Analytical and Numerical Methods for the Evaluation of Critical Conditions in Longitudinal Bars of RC Columns

Buckling collapse of reinforcing bars in concrete members is usually observed in framed structures after severe earthquakes. Second order effects modify the compressive response of steel bars, reducing ductility and affecting the post-elastic branch. Literature investigations show that instability can involve more stirrups, or it can be limited to the pitch. If the critical length is not carefully estimated, transverse steel’s failure can be achieved in brittle manner, causing the sudden loss of confinement in the inner concrete. This paper presents the results of a theoretical investigation, aiming to evaluate the reliability of different approaches for calculating critical conditions of longitudinal bars. A discrete mechanical model is proposed, based on the solution of a continuous beam with elastic supports. It allows describing transition from local to global buckling, on the basis of the relative stiffness between stirrups and bar. Two other approaches with different computational efforts are also analyzed for comparison. In particular, non-linear finite element analyses are performed, including the effect of 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 evaluate the reliability of simplified expressions, able to give design provisions