Linear Oscillations of the High-Rise Buildings

Abstract

Seismic calculations are based on the hypothesis that maximum seismic horizontal displacements of inelastic systems are equal to displacements of elastic systems of equivalent frequencies.Analysis of strong earthquakes of recent years (San Francisco, USA, 1971, Spitak, Armenia, 1988, Kobe, Japan, 1995 and others) led scientists to the conclusion that this hypothesis cannot be recognized as acceptable. In a number of cases, the maximum horizontal displacements turned out to be 2–3 orders of magnitude higher than the maximum displacements of elastic systems. For example, a displacement graph based on the 1985 Mexico City earthquake shows that the actual plastic displacements are 100 times the expected plastic displacements. In the case of other earthquakes, there are hundreds of subtle inconsistencies. The quantitative results concluded that the intensity of building vibrations exceeded 1.5 times the 9-point design seismic intensity 2.5 and that a special approach, including the need to consider impact effects, is needed and is particularly serious in such zones. This should also be taken into account. Inelastic deformations are indicated. The new calculation is used to study non-linear oscillations caused by impulsive actions of a continuous system. In the case of elastic vibration, changing the mass gives very different results. Reducing the lower mass by a factor of 3 reduces the displacement by a factor of 2.2 for the upper mass and 2.4 for the second mass. The same impact was applied to a 16-story building and the stiffness distribution of the rods was studied in different ways. The stiffness was constant everywhere, constant within 4 stories, where it varied linearly and parabolically with height. Displacements during the course of the pulse shock were greater in the stiffer buildings. Furthermore, the vibration decreases in amplitude by a factor of 3 or more for the upper mass and by a factor of 4 for the lower mass. The force on the upper rod is reduced by a factor of 4 and the force on the lower rod is reduced by a factor of 6. This will make it possible to perform calculations for a small time scale, which is necessary to take into account high-frequency oscillations that occur in the epicentric zone.