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RANDOM VERTICAL SEISMIC VIBRATIONS OF THE CANTILEVER CONSTRUCTION-ABSTRACT

S. ESADZE1,*
1: Dept. of Civil and Industrial Engineering, Georgian Technical University, Georgia
* Correspondent author: s_esadze@gtu.ge

Keywords: random vibration, cantilever construction, vertical acceleration, multiplicative nonstationary effect
ABSTRACT
Strong earthquakes are characterized by nonuniform spread of the ground surfaces vibration; accordingly, this is related to the bearing points of the buildings too. The vertical component of the ground acceleration in fixed conditions, especially for the epicentral zone, have destructive effect. Some constructive elements of the buildings, defending on its characteristic, must be calculated on effect of the vertical seismic acceleration. The cantilever construction belongs to such constructive elements. In addition, for the determination of the effect of the mentioned load on the cantilever construction, it is possible to use calculation model which includes only cantilever element, taking into account the stiffness of the adjacent elements.
In general, an earthquake is a random phenomenon. Accordingly, the most adequate model of the seismic load is the model presented as the random process.
In the submitted paper, we consider random vertical vibration of the cantilever with long overhang. As calculation model of the construction, we consider mechanical system in the form of cantilever with two lumped mass. Cantilever is built-in in absolutely rigid element with mass equal to the mass of the buildings over cantilever part and is exposed to the vertical moving of the base trough brace, stiffness of which may be infinitely large (oversize bearing elements e.g. columns) or finite (more supple bearing elements) quantity.
As the calculation model for the random vertical seismic acceleration we take multiplicative nonstationary (quasistationary) effect, main feature of which is the scalability in time of the stationary component, by superposition with deterministic envelope function.
Taking into account that according to the vertical seismic acceleration records, taken from construction elements of buildings, the maximal value of vertical accelerations may be different from maximal accelerations of base, we consider two variants of effect: (1) when built-in point of the cantilever construction vibrating as well as the base (infinitely stiff brace. see above); (2) when built-in point of the cantilever construction and the base are vibrating in different ways (brace with finite stiff) i.e. we have analogue of two ``log-in``.
The problem is solved within the bounds of correlation theory. Numerical examples are given and comparative analysis is conducted with deterministic calculation of the same construction.