Seismic Analysis Of Balanced Cantilever Bridge Considering .
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 3 Issue 7, July - 2014Seismic Analysis of Balanced Cantilever BridgeConsidering Time DependentPropertiesMs. Rubina P. Patil 1Dr. R. S. Talikoti2Department of Civil Engineering, ProfessorLate G. N. Sapkal College of Engineering, AnjaneriNashik-422413, Affiliated to Pune University, India.Department of Civil Engineering, PG studentLate G. N. Sapkal College of Engineering, AnjaneriNashik-422413, Affiliated to Pune University, India.Abstract— Long span bridges are generally constructed bybalanced cantilever method with segmental construction. Forconcrete and steel the time dependent factors such as creep,shrinkage and relaxation etc. are the factors which causehigh variation in stresses throughout the life of long spanbridges and in such situation, seismic assessment becomecritical and imperative.Earlier research has emphasized the importance of timedependent factors like creep, shrinkage and relaxation etc. inthe analysis of balanced cantilever bridge, however thepresent codes and authorities in this field suggests the lumpsum provisions, leading to inadequate estimation of residualstrength/service stress which may lead to critical condition. Ifsuch bridges are subjected to earthquake forces/actions, thecriticality could be higher and leading to unacceptablecondition. Therefore, the analysis should be updated /carriedout considering the combined impact of time dependentproperties and seismicity. Such studies are scanty orunknown and hence a study of seismic behavior of balancedcantilever bridge with consideration of time dependentfactors is carried out.The outcome of this study is reported such as, impact oftime dependent factors and seismicity on analysis of balancedcantilever bridge and its comparison with conventionalmethods of analysis. The combined impact of seismicity andtime dependent properties of the design moment of balancedcantilever bridge is studied.IJERTmore which the structure experiences continuous changesin the statical system and in support, loading andenvironmental conditions. Because of these conditions, thedeformations and internal forces within a constructed partof the bridge changes.Due to this reason, aftercompletion of construction is highly affected by themethod and sequence of construction. Among the variousparameters that affect the long term behavior of bridgestructures, creep and shrinkage which are the timedependent properties of concrete and prestressed steelhave the greatest effects on the bridge behavior during andafter construction. Changes in deflection and stresses arestrongly affected by creep and shrinkage of concrete andrelaxation of prestressed steel.The balanced cantilever construction method is thecomplex method of bridge construction in which spans areconstructed in cantilever manner and made continuousafter completion of construction. Thus, the momentsdeveloped in the span and at support during construction,after completion of construction and in entire service lifedid not remain constant due to developed continuity andother factors. The time dependent material properties andseismicity are two major influencing factors on theanalysis and design of balanced cantilever bridge. Thus itis again become necessary to study the combined effect oftime dependent material property variation and seismicityon the analysis of balanced cantilever bridge. Or broadly itcan be stated that it is very important to study the behavioror response of balanced cantilever bridge when earthquakeoccur at various time stages of life span of balancedcantilever bridge. This life span can include period ofimmediately after completion of construction, at any stageof service life of the bridge and after long time at end oflife span of the bridge.Keywords—Balance Cantilever Bridge, Time HistoryAnalysis, Creep, Shrinkage, Relaxation, Moment variationINTRODUCTIONThe method is useful for bridge site where base shutteringis not possible and foundation is costly, also the method isbeneficial over cable stay construction in complexity andtime point of view. Concrete cantilever bridges built withthe balanced cantilever method have become very populardue to the many advantages offered by the constructionmethod and the structural form. Nowadays segmental,cast-in-place concrete cantilever bridges are routinely builtfor long span bridges. Use of prestressing in bridges is avital component as they are subjected to high internalforces and stresses. For the prestressed concrete bridgessegmental construction is one of the most populartechniques. Mainly advantage of this technique iselimination of false work and temporary supports byadopting the cantilever construction method which resultsin no objection to traffic or water way beneath the bridge.Time required for constructing multi-span bridges areOBJECTIVESIn this paper time dependent seismic analysis study ofbalanced cantilever bridge is carried out on one balancedcantilever bridge model with following steps: 1. Thevariation in response i.e. moment, stresses etc. duringconstruction and at various time stages during life span ofthe bridge under constant loads i.e. self-weight, so as toobserve the effect of time dependent material properties. 2.Study of the various conventional methods of long termmoment calculation for design of balanced cantileverbridge. 3. Compare the results of analysis carried out with IJERTV3IS070751www.ijert.org658
