The Deformation Analysis of the Curved Box Girder Bridges under Different Radius

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1 The Defomation Analsis of the Cuved Bo Gide Bidges unde Diffeent Radius Liu Fangping (Coesponding autho) School of Civil Engineeing & Achitectue, Chongqing Jiao tong Univesit 66 Xuefu Road, Nan an Distict, Chongqing , China & School of Civil Engineeing, Chongqing Thee Goges Univesit 780 Eduan Shalong Road, Wanzhou Distict, Chongqing , China Zhou Jianting School of Civil Engineeing & Achitectue, Chongqing Jiao tong Univesit 66 Xuefu Road, Nan an Dist., Chongqing , China Received: Febua 17, 01 Accepted: Mach 9, 01 Published: Apil 1, 01 doi: /mas.v6n4p71 URL: Abstact This pape investigates the influence of adius on the defomation of cuved bo gide bidges unde the action of pe-stessed tendons. A spial pe-stessed concete bo gide bidge in Chongqing is analzed b using nonlinea finite element pogam ANSYS. The five diffeent cuved bidge models unde weight and pestessing wee ceated and the sameness and diffeence among them ae gained and compaed b numeical simulation. The esults showed: 1. In five diffeent situations, the bo gide all occus the vetical, adial and longitudinal defomation, among which vetical defomation is the main. At the same time, the bo section occued evese and distotion, and the whole bod of the beam olls out.. The value of vetical displacement of mid-span of continuous cuved bo gide bidges elates with the hoizontal adius. When the adius between one hunded metes and one hunded fift metes, the influence of displacement is most sensitive, on the conta, when the adius geate than two hunded metes, the influence of displacement is almost no effect to mid-span displacement. Kewods: Cuved Beam Bidge, Radius, Numeical Simulation, Defomation 1. Intoduction With the development of taffic constuction, the cuved pe-stessed concete (PC) bo gide bidges have got a wide ange of applications. The stuctue has lage tosion stiffness, beautiful shapes, and it is often used in comple intechange and cit viaduct. Relative to the einfoced concete bidge, cuved PC bo gide bidges have high stength and small section, and the pe-stessed tendons usuall use thee-dimensional shape in bo gide space, mainl aanged in the webs of bo gides. The use of pe-stessing, on one hand, geatl impoves foce condition of the bidge, thus enhanced its spanning capacit; on the othe hand, because of the eistence of hoizontal cuvatue, the cuved pe-stessed tendons make the gide become moe comple, often poduce some advese effects. The cuved bo gide bidges is diffeent fom staight one, we should pa much attention when in design and constuction. In this pape, a spial pe-stessed concete bo gide bidge in Chongqing is analzed b using nonlinea finite element pogam ANSYS. The five diffeent cuved bidge models unde self-weight and pestessing wee ceated and the sameness and diffeence among them ae gained and compaed b numeical simulation (Zhou X. H., 007).. Related Analsis Methodolog.1 Static Equilibium Equations We could take out a mico segment fom the cuved gide, and then, take the tangential diection of beam as z Published b Canadian Cente of Science and Education 71

2 ais, the centipetal diection of cuve as ais, and the down diection pependicula to the cuve plane as ais. Then, a thee-dimensional fluid ectangula coodinate sstem is established. Si possible load tpes would eist in the beam segment which wee distibuted-load q, q, q z along the coodinate ais and moment m, m, m z aound the coodinate ais. The coodinate sstem and each tpes of load wee shown in Figue 1. Intenal foces in the beginning section of mico segment including aial foce N, toque foce T, shea foce Q, Q and bending moment M, M wee caused b load above. A diffeential incement came out in the teminal section of mico segment though d, as is shown in Figue. Static equilibium diffeential equations of cuved gides could be established b si equilibium conditions of space foce sstem. The equation is as follows: Q N q M T Q. Geometic Equations m Q (1a) q M (1d) Q m N Q (1b) qz T M (1e) mz The elationship between inne foce and defomation in sections can t be concluded without establishing the geometic defomation elationship of mico segment. Fo an possible point in the cuved ais of the cuved beam, u, v, w wee taken as the displacement along ais, and z, and is taken as the tosion angle. Accoding to liteatue (Yao, L. S., 1986), geometic equations of cuved beam wee found out as follows: du v d v v d w d 1 dw z (a) k dz (b) k (c) k z (d) dz dz dz dz In fomulas above: z is the aial stain; k and k epesent to the vaiation of cuvatue in ais and sepaatel; k is the tosion angle pe unit length in the cuved beam. z.3 Basic Diffeential Equations The inne foce and defomation could be connected b phsical equations of mateial mechanics. Equation (3) below is the basic diffeential equation of cuved bidges conclude fom Equation (1) and (), which is called Vlasov diffeential equation (Liu, 007; Zhu,1984; Xiong,1984). EI IV EI GI d ''' IV '' EI w w EI GI d m z (3a) R R R 3. Numeical Simulation 3.1 Poject Oveview IV EI IV GI d ''' EI GI d EI '' m ( EI ) w w ( ) q (3b) R R R R ( EI ( v V (1c) (1f) ''' 1 ' q q m m z z ) (3c) 4 R R R R The full bidge length is m, width is19 m, two-wa fou-lane. Hoizontal cuve adius is 55 m and design load is Cit Class-A. The stuctue used pe-stessed concete bo gide, of which coss-section is the discete two-bo and each with single-chambe and has big tosion stiffness. The whole spial bidge is shown as Figue 3. Five diffeent goups of adius which ae commonl used in engineeing wee adopted in simulation. The values ae: 50 m, 100 m, 150 m, 00 m and 50 m. 3. Finite-Element Modeling The full bidge model was established use finite element pogam ANSYS. The bidge has lateal inside one-wa coss slope of % and use the same coss-section. The thickened weight of the bo gide at the beaing is eplaced with a vetical unifom line load. The concete bo gide unit use solid65 and pe-stessed steel with link8 unit in ANSYS. The Full-bidge finite element models of adius fift shown as Figue 4 and Figue Calculation Results The pape analzed displacement chaacteistic in five diffeent bo-gide adius, the esult as Figue 6. Fom it we can concluded that: 7 ISSN E-ISSN

