## 1 Introduction
If the quantitative relationship for the damage condition of hinge joints with live load distribution can be obtained, damage identification of hinge joints can be achieved. Therefore, it is essential to calculate the LLD with the damage of lateral connections. Lateral load distribution theory is to convert the spatial live load analysis into planar one, which plays a significant role in bridge design and construction. The main computing methods are determined by the American Association of State Highway Transportation Officials (AASHTO) Standard Specifications and the AASHTO Load and Resistance Factor Design (LRFD) Specification in the United States [13; 14], while calculated by the rigid-diaphrag method, hinge plate method, etc. in China [15]. [PERSON] et al. [16] proposed a simplified equal distribution factor method of live load shear which originated from  
Figure 1: Hinge joint damage on a simply supported slab bridge. [PERSON]'s [16] method with consideration of the skew angle and span, etc. [PERSON] et al. [17] studied a nine-beam hinged slab bridge which was calculated by comparison with the hinge plate method and the grillage method. [PERSON] et al. [18] proposed a method based on modal properties for computing the LLD, which was verified by comparison with FEM and the traditional simplified numerical method. The abovementioned methods can accurately calculate the LLD of intact bridge, but it will highlight its limitations for the damaged one. Researchers make a further study on the quantitative relationship of damage conditions and LLD. [PERSON] et al. [19] took into consideration the influence of hinge joints and deck pavement damages and evaluated the LLD with various degrees and locations of damages by the combination of hinge plate method and FEM. [PERSON] et al. [20] calculated the LLD under different hinge joints damages and used genetic algorithm to identify the damage degree. [PERSON] et al. [18] utilized the position for cross phenomenon of distribution factor curves between damaged and undamaged bridges as the damage indicator for localizing. The literature demonstrates the great progress in the damage identification of lateral connections, but there is still a great deal of deficiencies. The mentioned methods have their own limitations, for example, it is only suitable for damage identification of a lower degree and it is difficult to guarantee identification accuracy. The purpose of this paper is to establish a modified hinge plate method (MHTM) which can calculate the LLD under arbitrary hinge joint damage conditions. In practical engineering, it is easy to obtain the LLD of simply supported hinged-slab bridges, which can be equivalently calculated by deflection of the bridge. When parameters such as structural geometries and material properties, etc., are known, the damage identification will be solved by means of MHTM, which can be regarded as an inverse problem of LLD calculation with damages. For such problems, swarm intelligence algorithms including genetic algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), and artificial bee colony algorithm (ABC) present favorable performances [21; 22; 23; 24; 25]. For application in practical engineering, [PERSON] et al. [26] determined the best configuration of the phase-locked loop system by [PERSON] et al. [27] who utilized the glowworm swarm optimization algorithm (GSO), which was a new type of PSO, to determine the optimal values of a photovoltaic system, and the results indicated the GSO was obviously superior to traditional algorithms. Among these algorithms, ABC outperforms other algorithms due to its simple structure, easy implementation, and outstanding performance [28; 29; 30], which have been applied in structural damage identification. [PERSON] et al. [31] presented a modified ABC to identify structural systems, which can realize excellent parameter estimation, even with few measurements and high-noise corruptions. [PERSON] et al.