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38 Figure 4-12. Typical curved grillage bridge model (showing 3-span unit with 3 webs). unconservative by less than 4% up to this limit unless the Bearing forces (i.e., shear at the abutments) obtained from bridge has a low span length-to-width ratio (i.e., short- a spine model must consider the effect of torsion. Bearings span 5-cell sections) must be designed considering the curvature effect. Bridges with L/R larger than 0.8 shall be analyzed with more detailed analysis models such as grillage or finite ele- Special Studies ment models. Figures 4-16 and 4-18 reveal that spine beam analysis will generally become increasingly unconservative In addition to the above parametric study, special studies beyond the 0.8 L/R limit. were performed to get a better understanding of the effect of Curved bridges with length-to-width ratios of less than 0.2 diaphragms, bearing conditions, skewed abutments, and and an L/R larger than 0.2 also require detailed analysis as long-term creep when combined with curved geometry. revealed by the unconservative results for tightly curved short-span 5-cell bridges in Figures 4-16 and 4-18. Diaphragm All 5-cell grillage bridge models used in the parametric Two-Cell CIP Dead Load: Midspan Moment study were also modified to have a stiff diaphragm in the -70000 -60000 -50000 -40000 -30000 -20000 -10000 0 center of each span. The results from each model with and 0 without diaphragms were compared for dead load, live load, -10000 and post-tensioning. These results were compared using scatter-grams and ratios (line diagrams) similar to the results -20000 Single Line Model shown in Figures 4-19 and 4-20. The overall conclusion from -30000 these results is that interior diaphragms have minimal effect on the shear and stress responses and therefore may be elim- -40000 inated altogether. -50000 To verify the conclusions relative to interior diaphragms, the two-cell finite element model used in the model verifica- -60000 tion studies was modified to include interior diaphragms. These diaphragms were placed at the center of one of the end -70000 spans and at one of the third points in the center span. These Grid Model diaphragms were located on one side of the midpoint of Figure 4-13. Scatter-gram comparison of results the bridge, which was otherwise symmetrical. Results were from spine and grillage models. compared on both sides of the bridge and found to be nearly