Seimic repone analyi of long continuou rigid-framed ridge ujected to multi-upport excitation Jitao Li 1 and Qinghan Yang 2 1 Potgraduate, School of Civil Engineering, Beijing Jiaotong Univerity, Beijing. China 2 Profeor, School of Civil Engineering, Beijing Jiaotong Univerity, Beijing. China Email:rockman6098@ohu.com, qhanyang@jtu.edu.cn ABSTRACT : In thi paper, effect of multi-upport excitation on eimic repone of an exiting long pan pretreed concrete continuou rigid-framed ridge are invetigated y time-hitory method. Thi ridge i named Houzhu Bridge, in Quanzhou, Fujian province. There i no material difference etween the reult of the 3-D finite element model modal analyi and modal tet that confirm the 3-D finite element model reaonale. The ground motion come from relatively non-tationary earthquake accelerogram imulation with EI-centro wave. Wave paage effect, incoherence effect and local effect i conider in the numerical imulation. The contrat of reult multi-upport excitation and i that the wave paage effect i very important for the continuou rigid frame ridge, the other effect i not very important. A concluion i given that the uniform eimic excitation i not ale to control the eimic deign for long pan pretreed concrete continuou rigid-framed ridge, and the influence of the multi-upport excitation on the eimic repone of the long pan pretreed concrete continuou rigid-framed ridge mut e conidered. KEYWORDS: continuou rigid-framed ridge, multi-upport excitation, eimic repone analyi 1. Introduction The eimic excitation of large-pan tructure i quite complex with a high variaility in time and pace. In calculation of the dynamic repone aout thee long-pan tructure, the aumption of the uniform ground upport motion cannot e conidered valid. For long-pan ridge, many reearcher have tudied aout multi-upport and traveling eimic wave effect. Nazmy AS and Garevky epecially have illuminated the requirement of conideration of multi-upport and traveling eimic wave effect for the dynamic repone analyi of long-pan ridge [1-2]. Adel-Ghaffar and Ruin ha analyzed long-pan ridge under multi-upport eimic excitation through random viration method [3]. Harichandran tudied the Golden Gate upenion ridge to a general patially varying earthquake ground motion which neglect the ite-repone effect through coherent model in reference [4]. It wa concluded that the ue of identical excitation i in general unacceptale for thoe long-pan ridge [5]. Zematy preented a numerical enitivity tudy of the local ite effect on a four-pan ridge repone with an analyi of a ridge repone with upport founded on different oil [6]. Zanardo et al. carried out a parametrical tudy of the pounding phenomenon aociated with the eimic repone of multi-pan imply upported ridge and highlighted that multi-upport analyi give reult markedly different from the uniform dynamic analyi [7]. Dumanoglu and Soyluk invetigated the tochatic repone of a cale-tayed ridge ujected to patially varying ground motion aed on a recently developed model. The patial variaility of ground motion i conidered with incoherence, wave-paage and ite-repone effect. The importance of ite-repone effect wa invetigated particularly [8]. Nichola A. Alexander invetigated a novel correction cheme which i employed to reproce the SART-1 data. The error in eimically induced force i conidered, that can e accrued if identical upport excitation (ISE) analyi i ued in place of a multi-upport excitation(se) analyi [9]. any long-pan ridge i analyzed with multi-upport eimic excitation in the world. But thee kind of ridge mainly i including upenion ridge, cale-tayed ridge and arch ridge, the rigid frame ridge i le invetigated with multi-upport eimic. And now total length of many continuou rigid-framed ridge i more than hundred of meter. It i very importance to analyze rigid-framed ridge with multi-upport eimic. 2. Decription of the ridge model Thi continuou rigid-framed ridge i Houzhu Bridge, in Quanzhou, Fujian province, 66m+3 120m+66m Zong Zhouhong et al invetigated modal and dynamic characteritic of thi ridge through tet [10]. Thi paper compare with thi ridge mode reult of Zong Zhouhong through finite element renew imulating. Zong Zhouhong reult mi four mode through initial 20 mode comparion of Houzhu ridge. Other mode of thee 20 mode are conitent etween tet reult and finite element imulating reult. It illuminate that the ridge dynamic characteritic of the finite element imulating are coincident with dynamic characteritic of actual tructure. There how reult of oth
