The installation of seismic-insulating systems is one of the most effective methods of earthquake protection of buildings and structures in highly seismic-prone regions. A sizable number investigations and monographs are devoted to problems of the analysis, design, and practical application of such systems [1,2,3,4]. Currently, however, many important problems of the theory of seismic-insulating systems are under discussion, and design solutions are occasionally incorrect. Examples of this kind of errors are brought to light in [5,6].Systems on kinematic supports can be divided into three types: "locally linearizable," "globally linearizable," and nonlinearizable. These types of supports are described in [6]. The first two types are characterized by increasing restoring force with increasing displacements. For "locally linearizable" supports, the restoring force may be considered linear for small turn angles of the support. For example, V. V. Nazin's supports, spherical, and other supports apply to foundations with this type of supports. "Globally linearizable supports" are characterized by the possibility of blocking their movement under small (in-service) loads. This leads to significant nonlinearity of the support near the equilibrium position, but the restoring force becomes close to linear with increasing turn angle of the support. Yu. I. Bezrukov's supports are, for example, referred to as foundations with this type of supports. Nonlinearizable supports are the most complex from the standpoint of performance under load. For these supports, the restoring force decreases with increasing turn angle. In other words, they are characterized by negative stiffness, and the restoring force is represented in the form F = F 0 − cu, where F 0 is the initial restoring force, c is the stiffness coefficient, and u is the displacement of the system. We will call the indicated supports negative-stiffness supports. Supports of this type are used in foundations designed by Yu. D. Cherepinskii, A. V. Kurzanov, and others. The inaccuracies and errors associated with use of seismic-insulating foundations on kinematic supports with negative stiffness are discussed below. Equations are derived for the vibrations of a building on the foundations under consideration. Impossibility of use of traditional methods of the linear-spectral theory for analysis of their earthquake resistance is demonstrated. It is established that the systems under consideration do not possess a natural vibration period, and may have ambiguous solutions for forced vibrations. Algorithms are proposed for evaluation of the earthquake resistance of buildings on such foundations. The possibility of high efficiency of use of the indicated foundations is noted with correct assignment of their parameters.

Estimating the reduction factor for calculating massive reinforced concrete bridge piers was made. For this purpose a quasi-static “force-displacement” diagram was built up using the ANSYS software. This diagram has the form of a bilinear one, and the character of the bilinearity depends on the diameter of the reinforcing bars insignificantly. The percentage of reinforcement affects only the moment when all reinforcement bars begin to flow. The reinforcement flow takes place in the displacement interval from 3 to 5 cm. The collapse will occur when the reaction of the bearing part goes beyond the pier cross-section at pier displacements from 5 to 20 cm. Using “force-displacement” diagram, the behavior of the single-mass model with a bilinear deformation diagram and the limit displacement of 20 cm was analyzed. Then, it became possible to obtain for each accelerogram the limit elastic displacement and the limit position of the point corresponding to the maximum structure displacement during structure oscillations. It was done using real accelerograms of earthquakes with intensity 9 on the MSK scale without normalizing their amplitudes. In this case, long-period accelerograms had smaller peak accelerations, but resulted in greater plastic deformations. As a result, no evident dependence of plastic deformation on the input spectral composition was found and the value of reduction factor K1 turned out to be 0.25-0.27. However, it is shown that this reduction factor cannot be used to make transition from seismic loads obtained on the basis of time-history analysis by accelerograms to design loads.

The problem of seismic protection of the bridge for the conditions of Uzbekistan is considered. The bridge is located in an area with estimated seismicity of 9 points. It has massive high supports on a natural foundation and relatively small and light spans. When selecting seismic isolation, this made it possible to use the span structures as a dynamic damper for the support vibrations in the direction along the bridge. Due to the damping effect, it was possible to achieve that the seismic forces in the support in the presence of the superstructure were less than in the free support without the superstructure. At the same time, the rigidity of fastening the superstructure to the support increased in comparison with the rigidity of classical seismic isolation, which facilitated the design of the supporting elements.

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