To increase utilization of the old beam bridges with narrow deck and inadequate bearing capacity, the incremental loading balance method (ILBM) was proposed based on theoretical analysis and the widening and reinforcement method with longitudinal and transverse beams. Calculation analysis models of old beam bridges before and after reconstruction were established based on the fundamental principle of elastic mechanics and the principle of generalized force equilibrium, respectively. From the comparison of these two models, the method of calculating and optimizing sectional dimensions of new longitudinal and traverse beams was developed. Finally, the reliability and validity of the proposed method were verified using a 20 m-span simply-supported prestressed concrete girder bridge which is located in Yueyang City, Hunan Province of China. Results show that the ILBM could determine the size of new longitudinal and traverse beams. The stiffness of longitudinal beams is determined by the incremental bearing capacity of the entire bridge, whereas that of traverse beams is determined by the incremental bearing capacity of the single beam. The widths of the longitudinal and traverse beams increase with the increase in their stiffness, and the heights decrease with the increase in bending moment of the old bridge. The study can meet the demand of the reconstruction of old bridges.

The bearing capacity of old assembly slab bridges is reduced by component cracking, material aging, and structural damage. To avoid excessive dismantling of bridges with inadequate bearing capacity, the influence mechanism of overlaid pavement on existing assembly slab bridges was analyzed by theoretical analysis and numerical simulation in this study. The basic equation for assembly slab bridges was established by considering the bending resistance and shearing resistance of the overlaid pavement and based on the fundamental principle of force method. The formula for the vertical coordinate of the influence line of the transverse load distribution (TLD) was constructed using a half-sine unit load. On this basis, the variations in the vertical coordinate with rigidity, slab width, and bridge span were analyzed. Moreover, the influences of the overlaid layer thickness on assembly slab bridges with different spans (13, 16, and 20 m) were analyzed. Results show that the overlaid pavement can significantly affect the influence line of the TLD. The influence of the overlaid pavement on the TLD factor should be taken into account for assembly slab bridges with spans of 16 m or smaller. However, such influence is negligible for bridges with spans of 20 m or larger. The overlaid pavement can increase structural integrity and reduce the TLD factor to some extent. But an overlaid pavement thickness of more than 20 cm only slightly influences the TLD factor. The study can meet the demand of reconstruction of old bridges based on overlaid pavement. The proposed method solves issues related to the low bearing capacity of these old assembly slab bridges.