Calculation of the reliability of frame systems under seismic impact and survivability assessment during the formation of plastic hinges in the nodes

Aim. The research aims to develop mathematical models for evaluating the reliability of two-story frame systems under the seismic impact, covering all possible ways of transition to the mechanism state due to the formation of plastic hinges in the frame nodes. Methods. The study is based on the application of the theory of Markov random processes in continuous time and their discrete states to describe the transition of a system into a different state. Such states include faults resulting from the formation of plastic hinges in the frame nodes. Results. Possible schemes of forming plastic hinges in two types of statically indeterminate frames under horizontal seismic impact are described: in the frame of a 2-story industrial building with a large-span upper floor and with the support of the roof truss on the heads of columns and a two-story two-span frame of a simple regular structure with rigid nodes. Possible states are noted and transition graphs are compiled, which are typical for the frames under consideration in the case of rigid disks of floor slabs during seismic impact, represented as a stationary random process. By representing the transition of systems to the states under consideration caused by the formation of plastic hinges in one or another sequence under seismic action in the form of a Markov random process in continuous time and discrete states, systems of first-order differential equations describing these transitions are obtained. Having solved them by applying the Laplace transform, analytical expressions for estimating the probabilities of finding frame systems in the states under consideration and expressions for estimating the probabilities of failure-free operation of these systems are obtained. Conclusion. By constructing transition graphs covering all possible states of frame systems during the formation of plastic hinges in nodes under seismic action and describing the process of frame transitions from one state to another by a Markov random process in continuous time and discrete states, analytical expressions for evaluating the probabilities of these system states, as well as their reliability and survivability under seismic action, can be obtained.

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