Abstract
Mathematical models are presented for calculating the stress–strain state (SSS) of structures under seismic impacts. The general mathematical formulation for determining the SSS is considered. For linear models, two methods are presented for calculating the SSS characteristics by decomposition of the eigenvectors: a method that integrates the time equations for given accelerograms of the base and a method that uses standard seismic spectra. In calculating seismic spectra, various methods for summing the tones of oscillations of structures are proposed to evaluate the structural response. In order to assess the forces and moments of interaction between a structure and the foundation supports and to test the calculation programs, mathematical models of structures are presented in the form of simple mechanical analogs: angular oscillators. These calculation methods take into account building code requirements and have been adapted to modern software packages that use the finite element method.
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