4, MPC184

St 2.10 1057850

Rd nk o tows

Gd

Rd nk o ds

BEAM4 St 2.10 105 7850

BEAM4 Conct 3.00 104

2400MPC184

C Lnk10 St 2.00 105 7850

shows th popts nd mnt typs o th stctmms tht sd n th FE mod o th t Bd.

T ondy condtons t th ps, t th s o thtows nd t th conncton o ch tmnt, smtdn th FE mod. T tow ss consdd s nfxd n ds o dom. T nd connctons pmtth nd o th dck to ott y ot th vtc ndtnsvs xs. Rotton ot th ontdn xs () ndtwo tnston ds o dom t ch tmnt

fxd. Estc ns w sd o vtc ns on thtow-to-dck connctons. Ts, th spn constnt ot

3.92 106 (N/m) s doptd o mt d dspcmnt nth dcton o th d xs sd on dsn nomtonot th d. F 6 psnts th ondy condtonsssnd to th FE mod o th d.

On o th mpotnt ts o c-styd ds sth dd od nnc on th stnss o th d. oncd ths nnc, th sttc nyss nd s-wht


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able 2: Compson o nt qncs (Hz) twn fd tsts nd FE modn.

Mod no. FE qncs (HZ)Dck componnt o motons ow componnt o motons Msd

qncsFqncy

o (%)Vtc Lt oson Lontdn Lt oson

V1 0.216 0.225 4.0

L1 0.120 0.097 23.0

V2 0.270 0.263 2.7

L2 0.320 0.248 29.0

V3 0.367 0.365 0.5

L3 0.564 0.470 20.0

V ndcts vtc mods; L ndcts toson-t mods.

170.0050.0050.00

+226.00

+44.46

+0.001AP1

P2 2P

PC girder

105.50

+6.00

890.00

+47.660

1312.00

Steel girder

3P

+6.00

270.0050.00

4PP3

+44.135

62.50

PC girder

Figure 4: Gn nmnt o th t c-styd d.

nd c ptnson, n whch th stct mms pstssd, s pomd o th mod nyss. T sct, th most mpotnt nonn ct, s consdd toncd omtc nonnty n th sttc nyss. Tsts o cnt stds show tht nonnts mo

snfcnt n sttc nyss thn dynmc nyss o thc-styd ds nd th most ctv nonnty s ths ct [4, 5, 2225]. Foown nonn sttc nyss,th n pstssd mod nyss s condctd to xtctth nt qncs nd mod shps o th nt FEmod o th d.

3.3. Verifcation o FE SimulationResults with Field est Resultso theBridge. T nt qncs ndmod shps o thFE mod nyss shod vfd wth fd tst sts tons tht th stct pmts sd n thFE modnct th dynmc chctstcs o th d.

T fd ocd vton tst o th t Bd hd

n pomd n 1998 whn th constcton o pvmntws most compt. T xcts vtd th d nth vtc dcton to nvstt th vtc ndn

vton mods nd n th hozont dcton to nvsttth ndn vton mods n th nom dcton oth d xs [26]. In th cs o th t Bd, th tststs v ony o fst-mod qncs. Ts,th sts o FE modn vfd wth w msdmod qncs. Howv, th sts o cnt stds showtht whn th ppos o pmtc pdtn s th sponsstmton o on-spn d nd wnd xctton, th

vfcton o th owst w vtc nd t-tosondck mods wod scnt. It s concvd tht th

spons o d cn qt ccty spnnd yth ow mods [27]. 2 shows th compson o FEcctd qncs nd dntfd qncs om tststs.

T oth mthod v to comp th sts o FE

modn wth tst sts nvovs sn th MAC v,whch comps th odnts o mod shps nd vs v o nty o pct coton, wh tnn vo zo o ncotd mods. T MAC vs notcompd n ths stdy wth spct to ck o nomtonot ct mod shps om tst sts. Howv, thcompson o nt qncs s consdd to ssssth snstvty o th dynmc chctstcs o th d todnt pmts.

4. Model Updating Results

4.1. Sensitivity Analysis o the Parameters. Hvn stshd

th sc mod, th snstvty o th nt qncs snvsttd o vtons n mt nd stct pop-ts o th dck, tows, nd cs o th modd d.Bsd on th nt chctstcs o th d mxmmo 30% s consdd o ow nd hh chn vs opmts.

