Earthquakes are one of the most frequent and destructive influences on buildings and structures. Annually on the whole Earth there are about one million earthquakes. Most of them are insignificant in strength and not accompanied by catastrophic consequences, however, sometimes (up to several times a year) there are earthquakes, accompanied by destruction and human casualties [1-3]. The problem of increasing the seismic resistance of buildings and structures is currently very relevant. In this area, many Russian [3-11] and foreign [12-17] specialists work. One of the areas of development of anti-seismic measures is the development of effective methods and techniques for calculating structures for the action of seismic forces to improve the strength and survivability of buildings in an earthquake. Currently, the main methods of calculating buildings and structures for seismic actions are the normative method [18-21], the method of decomposition in terms of eigenmodes, and also the finite element method. In this paper, the application of the time analysis method (TAM) [18] to the calculation of a 3- storey building modeled by a vertical cantilever rod with 3 degrees of freedom under the action of a seismic load is considered. The load is given by the earthquake accelerogram.

۲٫ Numerical implementation of the problem

As an example, consider the time analysis of the elastic oscillations of a three-story building. The design dynamic model (DDM) of the building is adopted in the form of a flat cantilever rod with point masses located in floor and coverage levels (figure 1), thus the system has n = 3 dynamic degrees of freedom. The flexural rigidity of the rod is EJ = 19,321×۱۰۷ kNm2 . Figure 1 also shows the calculated cross sections nj, in which the values of the bending moments are the largest. 2. Numerical implementation of the problem As an example, consider the time analysis of the elastic oscillations of a three-story building. The design dynamic model (DDM) of the building is adopted in the form of a flat cantilever rod with point masses located in floor and coverage levels (figure 1), thus the system has n = 3 dynamic degrees of freedom. The flexural rigidity of the rod is EJ = 19,321×۱۰۷ kNm2 . Figure 1 also shows the calculated cross sections nj, in which the values of the bending moments are the largest.