Analysis Of Steel Highway Bridges By Line-girder And Exact .

Journal of Structural Engineering & Applied Mechanics2018 Volume 1 Issue 1 Pages ww.goldenlightpublish.comRESEARCH ARTICLEAnalysis of steel highway bridges by line-girder and exact calculationmethodsF. Ulker1, R. Ince2*12General Directorate of State Hydraulic Works, Ankara, TurkeyFırat University, Engineering Faculty, Civil Engineering Department, Elazığ, TurkeyAbstractA three-span steel bridge is analyzed in this research with Line-Girder and SAP2000 program. With the LineGirder method, analysis, calculations and design have been seen to be quite complex, tedious and timeconsuming, with conclusions that are uncertain. It has been demonstrated in this study that the analysis isdone effectively in a short period of time by using precise calculation methods instead of this method andthe appropriate results are achieved.KeywordsApproximate methods; Bridge design; Finite calculation methods; Line-girder; Steel bridgesReceived: 16 March 2018; Accepted: 23 March 2018ISSN: 2630-5763 (online) 2018 Golden Light Publishing All rights reserved.1. IntroductionBridge design and bridge construction methods arequite in the world. Bridges are important structuralsystems in transport, trade and economicdevelopment and contribute to the well-being of thepeople. Bridges in the United States are designedaccording to the specifications published byAASHTO. In Turkey, based on the AASHTOspecification in 2016, “AASHTO Bridge DesignSpecification (LRDF-2010)” has been prepared [13].It is possible to perform analysis and design ofsteel highway bridges by approximate and precisecalculation methods. The Line-Girder method,which uses the influence lines, is an approximatemethod. In 2D and 3D analysis with the SAP2000program, the exact results are achieved using thefinite element technique [4,5].*Corresponding authorE-mail: rince@firat.edu.trMost line-girder (1D) analysis programs useinfluence lines to create moving load envelopes(maximum of maximums). The graphicalrepresentation of the moment effect generated bythe movement of a unit load on the beam is knownas the influence line. Influence lines and influencesurfaces are commonly used to calculate maximumand minimum force effects at a specified point on abridge due to moving loads. The application ofinfluence lines is limited to linear-elasticconstructions. In an isostatic bridge beam, theinfluence line changes linearly. For these systems;the influence line is determined by unit deflections,no force is required. In statically indeterminatestructures, the influence lines are usuallydetermined by a hyperstatic analysis [4].Influence surfaces are used in 2D and 3Dprecise analyzes with the SAP2000 program. Theuse of moving load distribution coefficients in

35curvilinear and skewed bridges, generally does notprovide a suitable solution with the onedimensional Line-Girder technique. In such bridgesystems, it is possible to obtain more sensitiveresults by referring to the influence surfaces of 2Dand 3D precise analysis programs to determine theeffects of moving loads. Both the transverse andlongitudinal position of the moving load is takeninto account by the influence surfaces.2. Analysis by the line-girder methodIn this study, continuous line-girder steel bridgeanalysis is carried out with SAP2000 program withinfluence lines. When analyzing with SAP2000, itis necessary to define a lane especially for vehicleload having moving load. As the line-girderanalysis is performed, only one lane is taken alongthe continuous beam. As the vehicle identification,not a vehicle like the HL-93, a general vehicledefinition is made. The axle load of this generalvehicle is taken as unit and the load of the lane istaken as zero. These loads are affected on the beamand the influence line diagrams are obtained.The HL-93 vehicle load from AASHTO LRFDis considered as the moving load in the steel bridgesystem. The HL-93 vehicle load is impacted onsteel bridge as “Design Truck Load” and “DesignLane Load”. The design truck loads (wheel loads)are placed in spans to obtain maximum momentsand are multiplied by the influence line ordinates.Also, the design lane loads are placed in the firstand last spans where the positive influence lineordinates. 33% impact factor are applied to designtruck force effect. However, the impact factor is notapplied to the design lane load.To calculate the forces created by the uniformlane load, the curvilinear influence line areas aremultiplied by the lane load [4]. However, theclassically calculated curvilinear areas areapproximate and it is caused the results to beapproximate. An appropriate curve function isdetermined in MS-EXCEL to calculate the exactcurvilinear area. Afterwards, using numericalintegration techniques, the real area is calculatedusing this function and the maximum bendingmoments are obtained by multiplying by the laneUlker and Inceload. Hence, an improvement is made in LineGirder method which is approximate analysistechnique, and in a way the results are corrected.The ordinate values of the influence lineobtained with the SAP2000 program are exactresults. However, the program gives the ordinatevalues as a default at certain points. To calculate theenvelope force effects with HL-93 Design Truck,the influence lines is fitted to the curve at MSEXCEL. Thus, the default influence line ordinatescalculated in the SAP2000 program are transferredto MS-EXCEL, two functions are fitted in eachspan, their integration and their total area areobtained. The fictional functions include 20polynomials, and the correlation coefficient is 1.Hence, it is said that this is a well-approach for thedefinitive solution. By enveloping the design truckloads and force effects created by the design laneload, the forces to be considered in design aredetermined. The calculation of these forces, theimpact factor IM %33 given in AmericanAASHTO LRFD Specification and the movingload distribution coefficient LLDF 0.56 are used.3. Analysis by SAP2000 and CSIBridgeprogramsSAP2000 and CSiBridge which are the programs inanalysis of steel bridges are the most commonanalysis and design programs. In these programs,2D and 3D analyzes are performed with finiteelement method and exact results are achieved.After SAP2000 V14 for bridge analysis, CSiBridgeprogram is presented as a separate module. Thebridge analysis is performed successfully in bothSAP2000 v14 Bridge and CSiBridge programs.The complex calculations such as Line-Girder orSAP2000 Influence line analysis have beenextinguished. With bridge programs, the preciseanalysis is performed not only on Line-Girderbridge but also on curvilinear and skewed bridges.Moreover, these programs provide huge flexibilityin the limit situations, loading combinations andcalculation of moving load distribution coefficients[5-7].In analyzing and designing in SAP2000 andCSiBridge programs, HL-93 truck from AASHTO

