The creation of a mathematical model of physically nonlinear oscillations of a multistory frame

The paper presents a mathematical model of oscillations of a multi-storey frame under elastoplastic work of a material with a restoring force, varying according to the bilinear law with unloading. Physically nonlinear pattern of deformation of the columns of the floors of the frame is given in the form of the stiffness diagram “restoring force - relative displacement”. The diagram is of a multi-cycle character and is set by the elastoplastic hysteresis loops, which allows us to take into account the repeated yielding and uploading at the floors of the frame. The analytical patterns of the dynamic restoring force are given for the unrestricted half cycle of the deformational diagram and for its sections: loading, hardening and uploading. The mathematical model can be used in the time analysis of the response of building structures.