Modeling of reinforcement global buckling in RC elements

Abstract

Buckling of longitudinal reinforcement in reinforced concrete (RC) columns or walls is commonly seen with a length equal to the spacing between stirrups (local buckling), but experimental observations have shown that the length of buckling can span a larger length, deforming several stirrups within the buckling length (global buckling). The behavior of the longitudinal reinforcement under compression resulting in global buckling is studied in this work, based on a concentrated plasticity fiber model that considers four (4) plastic hinges. The model was originally validated for local buckling and here is extended to global buckling by introducing the effect of transversal reinforcement and expansion of the core concrete in the analysis. Modeling of the forces from the stirrups acting on the longitudinal bar assumes that part of the force is transferred directly to the expanding concrete core and the remaining force is balanced by internal stresses in the longitudinal bar. The bar buckling behavior is evaluated for different buckling length values and the length is chosen such that it delivers the lowest maximum stress. The proposed model is validated by comparison of the predicted buckling mode with experimental test results from the literature. The average error in the mode prediction is 0.59 (about half the space between stirrups), which is a reasonably good value considering that the database of tests used covers buckling modes from 1 to 7 (stirrup spacing). Besides of providing good critical buckling length predictions, it allows obtaining the stress versus strain curve for the overall buckling bar. Analysis of three column specimens from the literature indicates that the overall stress versus strain response can be obtained with a reasonable accuracy. Peak stress is obtained within an error of about 10% compared to the test result for a strain well represented by the model. The post-peak slope also gives a good estimate for the degradation stage.