Analysis of steel highway bridges by line-girder and exact calculation methodsLRFD Specification is taken as a vehicle load.When this truck is defined in the program, TandemTruck (HL-93M), Single Truck (HL-93K), TwoTruck (HL-93S) and Fatigue Truck (HL-93F) areautomatically defined. Also, the dynamic effectcoefficient (impact factor) is included by defaultwith a factor of %33.bending moments are determined. It is necessary tomention that the influence lines obtained arecurvilinear.The ordinate values of the influence lines shownin Fig. 2 are given in Table 1 for each span. In Table1, it is clear that the ordinate values of the influenceline do not indicate any linear change.4. Steel bridge analysis with the line-girdermethodIn this study, the influence lines of a three-spancontinuous steel bridge shown in Fig. 1 isdetermined by the Line-Girder analysis method inSAP2000 program. The continuous beam isanalyzed with SAP2000 program, influence lines isobtained and ordinate values for unit load at eachspan are shown in Fig. 2.In analysis with the Line-Girder method, theunit load was applied to the first span at 0.4L1, tosecond span at 0.5L2, in the third span to 0.4L3distances and the influence line ordinates for the36Fig. 1. Three-span steel bridge beamFig. 2. Influence line ordinate values with the SAP2000 program for three-span continuous bridges

37Ulker and InceTable 1. Continuous bridge beam ordinate values calculated by SAP2000 program1st Span2nd 0331130.00The ordinate of the influence line is the reactionat a specific position of a unit load applied to aspecific ordinate point. Therefore; while a singlemoving load (wheel load) is applied to that point,the magnitude of the wheel load is multiplied by theordinate of the influence line. This process isillustrated in Fig. 3 for the AASHTO LRFD-93design moving load. The lane load is placed in thefirst and third spans where the influence lineordinate was positive.The center wheel load of the HL-93 Designtruck is placed at the turning point of the influenceline in the first span (0.4L1 12 m coordinate). Theordinates of the influence line are given at one-tenthpoint of the span. Also, SAP2000 program gives theordinates at one-tenth point and the span divided by10 slices. Because the front and rear axle loads ofthe design truck do not coincide with the ordinatesof slices, two functions are determined in MSEXCEL for the influence line.The following function can be written for theleft side of the first span line of influence:f x1 0.0021x 2 0.4843x 0.0039(1)The following function can also be written for theright side of the first span effect line:f x2 0.0075 x 2 0.2081x 0.0193(2)In Eqs. (1) and (2), the correlation coefficient is 1.3rd 31.4792.4583.5724.8016.1254.5272.9861.4840.000The front wheel ordinate value is calculatedfrom f(x1) and the rear wheel from f(x2). Theordinate values of front and rear wheels arecalculated as in the equation 3 and 4.f (7.7) 0.0021(7.7) 2 0.4843(7.7) 0.0039 3.858(3)f 13.7 0.0075(13.7)2 0.2081 13.7 0.0193 4.239(4)The area under the influence line is required tocalculate the effect of the lane load. Total area withthe integration of the curvilinear areas f(x1) and f(x2)of the influence line is given in Eq. (5).12I 0.0021x2 0.4843 x 0.0039 dx018 0.0075 x 2 0.2081x 0.0193 dx(5)0 84.07 m 2In Line-girder bridge beams, the dynamic loadfactor (impact factor) is given as IM 1.33 andapplied only to vehicle (truck) load. Because theinfluence lines are applied to one-dimensional (1D)Line-Girder beams, transverse moving load effectsis calculated by applying the multi-lane movingload distribution coefficient (LLDF). According toAASHTO-LRFD 4.6.3.1, the coefficient of LLDF