T oown popts consdd to nvstt thsnstvty o th mod sponss o th d:

() Yons mods, s-wht (whch s tv tomss dnsty), nd scton popts o st ds(1, 1, 1, (1), (1) , (1)) nd PC ds(2, 2, 2, (2), (2) , (2));


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T.P.+226.000 T.P.+226.000

T.P.+46215 T.P.+46215

T.P.+45.400 T.P.+45.400

T.P.+38.500 T.P.+38.500

T.P.+6.000 T.P.+6.000

N.HHWL.T.P+2.200

2P 3P

8 500

25 000

25 000

15 420 15 420

6 000 6 000

180600

220000

180600

220000

32 500 32 500

3000

3000

3000

6000

3000

6000

32500

32500

36900

36900

2500

2500

39000

17 000 17 00012 000 12 000 12 000 12 000

43 000

43 000

8 50019000

C1 C

2

C3 C4

C5C6

C7 C

8

C9C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

C21

C22

C23

C24

C25 C

26

C27

C28

C29 C

30

C31 C

32

C33 C34

C35

C3

6

C37 C38

C39 C40

C41 C42 C

43 C44

C45 C4

6

C47 C4

8

C

49 C50

C51 C52

C53 C

54

C55 C

56

C57 C

58

C59

C60

C61

C62

C63

C64

C65

C66

C67

C68

C69

C70

C71

C72

C73 C

74

C75 C

76

C77

C

78

C79

C80

C81

C82

C83

C84

T.P.33.000

T.P.13.000

N.H.H.W.L.T.P.+2.200

Figure 5: Mn tow n nmnt [21].

Figure 6: Bondy condtons o th t c-styd d.

() th mss dnsty nd Yons mods o th tows(, ) nd cs (, );

() th constnt o tnsvs spns n th dck-to-tow connctons ().

T snstvty cocnts dfnd s (/)(/), nd thy psnt th chn n ntqncs o n ppoxmty 60% chn n pmts(30% n ch dcton). T snstvty o th modto chn n th dck, tow, nd c popts snvsttd n th pstssd mod nyss to comp thnt qncs. T tnsons n th cs djstdmny to cospond wth th djstmnts n dck mss.

T stc mod o cs modfd tomtcy nANSYS to consd th s ct.

Yons mods nd th wht o st ds ctth d sponss snfcnty, wh th sm pmtso PC ds hv most no ct on nt qncs(s 3 nd 4). It cn jstfd tht th PC ds mch sm thn th st ds o th mn spn; th PC

ds pom ony s contwhts nd do not hv nysnfcnt ct on th dynmc chctstcs o th d.Ts, th popts o stds consdd oth sn-stvty nyss o th dck (dck, dck, dck, , , ).T nspcton o th snstvty cocnts o th fst v-tc nd toson-t mods o th pmts o stds (s shown n F 7) cy vs th oown.

() T dck nd dck chn th nt qncsnvsy, wh dck chns th fst vtc modsmo snfcnty. T chn o dck pmycts th fst toson-t mods o th dck.


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Advncs n Cv Ennn 7

able 3: Compson o nt qncs (Hz) wth chns nYons mods o st ds (1) nd PC ds (2).

dck L1 V1 V2 L2 V3 L3

0.71, 2 0.103 0.209 0.26 0.276 0.355 0.535

0.81, 2 0.109 0.212 0.264 0.293 0.359 0.547

0.91

,2

0.115 0.214 0.267 0.308 0.363 0.555

1.11, 2 0.126 0.217 0.273 0.327 0.370 0.571

1.21, 2 0.130 0.218 0.275 0.331 0.373 0.578

1.31, 2 0.135 0.220 0.277 0.333 0.376 0.585

Ed1

, Ed2

0.120 0.216 0.270 0.32 0.367 0.564

0.72, 1 0.120 0.215 0.269 0.320 0.367 0.564

0.82, 1 0.120 0.215 0.269 0.320 0.367 0.564

0.92, 1 0.120 0.215 0.270 0.320 0.367 0.564

1.12, 1 0.120 0.216 0.270 0.320 0.367 0.564

1.22, 1 0.120 0.216 0.270 0.320 0.368 0.564

1.32, 1 0.120 0.216 0.270 0.320 0.368 0.564

able 4: Compson o nt qncs (Hz) wth chns nmss dnsty o st ds (1) nd PC ds (2).

