Reliability Analysis of Pre-stressed Concrete Continuous Girders Bridge using Incremental Launching Method on Different Codes

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1 Applied Mechanics and Maerials Submied: ISSN: , Vol. 681, pp Aeped: doi: / Online: Trans Tech Publicaions, Swizerland Reliabiliy Analysis of Pre-sressed Concree Coninuous Girders Bridge using Incremenal Launching Mehod on Differen Codes Dong Fenghui 1,a, Du Yueao 2,b, Cui Fengkun 3,c 1 Deparmen of Bridge Engineering, Tongji Universiy, Shanghai, China 2,3 Deparmen of Bridge Engineering, Chang an Universiy, Xi an, China a nuaadfh@163.com, b duyueaohao@163.com, c @qq.com Keywords: Pre-sressed Concree; Girder Bridge; Incremenal Launching Consrucion; Consrucion Sage; Service Sage; Reliabiliy index. Absrac:The objec of his paper analyzes he reliabiliy level of pre-sressed concree coninuous girder bridges using incremenal launching mehod during consrucion sages. Typical cross-secions used in he example bridge are considered a consrucion and service sages, respecively. The calculaed resuls indicae ha he reliabiliy indices on he code of D vary considerably o he code of JTJ Comparing he reliabiliy indices beween he consrucions shows he differen regulariy. 1. Inroducion I is esimaed ha over 1,000 bridges worldwide have been consruced by he incremenal launching mehod[1], he vas majoriy of which have been pos-ensioned concree box girder bridges. So far, o he auhors knowledge, he reliabiliy analysis has no been applied o he pre-sressed concree coninuous girder bridges using incremenal launching mehod. This sudy focuses on analyzing he reliabiliy indices of pre-sressed concree coninuous girder bridges designed wih he Chinese code for design of highway reinforced concree and pre-sressed concree bridges and culvers of JTG D [2] and JTJ [3] using incremenal launching mehod during consrucion he sage. 2. Basic Informaion of he Bridge The bridge, which is a double-parallel pre-sressed concree pos-ensioned coninuous girder bridge wih he span of 30m+3 40m+30m, is consruced by incremenal launching mehod in he highway, and is oal lengh is 180m. The launching nose is 25m long. The geomery of girder is shown in Figure R= Figure.1 Girder geomery (uni: cenimeers) The bridge is calculaed by he finie elemen procedure. There are 72 elemens and 73 nodes in he oal bridge. The lengh of calculaed elemen is 2.5m, which includes 10 elemens and 11 nodes of he launching nose wih he lengh of 25m. The numbers of nodes and elemens of he launching nose All righs reserved. No par of conens of his paper may be reproduced or ransmied in any form or by any means wihou he wrien permission of Trans Tech Publicaions, (ID: , Pennsylvania Sae Universiy, Universiy Park, USA-21/02/16,07:05:52)

