## 1 Introduction  
In recent years, a considerable number of bridges have required replacement, repair, and strengthening owing to their degradation in performance with aging induced by deterioration, accidents, and natural disasters [1]. Maintenance and replacement of an existing bridge or construction of a new bridge is a labor-intensive involving a series of on-site fabrication processes that require a long construction period. Other problems arise, including environmental impacts and passage restrictions around the site. Accordingly, many studies have been conducted on the prefabricated bridges that can cope with various demands such as the minimization of traffic congestion and environmental impacts, cost reduction, securing site safety, and the improvement of quality and constructability [2, 3]. A precast modular bridge involves the application and implementation of a plug-in technique in which a bridge is constructed by combining prefabricated standard members. An additional function can be assigned, and performance can be upgraded by replacing the module. Accelerated construction is enabled in the case of a modular bridge, and uniform quality and economic feasibility improvements are expected through the minimization of cast-in-place construction based on the partial replacement of damaged members using precast members. However, the use of a number of precast membersproduces joints that are disadvantageous in terms of integrated behavior, safety, and serviceability such as in the case involving the deflection of a structure. Accordingly, several studies were conducted to improve the performance of such joints [4; 5; 6]. With respect to the prompt maintenance of a bridge, a study on the accelerated construction of a bridge was conducted by installing a precast deck that could promptly replace the deteriorated deck part of a bridge and by applying cast-in-place ultra-high-performance concrete (UHPC) to the joints [7]. The performances of the joint using high-performance concrete (HPC) and UHPC were verified by applying a prestress [8; 9]. Three types of joint reinforcement shapes were suggested using the shape of a joint, the type and arrangement of reinforcements, and a lap splice as the variables, and a performance test was performed [10; 11]. Moreover, the longitudinal and transverse performances of a U-bar precast joint were verified [12]. Additionally, a headed bar was used to enhance the construction efficiency of the modular bridge and transfer a force sufficiently to the adjacent module with 72% smaller lap length that corresponded to approximately 152 mm [5; 11]. Various shapes of joint were designed and verified as mentioned above. In the case of a precast modular bridge developed in South Korea, the width and cross section of a joint were calculated based on the development and lap splice length of a reinforcement to design a transverse joint between members. The Korean Highway Bridge Design Code (2010) is based on the strength design method. When a joint was designed based on this code, an issue with respect to a limitation of the increased self-weight, caused by the height of the cross sections, to provide a sufficient strength and wide joint width based on reinforcement splice length of criteria was observed. Thus, the bridge design specifications of AASHTO (American Association of State Highway and Transportation Officials) were reflected in the design of the reinforcement development and splice length [13; 14; 15]. However, the current design method used both the strength design method as well as AASHTO design method; thus, the design standard is ambiguous. Therefore, the re-examination of a single design standard is required to optimize the design of a precast modular bridge and to efficiently design a joint. In South Korea, the Korean Highway Bridge Design Code Limit State Design (2015) based on a rational reliability analysis was recently established to secure a design standard in accordance with the international standard system [16].