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41 All 3-Span fline /fgrid Dead Load CIP1_6x18_sp3l_dl 1 CIP1_6x18_sp3m_dl CIP1_6x18_sp3s_dl CIP1_6x6_sp3l_dl CIP1_6x6_sp3m_dl 0.99 CIP1_6x6_sp3s_dl PC1_6x18_sp3l_dl PC1_6x18_sp3m_dl 0.98 PC1_6x18_sp3s_dl PC1_6x6_sp3l_dl PC1_6x6_sp3m_dl fline/fgrid PC1_6x6_sp3s_dl 0.97 CIP2_6x18_sp3l_dl CIP2_6x18_sp3m_dl CIP2_6x18_sp3s_dl 0.96 CIP2_7x7_sp3l_dl CIP2_7x7_sp3m_dl CIP2_7x7_sp3s_dl 0.95 CIP5_6x18_sp3l_dl CIP5_6x18_sp3m_dl CIP5_6x18_sp3s_dl CIP5_8x8_sp3l_dl 0.94 CIP5_8x8_sp3m_dl 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 CIP5_8x8_sp3s_dl Length/Radius (L/R) Figure 4-18. Ratio of outside corner dead load longitudinal stress from spine to grillage model. skew support at both ends, see Figure 4-21. The abutments for curved bridges. These corrections will be necessary when were supported on rollers. The obtuse and acute abutment the bridge is designed using a spine beam analysis. Skew can shear values were compared in straight and skewed bridges be automatically accounted for in a grillage analysis approach with and without curved alignment. The simple span bridge as shown in Figure 4-21. results were compared for dead load and live load and the three span results were compared for dead load responses. Long-Term Creep The results are shown in Tables 4-5 through 4-7. The final outcome of these results is that the curved alignment does not The effect of the time-dependant properties of concrete aggravate the effect of skewed abutments and therefore, any (principally creep) on the response of curved bridges was consideration taken for straight bridges can be equally valid investigated using the LARSA 4D computer program, which Midspan Outside Shear (kips) Midspan Outside Corner Stress (ksi) 1.0005 1.003 1 1.002 With/Without Diaphragm With/Without Diaphragm 1.001 0.9995 1 0.999 0.999 0.9985 0.998 0.997 0.998 0.996 0.9975 V_Out Sp1_M Sp1_S 0.995 St_O Sp1_M Sp1_S Sp3_L Sp3_M Sp3_S Sp3_L Sp3_M Sp3_S 0.997 0.994 200 400 600 800 1000 Straight 200 400 600 800 1000 Straight Radius (ft) Radius (ft) Figure 4-19. Scatter-gram comparison of live Figure 4-20. Line graph of ratio of results load results from grillage models with and from grillage models with and without without interior diaphragm. interior diaphragm.

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42 Skew at One Abutment Only Skew at Both Abutments Figure 4-21. Skew configurations studied. can consider both the 3-D geometry of the bridge plus the The torsion reaction and thus the relative bearing forces time-dependant behavior of concrete. The same structure in continuous curved concrete box-girder bridges vary used in the comprehensive example problem was analyzed over time and depend on both the radius of the curve and over a period of 10 years. The bridge was modeled as a 3-D the relative length of the end span with respect to the cen- spine beam. In addition, the model was modified by chang- ter span. The forces in outside bearings will increase and ing the curve radius in two cases and changing the length of inside bearings will decrease. Given the many possible the end span in another case. Therefore, four models were bridge-framing configurations, it is difficult to make an evaluated. In all cases the abutments were fixed against tor- accurate assessment of time-dependent bearing forces. sion. The end span and radii of these bridges are shown in The above study assumed bridges constructed on false- Table 4-8 work. Segmentally constructed bridges are expected to The long-term deflection of Models 1 through 3 did not behave differently. appear to be affected by the radius of the bridge. Therefore, The LARSA 4D program does not consider torsion creep, methods used for adjusting cambers for straight bridges as is the case with most other commercially available would appear to be applicable to curved bridges analyzed as software. Torsion creep is expected to mitigate long-term three-dimensional spine beams. changes in bearing forces, as would modeling the flexibil- The major concern, however, was abutment bearing re- ity of bearing systems subjected to torsion loads from the actions. These will change over time. This is manifested by superstructure. the change in the torsion reaction at the abutment, which in turn will affect the bearing reactions. Table 4-9 summa- Given these conclusions, it would appear to be safe to an- rizes the dead load and prestress results from the four alyze curved concrete box-girder bridges using commercially models investigated. available software, particularly for segmentally constructed The following conclusions can be drawn from this limited bridges. It is recommended that the vertical flexibility of bear- study: ings be considered in these analyses. Table 4-6. Live load shear results for 200 ft/single Table 4-7. Dead load shear results for 400 ft radius, span skew. 200/300/200 ft multi-span skew. Obtuse (Element 1) Acute Obtuse (Element 1) Acute Straight Value Ratio Value Ratio Straight Value Ratio Value Ratio Radial -577.89 1 -189.78 1 Radial -297.35 1 -296.59 1 Skew-Left -782.91 1.3547734 -58.279 0.30708715 Skew-Left -378.79 1.27388599 -197.35 0.66539668 Skew-Both -614.14 1.0627282 -183.66 0.96775213 Skew-Both -378.02 1.27129645 -197.66 0.66644189 Obtuse (Element 1) Acute Obtuse (Element 1) Acute 400' Radius Value Ratio Value Ratio 400' Radius Value Ratio Value Ratio Radial -81.618 1 -12.007 1 Radial -370 1 -202.2 1 Skew-Left -116.15 1.42309295 12.526 -1.0432248 Skew-Left -452.84 1.22389189 -135.81 0.67166172 Skew-Both -85.079 1.04240486 -9.1316 0.76052303 Skew-Both -453.89 1.22672973 -135.81 0.67166172

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43 Table 4-8. Models of two-cell bridge used to study the effect of creep. Model Number Radii (ft) End Span Length (ft) 1 400 200 2 800 200 3 1600 200 4 400 140 Table 4-9. Time dependence of abutment torsion moment. Model Number Torsion Moment Torsion Moment % Difference 7 Days (ft-kips) 3600 Days (ft-kips) 1 -8826 -10034 13.7 2 -7357 -9262 25.9 3 -6395 -8500 32.9 4 -4012 -5842 45.6 In the absence of such an analysis, it is recommended gating factors not considered in this limited study, it should that dead load torsion reactions at the abutment from a provide a reasonable hedge against bearing failure. In the 3-D spine beam analysis be increased by approximately case of a grillage analysis, the same adjustment can be made 20% for the final condition and bearings or bearing systems by resolving bearing reactions into a torsional moment, in- be designed to envelope both the initial and final condi- creasing that moment by 20%, and recalculating the new tions. This is a crude recommendation, but given the miti- bearing forces.