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 3 Issue 7, July - 2014The moment Mt, if acting in the cantilever, causes theelastic rotation at the point B, defined as β Mtl/EI, andalso accompanies the creep deformation. Since the creepfactor increases by d t during a time interval dt, thevariations in the angles of rotation will be α d t and dβ(the elastic deformation) β d t (the creep deformation)for α and β, respectively.From these relations and the fact that there no netincrease in discontinuity after the joint is closed, thecompatibility condition for the angular deformation(α d t dβ β d t) can be constructed. The integration ofthis relation with respect to t gives the restraint momentsoftware and results from conventional methods, andcomment. 4. Perform the seismic analysis of balancedcantilever bridge at various time stages of life span of thebridge with consideration of time dependent properties. 5.To study the variation of response i.e. moment, stresses,deflection etc. during various staged seismic analysis. 6.Comment on final moment to be considered for design,reversal of moment etc. 6. To study the conventionalmethods of time dependent seismic analysis and comparethe design moment obtained from these methods withdetailed analysis carried out.MOMENT VARIATION WITH TIMEM t ql 2The time-dependent behavior of a balanced cantileverbridge can be described using a double cantilever with anopen joint at the point B, as in fiureg.1 When theuniformly distributed load of q is applied on the structure,the elastic deflection of 𝛿 ql4/8EI and the rotation angleof 𝛼 ql3/6EI occur at the ends of the cantilever figure 1.b, where l and EI refer to the length of the cantilever andthe bending stiffness respectively.(1 e t )(1 e t ) qL2624IJERT(1)Where, t means the creep factor at time t, and L 2l.From above equation, it can be found that for a largevalue of t, the restraint moment converges to Mt qL2/24,which is the same moment that would have been obtainedif the joint at the point B had been closed before the load qwas applied. This illustrates the fact that momentredistribution due to concrete creep following a change inthe structural system tends to approach the momentdistribution that relates to the structural system obtainedafter the change from figure 2.Fig. 2 Moment Variation with timeWhere Mcr the creep moment resulting from change ofstructural system, MI the moment due to loads before achangeFig.1 Deformation of cantilevers before and after closureIf the joint remains open, then the deflection at time t willincrease to 𝛿 (1 t) and the rotation angle to α (1 t),where t is the creep factor at time t. However, if the jointat the point B is closed after application of the load, anincrease in the rotation angle α t is restrained, and thisrestraint will develop the moment Mt, as shown in fig.1.c. IJERTV3IS070751www.ijert.org659
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 3 Issue 7, July - 2014and Wolff, considering the construction sequence whilecalculating the internal moments at an arbitrary time t, thefollowing relation is introduced by Kwak and SonM T M S ,i (M E M S ,i )(1 e ( t c ) ) f ( t )(4)of structural system, MII the moment due to the sameloads applied on the changed structural system, and MIII the restraint moment Mt.TIME DEPENDENT CONSTANT LOAD ANALYSIS:CONVENTIONAL METHODSThe basic conventional method to consider timedependent effect is Dischinger’s Equation. Based on thisequation other two equations are developed further, whichare Trost and Wolff Equation and Kwak and Son Equation.Let’s discuss these methods in detail.DISCHINGER’S EQUATIONIJERTMoment Variation with Time, leads to following finalequation(2)Mcr MIII MI (MII MI)(1 e- t)Where,Mcr the creep moment resulting from change ofstructural system,MI the moment due to loads before a change of structuralsystem,MII the moment due to the same loads applied on thechanged structural system,MIII the restraint moment Mt.The above equation is most basic and widelyused for calculation of time dependent moment variation.TROST AND WOLFF EQUATIONFig.3 Combination of Ms,iWhere, f(ϕt) 𝜒 ϕt / (1- 𝜒 ϕt). 