# Simplified Plastic Hinge Model for Reinforced Concrete Beam-Column Joints with Eccentric Beams
## 1 Introduction  
For a safe and cost-effective design of building structures, the performance-based earthquake design is widely used. For the design approach, nonlinear behavior of structural components should be well described in analysis, including deformation capacity. In the case of reinforced concrete (RC) moment frames, the deformation capacity is significantly affected by shear damage and bar-slip at beam-column joints [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11], and the joint shear damage and bar-slip are unavoidable even if the requirements of current seismic design codes [12; 13; 14; 15] for beam-column joints are satisfied. Thus, to achieve a reliable design of RC moment frames, those characteristics affecting the nonlinear behavior of beam-column joints should be carefully considered in the analysis. In practice, a lumped plastic hinge spring element is predominantly used for beam-column joints, because it is available in most of commercial software for nonlinear analysis [16; 17]. Thus, it is reasonable to reflect those characteristics in the plastic hinge spring element. Meanwhile, joint shear strength degradation is also critical to the deformation capacity of beam-column joints. To address the nonlinear behavior of beam-column joints, a vast number of studies have been conducted: idealizing models, such as the strut-tie mechanism-based models [7; 8; 9; 10; 18; 19; 20] and the rotating-angle softened-truss model [21], and empirical equations [12; 22; 23] were proposed; the strain-increase in beam flexural bars due to cyclic loads was considered in the prediction of the joint shear strength degradation and deformation capacity [6]; the effects of joint shear demand, joint hoop bars, and yield strength of beam flexural bars on the joint deformation capacity were considered [24]; the effects of bar-slip, bar elongation, diagonal cracking, and shear deformation on the joint shear strength degradation were studied [8]; and the joint shear strength was defined as a function of target lateral drift ratio [9; 10]. Although the existing studies provide a deepunderstanding on the behavior of beam-column joints, the majority of the existing studies focused on concentric beam-column joints. However, eccentric beam-column joints, in which the axis of beams framing into a joint does not lie on the column centerline, are also common in practice. To investigate the effect of eccentric beams on the joint shear strength, several experimental studies were performed, and it was found that as the beam eccentricity increased, the shear strength capacity and ductility were decreased at interior [25; 26; 27; 28; 29; 30; 31] and exterior [32; 33; 34] beam-column joints. To consider the degradation in the shear strength of eccentric beam-column joints, a simple method of reducing the effective joint width was also proposed [27; 28]. On the other hand, it was found that slabs can alleviate the shear strength degradation of eccentric beam-column joints [35; 36]. Although the existing studies investigated the joint shear strength of eccentric beam-column joints, the deformation capacity and strength degradation were not evaluated, which were necessary for nonlinear analysis modeling. Recently, for an improved performance-based design, [PERSON] and [PERSON] [37] developed an advanced plastic hinge model, which is applicable to interior and exterior beam-column joints. In the model, the effects of beam bar-slip and joint shear strength degradation were taken into account covering various design parameters, and the joint shear deformation and beam flexural deformation were also combined for simple modeling and computation. However, the existing models, including the model of [PERSON] and [PERSON] [37], were developed primarily for concentric beam-column joints. Thus, more studies are required for eccentric beam-column joints, considering the facts that a considerable number of RC structures are designed to have eccentric beam-column joints in practice and the design of RC structures is subjected to seismic and dynamic influences.