3 (1) The continuous cuved bo gide bidge occued defomation in the vetical, tansvese and along the bidge unde the combined load of weight and pe-stessing. And the vetical, tansvese displacement cuve ae aismmetic along the centeline of the bidge; the displacement cuve along the bidge is centosmmetic (due to the povisions of second coodinates component diection of the clindical coodinate). () When the adius is between 50 m and 50 m, vetical defomation and defomation along the bidge is majo, and the defomation along the bidge in both ends is geate than the maimum of anti-ach vetical defomation.the adial defomation is small, which can be neglected. The vetical displacement of side span is geate than the middle span, the atio between 1.5 to.0. (Wang X. D. & Ding H. S., 006; JIANG J. J., 00). Fom Figue 7 to Figue 8, we can concluded that: (1) Figue 7 shows that the vetical displacement in middle of continuous cuved bo gide bidges is elated to hoizontal adius. When the adius is less than 170 m, as the adius inceasing, the maimum of the vetical displacement caused b pe-stessed steel inceases. Especiall when the adius is between 100 m and 150 m, displacement inceases moe apidl. When the adius is geatte than 00 m, the cuve gaduall tends to level, that is hoizontal adius no longe affect the value of vetical anti-ach significantl, at this time, foce chaacteistics same as the staight beam bidge. () In Figue 8, vetical displacement of the oute bo gide is less than the inside, which shows that bo gide coss-section poduces a clockwise otation defomation aound the cente of cuvatue unde weight and pe-stessed loads, and both inside and outside vetical displacement ae not linea. The coss-section occued distotion. With the adius inceasing, the diffeence of vetical displacement between the oute edge and the inne edge in bo gide coss-section deceases and vetical displacement distibution cuve gaduall tends to level. In othe wods, when the adius inceases gaduall, toque deceases and the "bending - twisting" coupling effect of the cuved bidge weakens, the foce chaacteistics is same as the staight bidge. 3. Conclusion (1) Continuous cuved bo gide bidges occu defomation in the vetical, Tansvese and along the bidge unde the combined load of weight and pe-stessing, vetical defomation is the main. The bo gide coss-section poduces evese and distotion and the stuctue olls out. () The vetical displacement of continuous cuved bo gide bidges in mid-span is elated to hoizontal adius. When the adius is between 100 m and 150 m, displacement inceases moe apidl, when the adius is moe than 00 m, displacement cuve gaduall tends to level, the foce chaacteistics is the same as staight bidge. Acknowledgements This wok was suppoted b the National Natual Science Foundation ( ), National Basic Reseach Pogam of China (010CB334710), Natual Science Foundation Poject of CQ CSTC008BA6038, CSTC009AB6148, CSTC009AB6149andCSTC011BA606, Scientific & Technological Reseach Pojects of CQ KJ11044, Minist of Education fo New Centu Ecellent Talent Suppot Pogam and Geological Disaste Pevention Reseach and Innovation Team of the Thee Goges Resevoi. Refeences Jiang, J. J. (00). Reinfoced Concete Stuctual Nonlinea Finite Element Analsis. Xi-An: Shani Science and Technolog Pess. Liu, G. Z. (007). Suface Displacement Mechanism Analsis of Cuved Bidge. Tanspotation Technolog, (3), 0-4. Wang, X. D., & Ding, H. S. (006). Analsis and Countemeasues of Lateal Displacement of Concete Cuved Continuous Bidge. Highwa and Tanspotation Reseach. Xiong, G., & Yang, L. B. (007). Based on ANSYS Solid Element Model of The Seconda. Development of The Intenal Foces fo Pusuing. Jounal of East China Jiao tong Univesit, 5(4), Yao, L. S. (1986). Cuved beam. Beijing: People's Communications Pess. Zhou, X. H., Dai, P., Di, J., et a1. (007). Effects Analsis of Spatial Pe-stessed Cuved Bo Gide Bidge. Jounal of Civil Engineeing, 40(3), Zhu, B. L., & Dong, Z. X. (1984). Nonlinea Analsis of Reinfoced Concete. Shanghai: Tong Ji Univesit Pess. Published b Canadian Cente of Science and Education 73

4 Figue 1. The thee-dimensional mobile Catesian coodinate and load components Figue. The section intenal foce of the mico-cuved beam Figue 3. The whole spial bidge model Figue 4. The finite element model 74 ISSN E-ISSN

5 Figue 5. Enlaged model of pat element (a) (b) (c) (d) (e) Figue 6. (a)- (e) Sepaatel epesents the oute-bottom edge of the bo gide displacement cuve when the adius in the case of 50 m, 100 m, 150 m, 00 m and 50 m Published b Canadian Cente of Science and Education 75

6 Figue 7. The mid-span vetical displacement-adius elationship cuve Figue 8. Mid-span vetical displacement distibution cuve of bo gide along the Tansvesal diection 76 ISSN E-ISSN