dck L1 V1 V2 L2 V3 L3

0.71, 2 0.136 0.243 0.305 0.333 0.374 0.577

0.81, 2 0.130 0.233 0.292 0.331 0.369 0.571

0.91, 2 0.125 0.224 0.28 0.327 0.365 0.569

1.11, 2 0.116 0.208 0.261 0.311 0.354 0.546

1.21, 2 0.112 0.202 0.252 0.303 0.343 0.529

1.31, 2 0.109 0.196 0.245 0.294 0.336 0.514

d1

,d2

0.120 0.216 0.270 0.320 0.367 0.564

0.72, 1 0.121 0.216 0.270 0.320 0.367 0.564

0.82, 1 0.120 0.216 0.270 0.320 0.367 0.564

0.92, 1 0.120 0.216 0.270 0.320 0.367 0.5641.12, 1 0.120 0.216 0.270 0.320 0.367 0.564

1.22, 1 0.120 0.216 0.270 0.320 0.367 0.564

1.32, 1 0.120 0.216 0.270 0.320 0.367 0.564

able 5: Compson o nt qncs (Hz) wth chns nth tnsvs stnss () o ns.

L1 V1 V2 L2 V3 L3 OW1 OW2

= 0.067 0.216 0.270 0.14 0.367 0.238 0.342 0.434

= 2 0.075 0.216 0.270 0.154 0.367 0.248 0.342 0.434

= 10 0.100 0.216 0.270 0.224 0.367 0.352 0.342 0.434

= 15

0.105 0.216 0.270 0.248 0.367 0.435 0.342 0.430

= 0.120 0.216 0.270 0.320 0.367 0.564 0.342 0.427

OW ndcts tow mods.

() T dck shty cts oth th vtc ndtoson-t mods o th d.

() T chns o , hv no snfcnt ct onmod qncs, wh th chn o hs nncsn ct on th fst two toson-tmods.

T snstvty cocnts o th fst dck nd towmods to th pmts o st tows nd cs shown

able 6: Ectv pmts on th fst mod sponss o thd.

Mod Ectv pmts

L1 dck, , dck, dck, L2 dck, dck, , , tow , tow

L3 dck, dck, dck, V1 dck, c, dck, dckV2 dck, c, dck, dckV3 c, dck, dck, dckOW1 tow , tow , OW2 tow , tow ,

0.40.30.20.1

0

0.10.20.3

0.4

0.5

TL1 TL2 TL3V1 V2

V3

Sensitivitycoefcient

Modeshape

deckdeckdeck

Figure 7: Snstvty o mods to th pmts o st dck.

n F 8. T tow popts (tow nd tow) chnth vtc ndtnsvs dck mods shty; howv, thyhv snfcnt ct on th oown tow mods. Tcoss-sctons o th tows ( tow) not consddo pdtn cs thy pmts tht cnnot pdtd smpy. Incsn Yons mods o th cs(c ) w consdy ncs th nt qncs oth fst mods, wh th mss dnsty o cs (c) dosnot hv snfcnt ct on th nt qncs.

T dynmc chctstcs o th cnt c-stydds pov tht th dck-to-tow ns ct n dc-tons nd sn nx spn mnts cnnot psntth dynmc hvo o th c-styd d ccty.

To, th tnsvs stnss o th spns () s soconsdd to psnt th ct hvo o ns nth dck-to-tow connctons. Lontdn nd tnsvsspns (, ) psntn th stnss o ns ndck-to-tow connctons mny ct th dck toson-t mods. 5 ndcts tht ncsn th tnsvsspn stnss () sts n n nhncmnt o th ntqncs. T spn pmts cn y pdtd,nd no vton onds ssmd cs thy qtnctn n th fst ppcton.