in tale1. The firt model hape i longitudinal, the econd model hape i tranveral and the third model hape i vertical ending. In tet: their fundamental frequencie in the three direction are 0.742Hz, 0.821 Hz and 1.222Hz repectively. And in computation: their fundamental frequencie in the three direction are 0.740Hz, 0.825Hz and 1.190Hz repectively. There are everal initial mode characteritic in Figure 1-3. Ta.1 Houzhu Bridge dynamic characteritic ode Computational Reult(Hz) Reference[10] tet reult(hz) 1 0.740 0.742 Firt Longitudinal odal characteritic 2 0.825 0.821 Firt Lateral(ymmetric) 3 0.893 0.97 Second Lateral(antiymmetric) 4 1.077 1.21 Third Lateral(ymmetric) 5 1.190 1.221 Firt Vertical(ymmetric) 6 1.408 ied Forth Lateral(antiymmetric) 7 1.448 1.475 Second Vertical(antiymmetric) 8 1.772 1.787 Third Vertical(ymmetric) 9 1.940 ied Fifth Lateral(ymmetric) 10 2.610 ied Sixth Lateral(antiymmetric) 11 2.702 2.754 Forth Vertical(antiymmetric) 12 2.809 2.8 Fifth Vertical(ymmetric) 13 3.399 3.428 Sixth Vertical(antiymmetric) 14 3.413 ied Seventh Lateral(ymmetric) 15 3.722 3.868 Second Longitudinal ode Reference[10] tet reult Computational reult Firt Vertical Second Vertical Third Vertical Forth Vertical Fifth Vertical ied Sixth Vertical Fig1.Vertical modal frequencie of Houzhu Bridge
ode Reference[10] tet reult Computational reult Firt Lateral Second Lateral ied Third Lateral Fig2. Firt 3 Lateral modal frequencie of Houzhu Bridge ode Reference[10] tet reult Computational reult Firt Longitudinal Fig3. Longitudinal modal frequencie of Houzhu Bridge 3.ANALYSIS ETHOD OF ULTIPLE EXCITATIONS There are three method alway ued in the eimic analyi of long-pan tructure, repone pectrum method, time hitory method and random viration method. The previou two method are determinate analyi and lat method i indeterminate analyi. The repone pectrum method aed on the excitation of SDOF, i widely ued, ut hard to adopt in the accurate eimic analyi under. The time hitory method, which i more accurate than other method if the inputted excitation are accurate, need more complex computing. But it i hard to determine the exact excitation that would e inputted. The random viration method which i often tudied in recent year may e widely ued in the future. There are till many prolem of the method hould e olved. There are two different analyi model of tructure under eimic in time-hitory analyi method. In the firt method, the diplacement time-hitory i putted a the ground excitation of tructure, and the dynamic equation i derived according to the diplacement of ground motion in the aolute coordinate. On the econd method, the acceleration time-hitory i putted a the ground excitation of tructure, and the dynamic equation i derived according to the acceleration of ground motion in the aolute coordinate [11]. In thi paper the diplacement time hitory method i ued in the eimic analyi of the continuou rigid-framed ridge. In the aolute coordinate, the ground motion lead to the motion of tructure under the eimic. The freedom of tructure can e divided into the freedom of upertructure and the freedom of ae. So, the dynamic equation of tructure under eimic can e written a u&& C C u& K K u 0 + u C C + = u K K 1 && & u R Where, u&&, u&, u are the motion vector of upertructure in the aolute coordinate; u&&, u&, u, are the ground motion vector in the aolute coordinate; ii, C ii, Kii are the matrix of ma, the matrix of damping and the matrix of tiffne, the meaning of lower figure,, are the freedom of upertructure, the freedom of ae and the freedom of their couple item; R i reaction of ae (If the repone of tructure have een got, the R can e calculated y the econd equation of formula (1). So the dynamic equation aout u&&, u&, u can e got from the firt equation of formula(1) a u&& + Cu& + Ku = ( u&& + Cu& + Ku ) 2 If the lumped ma model of tructure i ued, the i equal to zero; the damping matrix i difficult to e calculated, and the damping force Cu& i alway neglected [12] ; o the equation (2) can e written a
u&& + Cu& + Ku = Ku 3 Where, u i the vector of ground motion; Kui the force of upertructure for the ground motion in the aolute coordinate. Equation (3) i the diplacement model of analyi tructure under ground motion. 4.Spatially Varying Ground otion The deign aic acceleration of ground motion at Quanzhou, Fujian province i 0.15g and the ite cla i 2 aed with Code for eimic deign of uilding [13]. The ground motion come from relatively non-tationary earthquake accelerogram imulation with a known eimic record. The known eimic wave i EI-centro and interval i 0.01. The acceleration peak value i adjuted to location deign intenity from 0.307g to 0.15g. To enure the diplacement time-hitory i equal to zero at the tart time and end time, the acceleration i adjuted. The adjutment method i frequency filtering with SeimoSignal oftware. The ridge model ujected to patially varying ground motion i preented in Figure 4. The correlation function ued Harichandran-Vanmarcke (1986) model [14]. The diplacement time-hitory i integrated with the correction acceleration and howed in Figure 5. 