SYMPOSIUM Schwingungsreduktion durch den Einsatz passiver Systeme
Passive Vibration Reduction by Curved Surface Slider Systems by Christian Bucher
Schwingungen von Bauwerken durch äußere Anregungen wie Verkehr, Wind oder Erdbeben können häufig zu schweren Schäden führen, die entweder auf Überlastung oder auf Ermüdungseffekte zurückzuführen sind. Es ist daher wichtig, die Auswirkung solcher unvermeidbaren Vibrationen abzuschwächen. Eine weitverbreitete Möglichkeit ist der Einbau von passiven Systemen, die entweder die übertragenen Kräfte sofort reduzieren oder durch zusätzliche Dämpfung die Energie abführen. Natürlich sollte ein gutkonzipiertes System beide Prinzipien kombinieren. Passive Systeme wie Curved Surface Slider (CSS) oder Ähnliches haben sich im Zusammenhang mit Erdbebenlasten als sehr effektiv für den Schutz von Gebäuden erwiesen. Dieser Aufsatz konzentriert sich auf die Frage, ob solche Systeme für Brücken unter Erdbebenbelastung gleichermaßen wirksam sein können. Zu diesem Zweck wird ein veranschaulichendes Beispiele numerisch analysiert. Aus dieser Analyse werden einfache Entwurfsformeln abgeleitet und die Ergebnisse verglichen. Dies mit dem Ziel, ein einfaches Werkzeug zur Entscheidungsfindung bereitzustellen.
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BRÜCKENBAU | 1/2 . 2020
1 Introduction Curved surface sliders (CSS) are effective base isolators to reduce the effect of earthquake accelerations on civil structures. These isolators can be built in different configurations, i.e. with one (Single CSS) or two (Double CSS) or even multiple primary sliding surfaces (e.g. [1]). The secondary sliding surface of the calotte joint in case of Single CSS is lubricated to ensure high rotation capability of the calotte joint but must not be considered in the CSS design to produce damping ( Fig. 1). Common to all types of CSS is that their effective radius of curvature, which is the radius of an equivalent single pendulum, isolates the structure from the shaking ground by its low restoring stiffness and their damping, which is generated by friction on the primary sliding surfaces, augments the structural damping. [2] [3] In addition, the design of CSS must guarantee the minimum required re-centring of the primary structure which is achieved by appropriate designs of effective radius and friction. [4] In many papers dealing with CSS, the focus is on the effective seismic protection of structural and non-structural elements [3] [5] for which also the variation of axial loads on the isolators during the earthquake are considered. [6] In the studies [7] [8] also semi-active (tuneable) base isolation systems are considered in order to further enhance the structural isolation. Also, the residual displacement and re-centring error, respectively, of CSS have been investigated for different base isolators [9] and the method of sensitivity analysis is adopted in [3] [10] to identify the influence of the CSS design parameters on the resulting structural isolation performance. Earthquakes are considered to be highly random processes with non-deterministic magnitude and frequency contents which also applies to the Maximum Considered Earthquake (MCE). As an inherent consequence of this fact, the CSS displacement capacity requires to be computed in a probabilistic way. In this paper the characteristic displacement of the CSS is determined such that it is not exceeded with the probability of 99,99 %, which is a 0,9999 quantile, for the assumed MCE.
Due to the high level of randomness it is reasonable to formally represent the loading as a non-stationary random process. In order to match the analysis with typical seismic design procedures the analysis focuses on earthquakes with site-specific average peak ground accelerations (PGA) which are selected here to be 2 and 5 m/s2. The solution approach in this paper, which is partially based on the earlier research results [11] [12] but further developed here, is as follows: – The space of all sensible variations of effective radius of curvature Reff and friction coefficient μ is scanned by a so-called Design of Experiments (DOE) which utilizes 50 randomly sampled values of these parameters. – For each of these combinations, 128 different realizations of earthquakes are digitally generated, and from the results the statistical properties of the responses in terms of peak support displacement and CSS displacement are computed. – Generally valid functions for these statistical parameters valid for arbitrary numerical values of the system parameters are generated using a meta-modeling technique. – Based on mean values and standard deviations, the 0.9999-quantiles of the peak CSS displacement are computed assuming an extreme value (Gumbel) distribution. – All the previous steps are carried out for two levels of the ground accelerations, i.e. vor PGA values of 2 and 5 m/s2 and simple engineering approximations are derived.
