An approach based on theorem of total probability for reliability analysis of RC columns with random eccentricity

The load and resistance factors of reinforced concrete (RC) column in many design codes are based largely on reliability calibrations. In these calibrations, the fixed eccentricity criterion is often used and a simple linear failure function is built accordingly. However, the eccentricity of RC column is random under combined random horizontal and vertical loads. In this case, the limit state function may become a complex one. Consequently, there may be large errors in reliability calculation still with the fixed eccentricity criterion. Considering the random distribution of eccentricity, a practical reliability analysis approach is proposed for RC column based on the theorem of total probability. The essential steps of this approach include the solution of probabilistic eccentricity model and the solutions of probabilistic resistance model and probabilistic axial force model within a certain range of eccentricity. Then, such solutions are studied one by one. A main advantage of this approach is that it can explicitly give the ratio of the conditional failure probability within a certain range of eccentricity to the total failure probability. This is of help to design RC columns reasonably. Finally, the reliability calculation of several examples is carried out with the proposed approach. The results indicate that this approach is as accurate as the Monte Carlo method.