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Reliability of framed structures is studied assuming loads and component strengths are random variables. The incremental load model is extended to semibrittle failure of components. For brittle component failure, an efficient technique is introduced. The method is also extended to simultaneous multiple loads. Strategies are established to enumerate significant failure modes of a structure. Incomplete failure modes of structures are also studied. The significant modes are used in a Monte Carlo simulation to obtain accurately a safety index for the system. Applications and numerical examples are presented.
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