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This paper proposes a quick and simplified method to describe masonry vaults in global seismic analyses of buildings. An equivalent macro-element constituted by a set of six trusses, two for each transverse, longitudinal and diagonal direction, is introduced. The equivalent trusses, whose stiffness is calculated by fully modeled vaults of different geometry, mechanical properties and boundary conditions, simulate the vault in both global analysis and local analysis, such as kinematic or rocking approaches. A parametric study was carried out to investigate the influence of geometrical characteristics and mechanical features on the equivalent stiffness values. The method was numerically validated by performing modal and transient analysis on a three naves-church in the elastic range. Vibration modes and displacement time-histories were compared showing satisfying agreement between the complete and the simplified models. This procedure is particularly useful in engineering practice because it allows to assess, in a simplified way, the effectiveness of strengthening interventions for reducing horizontal relative displacements between vault supports.
The chapter initially provides a summary of the contents of Eurocode 8, its aim being to offer both to the students and to practising engineers an easy introduction into the calculation and dimensioning procedures of this earthquake code. Specifically, the general rules for earthquake-resistant structures, the definition of design response spectra taking behaviour and importance factors into account, the application of linear and non-linear calculation methods and the structural safety verifications at the serviceability and ultimate limit state are presented. The application of linear and non-linear calculation methods and corresponding seismic design rules is demonstrated on practical examples for reinforced concrete, steel and masonry buildings. Furthermore, the seismic assessment of existing buildings is discussed and illustrated on the example of a typical historical masonry building in Italy. The examples are worked out in detail and each step of the design process, from the preliminary analysis to the final design, is explained in detail.
Die Erdbeben in Albstadt 1978 (Magnitude 5,7), Roermond 1992 (Magnitude 5,9) oder in Waldkirch 2004 (Magnitude 5,1) haben verdeutlicht, dass die erdbebensichere Auslegung von Mauerwerksbauten auch in Deutschland von großer Bedeutung ist. Bereits im Jahr 1981 wurde die DIN 4149 (1981) “Bauten in deutschen Erdbebengebieten – Lastannahmen, Bemessung und Ausführung üblicher Hochbauten“ eingeführt, in der aber für Mauerwerksbauten nur wenige Anforderungen gestellt wurden. Diese Norm wurde durch den NABau-Arbeitsausschuss “Erdbeben; Sonderfragen“ des Deutschen Instituts für Normung e.V. (DIN) auf Grundlage des Eurocode 8 (2004) vollständig überarbeitet und durch die DIN 4149 (2005) abgelöst, die umfangreiche Regelungen für die seismische Auslegung von Mauerwerksbauten enthält. Mittlerweile liegen die DIN EN 1998-1 (2010) und der Nationale Anhang DIN EN 1998-1/NA (2011) vor, die nach Einarbeitung der Ergebnisse der durchgeführten Anwendungserprobung bauaufsichtlich eingeführt und die DIN 4149 (2005) ersetzen werden. Der folgende Beitrag gibt einen Überblick über die seismische Berechnung und Bemessung von Mauerwerksbauten nach dem europäischen Regelwerk und illustriert deren Anwendung an einem baupraktischen Beispiel.