Dimensional analysis of the earthquake-induced pounding between inelastic structures |
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Authors: | Elias G Dimitrakopoulos Nicos Makris Andreas J Kappos |
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Institution: | 1. Department of Engineering, University of Cambridge, Cambridge, CB2 1 PZ, UK 2. Department of Civil Engineering, University of Patras, 26500, Patras, Greece 3. Department of Civil Engineering, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece
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Abstract: | In this paper the seismic response of inelastic structures with unilateral contact is revisited with dimensional analysis.
All physically realizable contact types are captured via a non-smooth complementarity approach. The implementation of formal
dimensional analysis leads to a condensed presentation of the response and unveils remarkable order even though two different
types of non-linearity coexist in the response: the boundary non-linearity of unilateral contact and the inelastic behaviour
of the structure itself. It is shown that regardless the intensity and frequency content of the excitation, all response spectra
become self-similar when expressed in the appropriate dimensionless terms. The proposed approach hinges upon the notion of
the energetic length scale of an excitation which measures the persistence of ground shaking to impose deformation demands.
Using the concept of persistency which is defined for excitations with or without distinct pulses, the response is scaled
via meaningful novel intensity measures: the dimensionless gap and the dimensionless yield displacement. The study confirms
that contact may have a different effect on the response displacements of inelastic structures depending on the spectral region.
In adjacent inelastic structures, such as colliding buildings or interacting bridge segments, contact is likely to alter drastically
the excitation frequencies’ at which the system is most vulnerable. Finally, it is shown that the proposed approach yields
maximum response displacements which correlate very well with the persistency of real earthquakes for a bridge system with
considerably complex behaviour. |
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