# Unified Simplified Capacity Model for Beam-Column Joints into RC Moment Resisting Frame
## 1 Introduction
Strengthening based on fiber-reinforced polymer (FRP) or fiber-reinforced cementitious matrix (FRCM) [53; 54; 55; 56; 57; 58; 59] can be used to improve the structural capacity of RC joints. The best strategy depends significantly on the mechanical performance of the concrete support [60; 61]. Furthermore, these systems allow the application of local structural improvements without changing the global behavior [62; 63]. In particular, they can be used to improve the structural capacity without modifying the stiffness [64; 65]. The behavior of unreinforced and strengthened RC joints is a crucial aspect, especially from a designer point of view. Semi-empirical approaches to designing new RC joints are provided by recent building codes. Traditional strut and tie or truss models to predict the shear strength mechanism offer some drawbacks, especially for existing structures, as demonstrated in many scientific works [66; 67; 68; 69]. These are based on laboratory testing and, therefore, are characterized by limited applicability. Furthermore, these models neglect the impact of other key factors, such as the extent of the axial load or the flexural capacity of the members converging in the RC joint. Some studies have provided first efforts to identify the main key factors by means of a mechanical model [70; 71]. They constitute the basis of the improvements provided by the proposed model. Starting from the existing experimental results, it has been observed that the joint failure is not always due to an exceedance of joint shear stress capacity. This aspect is due to a particular phenomenon which has been experimentally observed (i.e., joint shear stress and story shear do not reduce equally during experimental tests [72]). A recent study [73] proposed an improved non-linear model for beam-column RC joints with additional calibrations. This model includes the influence of joints on seismic performance of RC frames in numerical analyses with their deformability, including several failure modes, such as the bond-slip behavior. Further studies [74] implementing this model on more complex structures (Finite Element Models (FEM)) have clarified many key factors in the behavior of beam-column RC joints. Other non-linear models based on rotational hinges have been refined [75], or macro-element models have been outlined [76], in order to simulate the ultimate behavior of the RC joints. However, this has led to complex and cumbersome FEM models, which are usually not acceptable for practitioners. This topic boasts several available scientific works in the literature, as several beam-column joint models have been proposed. Many of them are essentially oriented to research coupled with detailed and refined modeling of the structures. However, such models also have benefits and shortcomings; hence, there is definitely no wide consensus on which is the best modeling approach. The present paper proposes a unified, simplified approach suitable for analyzing seismic-resisting frames and detecting beam-column RC joint failure, thus obtaining a balance between practicality and accuracy.