𝜒 is the concrete agingcoefficient which accounts for the effect of aging on theultimate value of creep for stress increments or decrementsoccurring gradually after application of the original load.It is reported in the study carried out by Kwak and Sonthat an average value of c 0.82 can be used for mostpractical problems where the creep coefficient liesbetween 1.5 and 3.0.Out of the above three formulae, Trost and Wolffequation is not directly applicable to the balancedcantilever bridge, thus moment variation according toother two conventional formulae are studied for thepresent Balance Cantilever Bridge Model and it iscompared to the exact analysis carried out in the SAP2000according to CEB-FIP code.Generally, construction of a Multiplan continuousbridge starts at one end and proceeds continuously to theother end. Therefore, change in the structural system isrepeated whenever each cantilever part is tied byconcreting a key segment at the midspan.Moreover, the influence by the newly connected spanwill be delivered into the previously connected spans sothat there are some limitations in direct applications ofDischinger’s Equation to calculate the restraint moment ateach span because of the many different connecting times.To solve this problem and for a sufficiently exactcalculation of the final time-dependent moments, Trost andWolff proposed a relation on the basis of the combinationof elastic moments ( MS,i; equivalent to MI in Dischinger’sEquation) occurred at each construction step, tM T M S ,i ( M E M S ,i )1 t(3)PROBLEM STATEMENTThe Cantilever Bridge having 2 piers and 3 spans.Total Length of span 149 mSpan 1 44 mSpan 2 61 mSpan 3 44 mWidth of Span 13.2 mSlab thicknessTop slab (t1) 0.225 mBottom slab (t2) 0.225 mExternal Girder (t3) 0.431 m.Where, t and ρ represent the creep factor andcorresponding relaxation factor, respectively.KWAK AND SON EQUATIONWith the background for the time-dependent behaviorof a cantilever beam effectively describing the internalmoment variation in balanced cantilever bridges, and bymaintaining the basic form of equation suggested by Trost IJERTV3IS070751www.ijert.org660
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 3 Issue 7, July - 2014SEISMIC ANALYSISThe time elapsed stage considered to include the effectof time dependent material properties are 7 days aftercompletion of construction, 10 years, 50 years and 100years after completion of construction. After the 7 days ofcompletion of construction acceleration time history isapplied to Z direction of the bridge individually. Similarly,the time history is applied to other time stages (10 years,50 years and 100 years after completion of construction.)PROBLEM STATEMENTThe earthquake occurred on January 26, 2001 at Kachchhregion, Gujarat, with magnitude of 7.0. This event isrecorded at 1 accelerograph station at Ahmadabad.Following is details of ground motion:Fig. 04 Cross section of DeckCONSTANT LOAD ANALYSIS RESULTSThe span moment and support moment of presentbalanced cantilever bridge model is calculated at varioustime stages of life span with the current formulae. Since,there are limitations in direct applications of Trost andWolff Equation to balanced cantilever bridge, onlyDischinger’s equation and Kwak and Son’s equation isconsidered for conventional method of time dependentcontent load analysis. The moments coming fromformulae and from analysis carried out from SAP 2000, iscompared and presented in the graphs bellow. Origin Time – 08:46:42.9 IST Epicenter – 23.400N, 70.280E Focal Depth - 25 kmTable 1 Time History DataIJERTRecording StationAhmadabad(23.400N, 70.280E)Horizontal axis represents time in Days, vertical axisrepresents MomentsMoment(kN.m)Support ndLifeKwak & SonDurationFig.05 Moment Variation Calculation – Support Moment. (kN m)Moment(kN.m)Span Moment20000100000Exact3 Mid Enddays Life 80Vertical238.00.070Three time history data files are available with detailsdescribed above, out of two horizontal time history datamaximum PGA i.e. peak ground acceleration data isapplied to both lateral and transverse direction of thebridge.The moment variation in span and support due toearthquake analysis is represented from the bar chartsbellow. On the bar chart X axis represents time ofapplication of earthquake i.e. 7 days, 10 years, 50 yearsand 100 years after completion of construction. Y axisrepresents corresponding moments (span moment orsupport moment.) Out of the three bars, central red barrepresents the variation in moment due to constant loadonly at time stages of 7 days, 10 years, 50 years and 100years after completion of construction. The green and bluebars represents the maximum and minimum momentdeveloped from earthquake analysis.Exact3 daysDirectionDischngerKwak & SonDurationFig.06 Moment Variation Calculation – Span Moment. (kN m) IJERTV3IS070751www.ijert.org661
