Collapse Probability for Elasto-Plastic Beam Structures

In present design practice considerations on structural safety are usually concentrated on failure states corresponding to initial failure of an element. For a frame structure that means failure of a cross-section of the structure. Sufficient reliability with respect to this limit state is expected to be achieved by designing the structure on an element basis such that each member has at least a presctibed reliability. Most structures are redundant in the sense that failure of the first single element merely leads to redistribution of the load. The system reliability of the structure is in this paper defined as formation of a yield mechanism. System reliability aspects can be important in structural design and it is therefore relevant to consider limit state progressive failure in a probabilistic setting.
In reliability studies of progressive failures the analysis with respect to plastic collapse under proportional loading of linear elastic - ideal plastic structures has been undertaken in numerous works, but only a few authors have considered interaction of load effects in the yield condition. These works can be divided into two different formulations namely a total- and an incremental approach. The incremental approach has been used by Amdahl, Leira & Wu (1] and the total approach by Bjerager (2], Bådshauge & Bach-Gansmo (3], Ditlevsen (4], Høj & Loklindt (6], Murotsu, Okada & Matsuzaki (8] and Turner & Baker (12].