System Reliability Analysis Based On Plastic Limit Analysis Theory

System reliability is one of the most difficult parts in reliability theory, of which the distinction of main failure modes and its application to calculate system reliabilities are two difficult points, restricting the development of system reliability. At present it is of urgency to overcome the difficulties for the improvement of structural design criterion, with structural reliability as its foundation.Based on plastic limit analysis and system reliability theory, an elastic compensation method is applied to calculate coefficients of plastic limit loads for complex structures. Furthermore, the random plastic limit load is deduced by Algebra synthesis, taking random factors, such as physical parameters, geometrical parameters, external loads etc, into consideration. Therefore, a method of system reliability analysis is established with random plastic limit load and exterior loads independent of failure modes analysis. Without taking failure evolvement into account, it avoids the present difficulties. The main contents of this paper can be summarized as follows:Firstly, a contrast among narrow bounds expressions (second-order series bounds), proposed respectively by Ditlevsen, Murotsu, Feng and Dong, indicates that results generally tally with each other by both Feng and Dong's methods, varying from the lower bound to the upper bound in Ditlevsen's method.Secondly, a modified elastic compensation method is applied to calculate the coefficient of plastic limit loads for complex frame structure and reinforced concrete rectangular slab, with a contrast between theorems of lower and upper bounds. The analysis indicates that the elastic compensation method, based on an elastic-perfectly plastic material model, can simulate plastic failure mechanisms by adjusting the elastic modulus of each element systemically in a series of iterative elastic analysis. The elastic modulus of each element in a finite-element model is adjusted according to the ratio of the stress in the element to a nominal stress in order to redistribute the stress field away from highly stressed regions. Therefore, a series of different statically admissible stress fields are obtained in a simple and efficient way.Thirdly, a research into the relation between system reliability and the most possible failure mode shows that the former is controlled and can be calculated by the latter when both of them meet proper conditions.Finally, the limit state equation, established by random plastic limit and exterior loads, corresponds with the most possible failure mode. Without taking failure evolvement into account, a method of system reliability is established with the two types of loads, independent of failure modes analysis. Moreover, reliabilities of complex frame structures and reinforced concrete rectangular slabs are calculated by comparisons between traditional methods, where numerical examples prove it accurate, simple, efficient and rational.