A nonlinear model of failure function for reliability analysis of RC frame columns with tension failure

• A nonlinear failure function model is proposed for RC column with tension failure.
• The interaction curve of ultimate loads is nonlinear with positive correlation parts.
• The model can be used to obtain an accurate reliability result.
• The reliability variation can be predicted more effectively based on this model.
• The reliability is lower when the eccentricity produced by vertical load is smaller.

Based on the accordant capacity models in American and Chinese design codes, a nonlinear failure function of reinforced concrete (RC) frame columns with tension failure is built under combined vertical and horizontal loads. Then, we identify that the interaction curve of ultimate vertical and horizontal loads shows special characteristics; it is a nonlinear curve with some positive correlation parts, which is largely different from the case of a simple linear failure function as adopted in codes. The ratio of the positive correlation part to the whole curve is also studied. Subsequently, a practical nonlinear failure function model is built with the series expansion technique. Numerical simulation proves that the proposed model can be used to obtain an accurate reliability result, an effective prediction of reliability variation and also a convenient prediction of low reliability cases. The results based on this model indicate that there is a strong difference in the reliability of RC columns designed with the same safety factor but with different design parameters, and the reliability would be lower when the eccentricity produced by vertical load is smaller.