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31 CHAPTER 4 Global Response Analysis Studies This chapter summarizes the work performed for global Model Verification response analysis and the results and conclusions obtained from this study. Additional detailed results are presented in 3-D finite element analysis using plate and shell elements is Appendix E. accepted as the most accurate level of analysis available for box- girder bridges. However, the magnitude of analysis cases desir- able for parametric studies in this project was such that a more Objective simplified model was desirable. Given that the parametric stud- The global behavior of a curved bridge can be distinctly ies are based on bridges with radial supports, available guide- different from a straight bridge. The curvature results in lines for grillage analysis were used. In order to make sure that off-center placement of loads and, subsequently, such loads the grillage and finite element models produced similar results, induce torsion into the superstructure. The torsion, in a detailed model of a three-span bridge on a tight curve (400-ft turn, causes the shear stresses on the outside of the curve to radius) was created and results were compared for various load increase. Also, the curved geometry of the bridge will result effects. The models are shown in Figures 4-1 and 4-2. The re- in development of transverse moments, which can increase sults for superstructure dead load and a concentrated midspan the normal stresses on the outside edges of the bridge and load obtained from the two models (grillage and finite element) can result in higher tension and/or compression stresses. for a two-cell box are compared in Table 4-1. These results in- Post-tensioned bridges also have an additional equivalent dicate a very close comparison. As a result, grillage models were transverse load, which can result in significant tension on used throughout the rest of the study as the basis of comparisons the inside of the curve and compression on the outside and such results are deemed accurate for all practical purposes. edge. The magnitudes of such effects depend on the radius Guidelines for performing an analysis with a grillage analogy are of curvature, span configuration, cross-sectional geome- included in Appendix C. These guidelines may be used for de- try, and load patterns among other parameters. The struc- sign purposes when the bridge configuration requires it. tural analysis required to capture such effects, in most cases, is beyond the scope of day-to-day normal bridge de- Parameter Studies sign activities. The objective of the global analysis study in this research Analysis Cases was to quantify the effect of increased shear force and nor- To study the effect of various bridge parameters on the re- mal stresses in the cross section, identify common trends, sponse of curved bridges, a parametric study was performed and find approximate modeling methods to obtain accurate which focused on the variation of span configuration and results for design purposes. In particular, shear forces and length, bridge cross-section geometry, and loading. normal stresses due to dead loads, live loads, and post- Four bridge cross-section shapes were considered: tensioning were studied to obtain analysis modeling limitations and develop empirical adjustment factors for · Single-cell box based on a typical cast-in-place cross section, simplified analysis. A set of special studies was also per- · Single-cell box based on a typical precast cross section, formed to review the effect of diaphragms, pier connection · Two-cell box based on a typical cast-in-place cross section, (bearing versus monolithic), and skewed abutments on and curved bridges. · Five-cell box based on a typical cast-in-place cross section.