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 3 Issue 7, July - 20141.The Dischinger’s equation is compared with detailedanalysis carried out and it was found that for supportmoment, it differs by 17%, 14% and 6% at initial time oflife span, middle of life span and end of the life spanrespectively.2. For span moment the Dischinger’s equation differs by16%, 27% and 28% at initial time of life span, middle oflife span and end of the life span respectively whencompared with detailed analysis carried out.3. When Kwak and Son’s equation is compared withdetailed analysis carried out and it was found that forsupport moment, it differs by 6%, 5% and 4.8% at initialtime of life span, middle of life span and end of the lifespan respectively.4. For span moment the Kwak and Son’s equation differsby 7%, 3.5% and 3% at initial time of life span, middle oflife span and end of the life span respectively whencompared with detailed analysis carried out.5. Hence it can be concluded that the results derived byKwak and Son’s equation are in closed agreement withdetailed analysis carried out.Table 04: Combined seismic and time dependent analysis.7 Days10 Years50 Years100 YearsSupport17273154621529815257End Span6441562855785567Mid Span4435383138043800IJERTMomentkN.mFig.07 Moment variation comparison due to Bhuj, Jan 01 earthquake in Zdirection.CONCLUSION1. For support moment the difference in minimum andmaximum earthquake response at 7 days is 17273 kN m,that for 10 years is 15462 kN m, for 50 years 15298 kN m,and for 100 years earthquake difference is 15257 kN m.This difference is due to time dependent property effect.2.For End Span Moment the difference in minimum andmaximum earthquake response at 7 days is 6441 kN m,that for 10 years is 5628 kN m, for 50 years 5578 kN m,and for 100 years difference is 5567 kN m.3. For Mid Span Moment the difference in minimum andmaximum earthquake response at 7 days is 4435 kN m,that for 10 years is 3831kN m, for 50 years 3804 kN m,and for 100 years difference is 3800 kN m.Constant load analysis (Conventional method)Table 02: The Dischinger’s equation is compared with detailed analysisNo. of Days31800036000Support Moment17%14%6%Span Moment16%27%28%Table 03: The Kwak and Son’s equation with detailed analysisNo. of Days31800036000Support Moment6%5%4.8%Span Moment7%3.5%3%The above study concludes that there issignificant effect of time dependent properties on seismicanalysis of balanced cantilever bridge. Thus detail analysisof each bridge constructed by balanced cantilever methodmust be analyzed considering time dependent properties.Conventional methods of time dependent analysis arestudied and moment calculations were carried out for thebridge as described. The results are compared withdetailed analysis carried out, the following observations, IJERTV3IS070751www.ijert.org662
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 3 Issue 7, July - 2014REFERENCESIJERT[1] Richard Malm, Hakan Sundquist. ―Time dependent analyses ofsegmentally constructed balanced cantilever bridges.‖Engineering Structures 32 (2010) 10381045.[2] Sevket Ates. ―Numerical modeling of continuous concrete boxgirder bridges considering construction stages.‖ AppliedMathematical Modeling 35 (2011) 3809–3820.[3] H. G. Kwak , J. K. Son. ―Determination of design moments inbridges constructed by balanced cantilever method.‖ EngineeringStructures 24 (2002) 639–648.[4] Marc J. Veletzos, José I. Restrepo. ―Seismic response of precastsegmental bridge superstructures with bonded tendons.‖ 4thInternational Conference on Earthquake Engineering Taipei,Taiwan October 12-13, 2006. Paper No. 273.[5] Zdenek P. Bazant, Guang-Hua Li, Qiang Yu, Gary Klein.―Explanation of Excessive Long-Time Defections of CollapsedRecord-Span Box Girder Bridge in Palau.‖ Report, presented atthe 8th International Conference on Creep and Shrinkage ofConcrete (CONCREEP-8), held in Ise-Shima, Japan. September30, 2008[6] Celso Iglesias. ―Long Term Behavior of Precast SegmentalCantilever Bridges.‖ Journal of Bridge Engineering ASCE/May/June 2006[7] Francis T.K. Au, X.T. Si. ―Accurate time-dependent analysis ofconcrete bridges considering concrete creep, concrete shrinkageand cable relaxation‖ Engineering Structures 33 (2011) 118–126[8] P. J. S. Cruz, A. R. Mari. ―Nonlinear Time-dependent Analysis OfSegmentally Constructed Structures‖. Journal of StructuralEngineering / March 1998[09] Marc J. Veletzos, José I. Restrepo. ―Seismic Response Of PrecastSegmental Bridge Superstructures‖ 4th International Conferenceon Earthquake Engineering Taipei, Taiwan October 12-13, 2006[10] CEB – FIP Model code. s[11] IRC 112: Code of Practice for concrete bridges.[12] ACI 209R-92. Prediction of Creep, Shrinkage, and TemperatureEffects in Concrete Structures Reported by ACI Committee 209 IJERTV3IS070751www.ijert.org663
balanced cantilever bridge is carried out on one balanced cantilever bridge model with following steps: 1. The variation in response i.e. moment, stresses etc. during construction and at various time stages during life span of the bridge under constant loads i.e. self-weight, so as to
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