Probabilistic Study for Ultimate Bending Strength Theory of Reinforced Concrete Section

Abstract

In this study, the ultimate strength theories of reinforced concrete section are investigated probabilistically.
Ultimate bending moment depending upon the popular Hognestade and Whitney theory, and also the Elastic theory which is basic for the working stress design are probabilistically examined. The equations for calculating an ultimate bending moment are based on some assumptions and contain adjusting coefficiens. These assumptions and t coefficients are considered to provide safety margin against variations of the moment. For quantitative evaluation of this safety margin an unexcess probability is applied, which expresses the probability of ultimate bending moment not exceeding its deterministic one with each theory.
Some of the conclusions derived are as follows;
(1) For tensile failure, the safety margin of each theory is unvaried for different design condition and there is no wide difference between the degree of safety margin of each theory.
(2) However, for compressive failure, the safety margin shows different characteristic for each design condition and its degree varies from one to the other.
(3) With elastic theory, as compared with the other theories, under any design condition the results are always on the safe side.