T sts o th snstvty nyss cy v thtth dynmc chctstc o c-styd d modcn mpovd y chnn th stct nd mt


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8 Advncs n Cv Ennn

able 7: Compson twn cctd FE nd msd qncs.

Mods Msd qncs (Hz)

FE cctd qncs (Hz)Fn qncy o (%)

Int FE qncy (HZ)Estmtd qncs

Fst Scond Td Foth

L1 0.097 0.120 0.120 0.110 0.100 0.100 3

L2 0.248 0.320 0.269 0.260 0.255 0.250 3L3 0.470 0.564 0.390 0.410 0.450 0.463 1

V1 0.225 0.216 0.220 0.218 0.218 0.218 3

V2 0.263 0.270 0.269 0.269 0.267 0.267 1

V3 0.365 0.367 0.367 0.370 0.370 0.370 1

able 8: Updtd pmts o th d.

PmtsInt FE

pmtsUpdtd FEpmts

Chn (%)

dck (MP) 2.10 105 2.15 105 2.38

dck (k/m3) 7850 8242.5 5

dck (m2

) 1.367 1.367 0 (m

4) 140 133 5

c (MP) 2.00 105 2.05 105 2.5

(N/m) 3.92 107

Sensitivitycoefcient

0.50.40.3

0.20.1

0

0.1

0.2

0.3

0.4

0.5

TL1 TL2 TL3 V2V1 V3 TOW1 TOW2Modeshape

towercable

cabletower

Figure 8: Snstvty o mods to th pmts o tows ndcs (OW ndcts tow mods).

pmts. In th cs o th t c-styd d, thmost ctv pmts on th fst qncy mods

shown n 6. Bsd on th sts o snstvty stds,mt nd stct pmts cn pdtd to chvth cosst nt qncs to th xpmnt tsts o thd.

4.2. Manual FE Model uning o the Bridge. Bsd on thsnstvty nyss sts, th FE mod o th d spdtd sn th othm tht s psntd n F 1. Tmn mod tnn s consdd th thn tomtcmthods cs o th oown.

() In mn mod tnn, th scton o pmtso pdtn s mo mnn thn oth poposd

mthods. In th cs o th modd c-stydd, th homonos popts o st mndck nd tows pmt w chns n th mssdnsty nd coss-scton pmts o th dcknd tows n th pdtn pocd n compsonwth conct ons.

() In th mn tnn mthod th stctd ownd hh vs o pmts cn dntdn th pocd wth spct to nnn

jdmnt. T dnt vtons n th hh ndow onds o pmts ncs th cccy oth pocd. T dck-to-tow conncton pm-ts, whch ct s ns, cn pdtd ccod-n to ts nd os wth no vton onds,wh oth scton popts shod vy n stctd ond to pvnt mnnss sts. Amxmm 10% vton s consdd o th stcmod, mss dnsts, nd coss-scton s o componnts. Fo th momnts o nt o th

dck, mxmm 20% vton s consdd dto th tv compxty compd wth th othcomponnts.

() T nm o pdtn cnddts o pmts sow thn tht o oth mthods d to mntono som pmts sd on nnn jdmntnd nt chctstcs o th d.

Dspt th dvnts,th dsdvnt o th mntnn mthod s tht th vton n sctd stnssnd mss pmts cnnot vy fnd wthot nmpctc nm o mod vtons [8]. Howv, thmn mthod s consdd n ths stdy o mod pdt-

n o on-spn c-styd d consdn thmntond dvnts. 7 shows th dnt ttmptst mod pdtn o thd. T tnn pocd w stoppd whn th dncs twn th msd nd thcctd qncs com ss thn 3% o th sctdfst vtc nd t-toson mods o th d. T

vs o pdtd pmts shown n 8.Usn th psntd mn tnn mthod, mt

nd stct pmts pdtd to chv th cosstnt qncs to th xpmnt tsts o th d.T pdtd mod shps o th d shown n F 9.In th cs o th pdtd d mod, t sms tht thcomntons o pdtd pmts psnt th dynmc


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Advncs n Cv Ennn 9

X

Y

Z

XYZ

1st lateral bending mode (0.100 Hz)

()

3rd vertical bending mode (0.370 Hz)

()

X

Y

Z

X

Y

Z

1st vertical bending mode (0.218 Hz)

(c)

2nd vertical bending mode (0.267 Hz)

(d)

2nd lateral bending mode (0.250 Hz)

()

Figure 9: Fst mod shps om th pdtd FE mod.

hvo o th d ccty, nd th chns wod

not ctv n modn d sponss. T dynmcnd mod chctstcs o th FE mod show oodmnt wth th fd tst sts, nd th pdtd modcn sd s sn mod o t ss sch s hthmonton o th d.

