PSI - Issue 44

Francesca Barbagallo et al. / Procedia Structural Integrity 44 (2023) 363–370 Francesca Barbagallo et al. / Structural Integrity Procedia 00 (2022) 000 – 000

364

2

1. Introduction Beam-column joints are fundamental components of the system of resisting mechanisms that allows RC framed structures to resist seismic excitation. In the joint, the bending moment experiences a large variation in a short length, which determines horizontal and vertical shear forces of magnitude many times larger than that of shear forces of the adjacent members. Hence, in new designed buildings, horizontal and vertical reinforcements of the beam-column joint must be properly sized to sustain this large shear force, avoid the failure of the joint, which is a fragile component of the structure, and allow the development of the target collapse mechanism with formation of flexural plastic hinges in the end parts of the adjacent beams. To this purpose, capacity models that provide a reliable estimation of the shear resistance of beam-column joints are needed, to avoid under or oversizing of the joint reinforcement, and they should be simple enough, to allow the derivation of design equations from those of the capacity model. Effective capacity models for beam-column joint resistance are of paramount importance also in the assessment of existing RC framed structures, whose joints are often a critical component. Eurocode 8 (2005) bases the verification of the RC beam-column joint on the stress field determined in the uncracked concrete joint by the horizontal and vertical shear forces, the axial force transmitted by the column above the joint and the confinement effect of the horizontal reinforcement if it is present. The capacity is assumed equal to the horizontal shear force of the joint that determines principal tensile and compression stresses equal to concrete tensile strength or compression strength (reduced because of the presence of tension in the orthogonal direction), respectively. The capacity model is very simple but largely underestimates the joint shear resistance when the axial force is small. Statically indetermined strut-and-tie models were developed to better replicate the stress fields induced by seismic excitation in the RC joint, which is generally cracked, and consider all the possible resisting mechanisms activated in the joint. For instance, the capacity model proposed by Hwang and Lee (1999, 2000) considers three strut and-tie resisting mechanisms: a diagonal compression strut that connects the interception points of the external longitudinal rebars of beam and column, a horizontal mechanism constituted by two flat concrete struts and intermediate horizontal joint rebars, and a vertical mechanism that includes two steep concrete struts and intermediate vertical joint rebars. More recently, Fardis (2021a, 2021b) formulated a RC joint capacity model that considers two resisting mechanisms related to the stress fields in concrete, horizontal and vertical reinforcement. The concrete part of the joint is divided in a central diagonal strut and two triangular side-zones. The inclination  of the diagonal, which is assumed equal to that of the principal compression stress, is determined under the condition that it should maximize the shear resistance of the joint. This model is fully consistent with that stipulated in Eurocode 8 for shear design of RC members and it is simpler than that of Hwang and Lee. However, it still requires an iterative procedure to evaluate the joint resistance that may result impractical, especially to design the joint reinforcements. In this paper, an alternative capacity model for shear resistance of RC joint is formulated and validated. This model retains the hypotheses of the model of Fardis, but assumes also that the horizontal and vertical joint rebars are yielded. This further assumption simplifies the equations of the capacity model and eliminates the need of the iterative procedure. The proposed capacity model maintains the consistency with that stipulated in Eurocode 8 for shear verification of RC members. A parametrical analysis is presented to demonstrate that this model predicts joint resistance always very close to that determined by the model of Fardis. Finally, analytical equations (based on the proposed capacity model) for the design of joint reinforcements are discussed and used to obtain joint shear resistance and amounts of joint reinforcements in closed form. 2. Design shear strength of a beam-column joint according to Fardis model The capacity model proposed by Fardis (2021a, 2021b) and incorporated in the last draft of Eurocode 8 (2020) subdivides a joint in two triangular zones subject to shear (portions A in Fig. 1b and c) and a diagonal compression field B inclined of  with respect to the vertical. Being  the angle between the vertical and the diagonal of the joint (Fig. 1a), if  <  the diagonal compression field transmits the horizontal shear force from column to column (Fig. 1b) while when  >  the horizontal shear force is transmitted from beam to beam (Fig. 1c). Horizontal and vertical reinforcements of the joint are indicated as A sh and A sv , respectively (Fig. 1a).