## 1 Introduction  
Statically indeterminate reinforced concrete (RC) structures are some of the most common structural forms in engineering design. Owing to the cracking of the concrete, the strain penetration of the reinforcement, and the formation and gradual rotation of the plastic hinge regions, the relative stiffness of each cross section changes constantly during the loading process, which causes a redistribution of internal forces in the statically indeterminate structure. In structural design, the moment redistribution is considered since it can help to avoid the reinforcement congestion at critical sections, thereby improving the convenience of the construction and the correcting conditions. Moreover, moment redistribution can help fully exploit the reserved capacity of the non-critical sections and achieve an economic design. For practical applications, the current design codes allow designers to take advantage of linear elastic analysis with limit moment redistribution for structural design, in which the moment diagram derived from the elastic analysis of the structure is modified based on the degree of moment redistribution. Many definitions for measuring the moment redistribution have been proposed. The coefficient of the moment redistribution \(\beta\), defined by [PERSON] [1] and adopted in various design codes, is shown in Equation (1):  
\[\beta=\frac{M_{\text{elast}}-M_{\text{red}}}{M_{\text{elast}}} \tag{1}\]  
where \(M_{\text{elast}}\) is the elastic moment calculated by the elastic theory, \(M_{\text{red}}\) is the actual moment after moment redistribution, and \(\beta\) is between 0 and 1. A reasonable consideration of the degree of the moment redistribution is important for the analysis and design of structures. Traditionally, moment redistribution is considered to be heavily dependent on the ductile behavior of the critical section [2]. In most design provisions, moment redistribution is mainly related to the neutral axis depth factor (the ratio of neutral axis depth to the section effective depth), since it can well characterize the ductility of a section by combining the characteristics of the materials and the geometry of the cross section. In fact, evaluation of the moment redistribution is complex because it depends on the rotation capacity of the plastic hinge as well as the variation in the stiffness distribution and the bond between the reinforcement and concrete [3]. Numerous studies have focused on the behavior and influencing factors of moment redistribution in statically indeterminate structures. Nearly all of these studies are based on a basic model of continuous beams subjected to static loads. By using the concept of ductility demand, the effects of various parameters, including slenderness, stiffness, ratio of tensile and compressive reinforcement, concrete strength, and strength of the reinforcement, on the moment redistribution in continuous RC beams were studied by [PERSON] [4] and [PERSON] et al. [5]. Based on the experiments of continuous RC beams, [PERSON] et al. [3] concluded that a decrease in the tensile reinforcement and increase in the compression and transverse reinforcement would be beneficial for the moment redistribution. However, for high-strength concrete beams, the influence of the transverse reinforcement ratio is not significant, as observed in the experimental studies conducted by [PERSON] and [PERSON] [6]. Their study also indicated that the relationship between mid-span reinforcement ratio and intermediate-support reinforcement ratio had a significant effect on moment redistribution. [PERSON] et al. [7] experimentally studied the whole process of the moment redistribution in continuous RC beams. Their results show that the moment redistribution evolves through several stages and the parameters, such as the cross-section size, concrete strength and arrangement of the reinforcement, affect the moment redistribution in each stage.