5. Conclusions

A mn pdtn othm s psntd n ths pp omod tnn o hhy dndnt c-styd ds sdon snstvty nyss. T oown spcts concddom th poposd mod pdtn pocd.

() Snstvty nyss s pop wy to dnty th

cts o stct nd mt pmts on thdynmc hvo o c-styd ds. T stso th snstvty nyss on th FE mod o th sm-td c-styd dshow tht th vtc modso th dck mosty ctd y dck, dck, ndc, wh th t-toson mods ctdy dck, (dck) nd th stnss o dck-to-towconnctons. T sts o th mntond snstvtynyss cn hp ondstndn thdynmchvo o on-spn c-styd ds nd thth monton o ths spstcts.

() T vfcton o smton sts n ths stdyshows tht n FE mods o c-styd ds,


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10 Advncs n Cv Ennn

th vtc dck mods cctd mo cc-ty thn th t-toson ons, whch cod th st o os n pmts coss th wdtho th dck, ssmptons md n nt modnsmpfctons o nonstct mms, o dfndondy condtons nd connctons o th d.

T pmts tht nnc t-toson dckmods th fst pmts to pdtd n FEmods o c-styd ds.

() T poposd mn tnn othm cn sccss-y pdt th FE mod o on-spn c-stydds. In compson wth oth poposd to-mtc mod pdtn mthods th mn mthodmks mo son djstmnts n pmts.Fthmo, sctn w pdtn pmtsnd ssnn dnt ow nd hh vtonso pmts ncs th cccy o th tnnpocd.

Conflict of Interests

T thos do not hv ny conct o ntsts wth dto th contnt o th pp.

Acknowledgments

T thos wod k to thnk pvos schstht th stds hv n vwd n ths pp. Tsch potd n ths pp s sponsod y mkdGRA sch nts (UKM-HEJIM-INDUSRI-07-2010)ndd y th Nton Unvsty o Mys (UKM)nd (FRGS/1/2011/K/UKM/02/13) ondd y Mnsty o

Hh Edcton, Mys.

References

[1] J. F. Fmn nd E. A. Es, Dynmc hvo o c-styd d, Earthquake Engineering & Structural Dynamics,vo. 8, no. 1, pp. 116, 1980.

[2] A. S. Nzmy nd A. M. Ad-Gh, Nonn thqk-spons nyss o on-spn c-styd ds: thoy,Earthquake Engineering & Structural Dynamics, vo. 19, no. 1,pp. 4562, 1990.

[3] J. C. Wson nd W. Gv,Modn o c-styd do dynmc nyss, Earthquake Engineering & StructuralDynamics, vo. 20, no. 8, pp. 707721, 1991.

[4] W. X. Rn, X. L. Pn, nd Y. Q. Ln, Expmnt ndnytc stds on dynmc chctstcs o spnc-styd d, Engineering Structures, vo. 27, no. 4, pp.535548, 2005.

[5] P. H. Wn nd C. G. Yn, Pmtc stds on c-stydds, Computers & Structures, vo. 60, no. 2, pp. 243260,1995.

[6] M. I. Fsw nd J. E. Mottshd, Finite Element ModelUpdating in Structural Dynamics, Kw Acdmc Pshs,Dodcht, T Nthnds, 1995.

[7] H. Ahmdn, J. E. Mottshd, nd M. I. Fsw, R-ston mthods o fnt mnt mod pdtn, MechanicalSystems and Signal Processing, vo. 12, no. 1, pp. 4764, 1998.

[8] S. Z-Rd nd M. Imn, On th s o ztontchnqs o fnt mnt mod pdtn, Inverse Problemsin Engineering, vo. 7, no. 5, pp. 471503, 1999.

