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37 Table 4-4. Section properties for cap and column Table 4-5. Dead load shear results for 200 ft/single elements. span skew. Cap 6' x 18' 8' x 8' 7' x 7' 6' x 6' Obtuse (Element 1) Acute (Element 21) Section Column Column Column Column Straight Value Ratio Value Ratio Area Radial -389.35 1 -387.84 1 (ft2) 108 108 64 49 36 2 Skew-Left -605 1.55387184 -190.65 0.49156869 Avy (ft ) 108 108 64 49 36 Skew-Both -392.94 1.0092205 -342.23 0.88239996 Avz (ft2) 108 108 64 49 36 Obtuse (Element 1) Acute Iyy (ft4) 5000 324 341.33 200.08 108 400' Radius Value Ratio Value Ratio Izz( ft4) 5000 2916 341.33 200.08 108 Radial -577.89 1 -189.78 1 Jxx( ft4) 5000 1296 1365.33 800.33 432 Skew-Left -782.91 1.3547734 -58.279 0.30708715 Skew-Both -614.14 1.0627282 -183.66 0.96775213 ratios and standard deviations were also calculated for each group of bridges with same cross-section type and loading. lengths. Therefore, points designated as PC1_6x6_sp3m_dl These results are the primary source of the recommenda- are for a single cell precast bridge (PC1) with a 6 x 6 pier tions for design at the end of this study. Figures 4-15 and (6x6), 3-span configuration of medium length spans (sp3m) 4-17 show the ratios of Curve to Straight Bridge spine models. and dead load response (dl). These figures reveal the limit of radius of curvature beyond Detailed results from the parameter studies are presented which the curvature effects may be ignored altogether and in Appendix E. the bridge may be analyzed as if it were straight. The ratios of "Spine to Grillage Model" shown in Figures 4-16 and 4-18 Conclusions of the Parametric reveal if a curve spine model can be used in cases of tighter Study curvatures and the limit of this type of model to obtain accurate results for design purposes. In the case of the spine Study of the above results led to the following conclusions: models, shear forces were obtained by considering the shear flow from torsion in addition to the vertical shear. The Bridges with L/R less than 0.2 may be designed as if they stresses were also obtained from the combined effect of axial were straight. Figures 4-15 and 4-17 reveal results are force and longitudinal and transverse moments. within 4% of a curved spine model when this is done. Figures 4-15 through 4-19 are for the four bridge cross sec- Bridges with L/R less than 0.8 may be modeled with a tions (cast-in-place single-cell (CIP1), precast single-cell single-girder spine model using a curved (spine) model (PC1), cast-in-place two-cell (CIP2), and cast-in-place five- and lateral effects shall be included in the analysis. cell (CIP5)) with different pier configurations and span Figure 4-18 shows that longitudinal stresses will be Figure 4-11. Typical curved line (spine beam) bridge model (showing 3-span unit).