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 efficiency of applying tuned mass damper is substantiated for reducing the damageability of structures under strong earthquakes. Two models of structure damage accumulation are considered. The first model is elastoplastic one, the damage degree of the model being determined by the work of plastic deformation forces. The second model is a model with degrading rigidity the damage degree of the model is connected with the development of cracks and is determined by the maximum displacement of the structure in its loading history. For the first type of nonlinearity, i.e. the first model there is an amplitude-frequency characteristic and the optimum tuning of the mass damper corresponds to the maximum of this characteristic. For the second model of accumulation of damages there is no frequency response, therefore the mass damper tuning obtained with harmonic action on the elastic system was used. Calculations of the system with mass damper and without it using earthquake accelerograms have been carried out. Accelerograms, the most unfavorable in terms of the spectral composition for the structures under consideration, were chosen taking into account peak accelerations and energy characteristics of the seismic action. It has been established for elastoplastic systems that tuned mass damper reduces the time of the structure being in plastic stage and the work of plastic deformation forces. For systems with degrading stiffness tuned mass damper reduces the maximum movement of the system in its loading history.
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