Buckling model of reinforcing bars with imperfections based on concrete lateral expansion

Unsupported bar length (L/d ratio), yield strength fy, and initial imperfections (e/d ratio) are believed to be the buckling factors in existing models for concrete column failure. Only the bar length and yield strength have been considered in existing buckling models, while the initial imperfections have been ignored, as it is so complex to quantify. The e/d ratio is used as a measure to take the initial imperfection of a reinforcing bar into consideration. Tests show that when the e/d ratio increases, the extremum of the skeleton curve gets lower. Through demonstration, the e/d ratio can be inserted into buckling models by quantifying the lateral expansion of the concrete columns. When a longitudinal bar has imperfections, its stiffness depends not only on axial stiffness but also on bending stiffness. Numerical models show that geometry is not the most significant difference between bars with initial imperfections and those without. The three numerical examples show that the most remarkable difference is not a geometrical factor.