Comparison of Reliability Based Design (RBD) With Eurocode 2 for A Singly Reinforced Concrete Beam

Abstract

This research compares the Reliability-Based Design (RBD) method with the Eurocode 2 (EC2) for a singly reinforced concrete beam. Advanced First Order Second Moment (AFOSM) was used and the equation for the ultimate limit state design consideration for Moment of resistance and Applied moment was applied. The parameters which were all functions of the Ultimate load, G were replaced respectively with variables and their derivatives G(x) obtained with being the characteristic strengths of concrete and the yield stress of steel respectively. Given the original vector space and the transformed reduced vector space, the Taylor series was used to expand the reduced vector space and thus reliability index ßx expressed. The procedure was then coded using JAVA to produce the Reliability Index and Probability of failure for respective steel ratio. The required probability index of 3.9 corresponds to 0.048% of the steel ratio. Typical analysis of a singly reinforced beam according to EC2 for b=300mm, h=500mm, d=447mm, cover of 40 mm, gave a steel ratio of 1.31 %. Comparing this to the reliability-based design of 0.048%, the code provision exceeded the RBD output by 2000 times and 63 times the minimum reinforcement requirement by the code.