[9] J. K. Snh nd M. I. Fsw,Mod pdtn: too o modn, dsn modfcton nd dnoss, Te Shock andVibration Digest, vo. 34, no. 1, pp. 2735, 2002.

[10] I. Kj, . Mksk, nd C. Szymczk, Adjont ppochsnstvty nyss o thn-wd ms nd ms, Journalo Civil Engineering and Management, vo. 11, no. 1, pp. 5764,2005.

[11] R. Bsys, G. Dnds, R. Kcnsks t ., Snstvtyo dynmc hvo o th FE mod: cs stdy o thnn NPP cto dn,Journal o Civil Engineering andManagement, vo. 14, no. 2, pp. 121129, 2008.

[12] R. M. F, Impctons on RC stct pomnc omod pmt snstvty: ct o chods,Journal o CivilEngineering and Management, vo. 16, no. 4, pp. 561566, 2010.

[13] R. Cntn, Updtn o nytc mods o xstn stcts sd on mod tstn, n Proceedings o the US-Europe Workshop on Bridge Engineering: Evaluation, Manage-

ment and Repair, pp. 153177, ASCE, Rston, V, USA, 1996.[14] A. Pvc, M. J. Hty, nd P. Wdon, Updtn o th

nytc mods o two ootds sd on mod tstno sc stcts, n Proceedings o the 23rd InternationalSeminar on Modal Analysis, pp. 11111118, Socty o Exp-mnt Mchncs, Bth, NY, USA, 1998.

[15] K. Mck nd B. Stojdnovc, Postc ssmc dmndmod o Con hhwy ds, Journal o Bridge Engi-neering, vo. 6, no. 6, pp. 468481, 2001.

[16] Q. W. Zhn, C. C. Chn, nd . Y. P. Chn, Fnt mntmod pdtn o stcts wth pmtc constnts,Earthquake Engineering & Structural Dynamics, vo. 29, no. 7,pp. 927944, 2000.

[17] J. M. W. Bownjohn nd P.-Q. X, Dynmc ssssmnt o

cvd c-styd d y mod pdtn, Journal oStructural Engineering, vo. 126, no. 2, pp. 252260, 2000.

[18] W. E. Dn nd J. H. G. Mcdond, Impovd fnt mntmodn o c-styd d thoh systmtc mntnn, Engineering Structures, vo. 29, no. 3, pp. 358371, 2007.

[19] F. Bndttn nd C. Gnt, Opton mod tstnnd FE mod tnn o c-styd d, EngineeringStructures, vo. 33, no. 6, pp. 20632073, 2011.

[20] ANSYS, Uss mn, vson12-0-1, Swnson Anyss Sys-tm, USA, 2009.

[21] A. Wson, A ctc nyss o t Bd, Jpn, nProceedingso BridgeEngineering, p.37, Unvsty oBth,Bth,UK, Ap 2009.

[22] R. Kom, Som modn spcts n th nonn fntmnt nyss o c sppotd ds, Computers &Structures, vo. 71, no. 4, pp. 397412, 1999.

[23] A. M. S. F, J. H. O. No, nd A. V. Lops, Gomtcnonnts on th sttc nyss o hhyx st c-styd ds, Computers & Structures, vo. 84, no. 31-32, pp.21282140, 2006.

[24] J. H, I. E. Hk, S. W. Smth, J. G, J. E. Cmp, nd R.C. Gvs, Bsn modn o th Ownsoo c-stydd ov th Oho Rv, Kntky nspot Systm RpotKC-64-04, 2006.

[25] Y. Y. Ln nd Y. L. L, Gomtcy non-n nyss oc-styd ds sjct to wnd xcttons, Journal o theChinese Institute o Engineers, vo. 26, no. 4, pp. 503511, 2003.


11/12

Advncs n Cv Ennn 11

[26] K. Ymsh, Vton tst o t Bd, Science LinksJapan, vo. 3694, pp. 493500, 2000.

[27] Q. W. Zhn, . Y. P. Chn, nd C. C. Chn, Fnt-mntmod pdtn o th Kp Sh Mn c-styd d,Journal o Bridge Engineering, vo. 6, no. 4, pp. 285293, 2001.


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