Theoretical approaches for modelling buckling effects in rebars of RC members

Buckling of longitudinal bars in reinforced concrete (RC) members is definitely a critical issue in framed structures subjected to seismic loads. Second order effects can affect the compressive stress-strain law of steel bars, influencing ductility calculations of RC structures. Moreover, literature studies show that buckling can occur over a length wider than stirrups' pitch (global buckling mode), involving more stirrups and inducing large deflections in the bar. If the critical length is not carefully estimated, stirrups' failure can occur, causing also the sudden loss of confining effects in concrete. This paper presents the results of different approaches for calculating the critical conditions in longitudinal bars. A discrete mechanical model is proposed, based on the solution of a continuous beam with elastic supports, with deflections restrained in one side to simulate the presence of the concrete core. It allows describing the transition from local buckling (between the stirrups) and global buckling, on the basis of the relative stiffness stirrup-bar. Two other methods corresponding to different computational efforts are also adopted for the sake of comparison. In particular, non-linear finite element analyses are carried out including the effect of strain hardening in the constitutive law of steel and finally, comparisons are made with a simplified closed-form solution proposed in the literature. This last comparison allows to assess the reliability of these expressions and their applications for obtaining parametric considerations useful for design.