The evaluation of the bending stresses in curved bridges indicated that fbu and fl
are deeply affected by the curvature and the position of the girder, i.e. outer or inner girder.
The analyses showed that the major-bending stresses in curved bridges are independent of the cross-frame spacing. However, they increase linearly with the curvature in the positive moment regions of the end spans. Conversely, these stresses at the middle span of the outer girder are not significantly affected by the curvature. Therefore, a linear model was proposed to estimate the major-bending effects in the positive moment regions of both exterior girders. This model computes the major-axis bending in curved bridges based on the major-axis bending stresses exhibited by their
straight counterpart. Therefore, the proposed equation allows estimating fbu in curved
bridges from structural analyses of simplified straight bridges. In the negative moment regions, the major-bending stresses also exhibit a linear trend but it is independent of the span length.
The assumption of computing fbu based on a simplified model with the real arc
length of the curved girder does not help to represent the curvature effects on fbu. In fact,
the AASHTO recommendation of ignoring the curvature effects for fbu when L/R is lower
than 0.06 introduces an error of approximately 10% in long span bridges.
The LFB in curved girders is caused by both the curvature and the overhang loads. However, it was shown that the participation of the overhang loads in the LFB is low compared to the curvature effects. In fact, the overhang-to-curvature effect ratio reduces as the length of the span and the curvature increase. Therefore, the overhang term was dropped from the final expression proposed for the LFB which simplifies to the curvature term only. However, the torsional effects due to overhang loads are implicitly considered since the curve fitting process is applied to the total LFB obtained from the parametric study. A comprehensive formulation to estimate the LFB effects due to curvature was developed for distributed and concentrated loads, respectively. The critical case between the top and bottom flanges was selected to define the equations proposed in this work to estimate the LFB in curved bridges.
The results indicated that the LFB is practically unaffected by the variation of the curvature, a slight effect was only observed in the positive moment regions of the middle span. This observation indicates that these effects need to be considered even in bridges with large curvature radii.
The equations proposed in this project to estimate the LFB in curved bridges work adequately in both exterior girders. Significant reductions were found in most of the cases compared to the estimations given by the AASHTO Specifications.
The major-axis bending effects in the AASHTO equation were computed using both the numerical and the estimated major-axis bending stresses, obtaining similar results. The estimated major-axis bending stresses correspond to the stresses computed
using the equation proposed in this work to estimate fbu in curved bridges from the results
obtained in their straight counterpart. Therefore, the LFB in a curved bridge can be conservatively approximated using the code equation together with the major-axis bending from the corresponding straight bridge. The advantage of the proposed equations over the code approximation is that it is not required to know in advance the major-bending effects to compute the LFB. However, the principal disadvantage is that different expressions are required to define the effects of distributed and concentrated loads, while the code approximation consists of one single equation that applies for all load cases independent of the girder location and flange position.
However, the results from the parametric study indicated that the code equation fails to predict the LFB due to distributed loads at the inner girder of highly curved bridges with long spans. Therefore, it is recommended to use the equation proposed in this work which predicts satisfactorily the LFB in all cases. It was also observed that the bottom flange under concentrated loads exhibits the most critical LFB effects compared to the top flange, especially for short span lengths.
The results indicated that the outer girder exhibits the most critical combined bending effects. On the contrary, the curvature decreases the magnitude of the major- bending stresses in the inner girder resulting in a combined bending action much lower than that corresponding to the outer girder. Therefore, the design of both exterior girders shall be based on the evaluation of the outer girder, unless an optimization of the inner
girder is pursued. In that case, the effects of the girder stiffness in the behavior of the whole cross section of the deck shall be investigated.
In general, it is recommended to distribute the cross frames such that a cross frame is placed at the maximum vertical bending moment to decrease the combined