2 206 Engineering Soluions in Indusry are 1~11 and 1~10 respecively, he main girders 11~83 and 11~82 respecively as well. The segmens of incremenal launching are 10m+5m+ 10m+5m+10m. The nodes and elemen in he bridge are shown in figure 1. The able.1 indicaes he consrucion sage division #abumen 1#pier 2#pier 3#pier 4#pier 1#abumen 3. Load model Fig. 1 The elemens in he oal bridge Table.1 The consrucion sage division Consrucion sage Insalling of elemens consrucion illusraion 1 1~14 Casing NO.1 segmen-10m 2 ~16 Casing NO.2 segmen-5m 3 17~20 Casing NO.3 segmen-10m ~76 Casing NO.17 segmen-10m 18 77~78 Casing NO.18 segmen-5m 19 79~82 Casing NO.19 segmen-10m 20 Temperaure piers removed 21 1~10 deleed The launching nose removed 22 2nd Pre-sressed endons drawn 23 Deck pavemen and aached Faciliies Dead load is he graviy load due o he self weigh of srucural and non srucural elemens (presressing force in his sudy) permanenly conneced o he bridge. Two componens are considered: D 1 =dead load due o cas-in-place maerials (bridge girder), and D 2 =dead load due o asphal overlay. All componens of dead load are ypically reaed as normal random variables. The bias facor (raio of mean o nominal), λ =1.03, and coefficien of variaion, V=0.08, for D 1, and λ =1.05 and V=0.10 for D 2 [4]. For asphal wearing surface i is assumed ha mean hickness is 80 mm. In concree srucures, pre-sressed effecs are generally considered as a force being applied o he srucure. A pre-sressed force P(x,) a a disance of x from he anchorage a ime may be expressed by he following[5]: P( x, ) = P P( x, ) 0 (1) where P 0, P( x, ) are he iniial pre-sressed force and he presressed losses, respecively. [5] proposes ha we reain he value given by he sandard or regulaion as a mean value for he losses, and o ake hose found in Table 2. as coefficiens of variaion. Table 2. Coefficien of variaion for pre-sressed losses and pre-sressed force Variaion coefficien Parameer Mean value = 0 = Pre-sressed losses P( x, ) Pre-sressed force P( x, )

3 Applied Mechanics and Maerials Vol Resisance model Resisance is a variable represening he load carrying capaciy. Therefore, i is log-normally disribued. Aording he JTG D and JTG respecively, he compressive sress mus mee he following minimum requiremens: σ 0.70 f (2) ck σ b a σ 0.75R (3) In hese formula, f ck and b a R are sandard value of compressive srengh of concree a he cener of he axis a various sages of manufacure, ransporaion and hoising. The resisance model saisical parameers of he codes for design of highway reinforced concree and pre-sressed concree bridges and culvers of JTG D and JTJ are shown in able.4. Table.4 The resisance model saisical parameers Probabilisic Coefficien Sandard value Mean value Variance disribuion of variaion C50 Normal disribuion 32.4MPa # Normal disribuion 35MPa Reliabiliy analysis An ieraive procedure is used o calculae he reliabiliy index [6]. The figure.2 shows he bending momen diagram in he consrucion sage, where he cross secion of NO.16 ( kN m) and NO.17 ( kN m) were chosen o calculae and analyze he reliabiliy index in he consrucion sage Figure.2 Bending momen diagram in consrucion sages As for he consrucion sage, he reliabiliy index of cross secion NO.16 and NO.17 are shown in Figure.4~ figure.5. In addiion, he able.5 shows he average reliabiliy. Figure.4 Reliabiliy index of cross secion of NO.16 in consrucion sage

4 208 Engineering Soluions in Indusry Figure.5 Reliabiliy index of cross secion of NO.17 in consrucion sage Table.5 The average reliabiliy indices in he consrucion sages Cross secion of NO.16 Cross secion of NO.17 Upper flange Boom flange Upper flange Boom flange D D D D Conclusions (1) The calculaed reliabiliy indices vary considerably for he wo considered codes boh on he consrucion sage and he service sage. (2) A he consrucion sage, generally, he calculaed reliabiliy indices resuls in he code of JTG D are larger han ha of JTJ References [1] Gohler, Bernhard and Pearson, P., Incremenally Launched Bridges Design and Consrucion, Erns and Sohn, Berlin(2000) [2] Code for Design of Highway Reinforced Concree and Pre-sressed Concree Bridges of JTG D Beijing: People s Communicaion Press. (2004) [3] Code for Design of Highway Reinforced Concree and Pre-sressed Concree Bridges of JTJ Beijing: People s Communicaion Press. (1985) [4] Nowak AS. Calibraion of LRFD bridge code. ASCE J Sruc Eng. (1995) [5] JCSS, Join Commiee on Srucural Safey, Probabilisic model code(2001) [6] Ming Zhang. Srucure Reliabiliy Analysis. Beijing: Science Press.(2009)

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