66 120 120 120 66 1pier 2pier 3pier 4pier acceleration diplacement Fig.4 Houzhu Bridge ytem ujected to patially varying ground motion 0.02 0.01 0.00-0.01 0.03 0.02 0.01 0.00-0.01-0.02 1pier 2pier 3pier 4pier -0.02-0.03 0 10 20 30 40 time() 0 10 20 30 40 Uniform Excitation ultiple Excitation Fig.5 Time hitory of diplacement of eimic excitation 5.Seimic repone analyi of ridge The dynamic repone of long continuou rigid-framed ridge i calculated. The model can e got in Fig.4. There are comparion of uniform eimic excitation and multiple upport excitation analyi. 5.1 Non-traveling wave effect The ridge i ujected with longitudinal eimic motion excitation without regard to traveling wave effect. Figure 6 how that the repone of the ridge are maximum total diplacement of deck. The deck diplacement repone with multiple upport eimic excitation i le than that of. The pier maximum diplacement repone i preented in Figure 7. Four pier diplacement repone with multi-upport excitation more than that with uing uniform upport excitation. time()
0.025 0 100 200 300 400 500 ridge-pan(m) Fig.6. Diplacement variance of the deck(non-traveling wave effect) 1 pier height(m) 0.04 0.02 0.00 0 2 4 6 8 101214161820222426 2 pier height(m) 0.017 0.013 0.011 3 pier height(m) 0.032 0.028 0.026 4 pier height(m) Fig7 Diplacement variance of four pier 5.2 Traveling wave effect Apparent velocity i 1000m/ 1500m/ 2000m/ repectively. Figure8 how the 4 pier different maximum diplacement repone of traveling wave effect from that under. All 4 pier maximum diplacement repone of eimic motion excitation with apparent velocity 2000m/ and 1000m/ i high than that of uniform eimic excitation, and repone of 2000m/ i mot. The deck diplacement repone of apparent velocity 2000m/ and 1000m/ are more than that, and the deck diplacement repone of apparent velocity 1500m/ i le. 0.032 0.028 0.026 0.008 0.006 0.004 0.002 0 100 200 300 400 500 ridge pan(m) v=1000m/ Fig.6. Diplacement variance of the deck traveling wave effect 0.026 v=1000m/ 0 2 4 6 8 101214161820222426 1 pier height(m) v=1000/ 0.008 2 pier height(m) 0.035 v=1000m/ 0.025 0.005 3 pier height(m) 0.040 0.035 v=1000m/ 0.025 0 2 4 6 8 101214161820222426 4 pier height(m) Fig8. Diplacement variance of four pier(traveling wave effect) 6.Concluion Baed on the diplacement time hitory method, The Houzhu continuou rigid-framed ridge i invetigated with and. The patial variaility of the ground motion i conidered with the
incoherence wave-paage and ite-repone effect. ean of maximum value of the four pier diplacement repone of more than that of whether conidered with wave-paage or no. ome mean of maximum value of the deck diplacement with i more than that with uniform excitation, and ome le. The long-pan tructure repone under may e more intenive than thoe under. Thu, eimic analyi under in indipenale a that under in the deign proce of long-pan tructure. Reference [1] Nazmy AS, Adel-Ghaffar A. (1987).Seimic repone analyi of cale tayed ridge ujected to uniform and multiple-upport excitation. Report no. 87-S-1. Princeton (NJ): Department of Civil Engineering, Princeton Univerity. [2] Garevki, Dumanoglu AA, Severn RT. (1988). Dynamic characteritic and eimic ehaviour of Jindo ridge, South Korea. Structural Engineering Review:1:141 149. [3] Adel-Ghaffar A, Ruin LI.(1989). Vertical eimic ehaviour of upenion ridge. Earthquake Engineering and Structural Dynamic:11,1 19. [4] Harichandran RS, Vanmarcke EH.(1986).Stochatic Variation of Earthquake Ground otion in Space and Time. Journal of Engineering echanic: 112,2, 154-174. [5] Harichandran RS, Hawwari A.(1996).Sweiden BN. Repone of longpan ridge to patially varying ground motion. Journal of Structural Engineering:122,5,476 484. [6] Zematy Z, Rutenerg A.(1998). On the enitivity of ridge eimic repone with local oil amplification. Earthquake Engineering and Structural Dynamic:27,10, 1095 1099. [7] Zanardo G, Hao H, odena C. (2002).Seimic repone of multi-pan imply upported ridge to a patially varying earthquake ground motion. Earthquake Engineering and Structural Dynamic:31,6,1325 1345. [8] Dumanoglu AA, Soyluk K. (2003).A tochatic analyi of long pan tructure ujected to patially varying ground motion including the ite-repone effect. Engineering Structure :25,10, 1301 1310. [9] Nichola A. Alexander. (2008).ulti-upport excitation of ingle pan ridge, uing real eimic ground motion recorded at the SART-1 array. Computer & Structure :86,1, 88-103. [10] Zong Zhouhong,Lai Canglin,Lin Youqin, Ren Weixin. (2003).Analyi of dynamic characteritic of a large-pan pretreed concrete continuou rigid frame ridge. Earthquake Engineering and Engineering Viration:24,3, 98-104.( in Chinee) [11] Wen-Hua LIU,Qing-Shan Yang. (2006).Comparion of different analyi method for multi-upport eimic excitation of large-pan tructure. IASS-APCS 2006 BEIJING 368-370. [12]Edward L.Wilon, Three-Dimenional Static and Dynamic Analyi of Structure, 3 nd edn, Berkeley,California, USA, 2002. [13]GB50011-2001. Code for eimic deign of uilding, China Architecture & Building Pre [14]Ronald S. Harichandran, Erik H. Vanmarcke. (1986), Stochatic Variation of Earthquake Ground otion in Space and Time, J. of Engineering echanic, ASCE, 112(2)