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Mathematical Problems in Engineering
Volume 2014, Article ID 615792, 11 pages
Research Article

Quasistatic Seismic Damage Indicators for RC Structures from Dissipating Energies in Tangential Subspaces

1Institute for Statics & Dynamics, Ruhr-University Bochum, 44780 Bochum, Germany
2Kraetzig & Partners Engineering Consultants, Buscheyplatz 9-13, 44801 Bochum, Germany
3Technical University of Berlin, Gustav-Meyer-Allee 25, 13355 Berlin, Germany

Received 4 September 2013; Accepted 29 September 2013; Published 12 January 2014

Academic Editor: Anaxagoras Elenas

Copyright © 2014 Wilfried B. Krätzig and Yuri S. Petryna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper applies recent research on structural damage description to earthquake-resistant design concepts. Based on the primary design aim of life safety, this work adopts the necessity of additional protection aims for property, installation, and equipment. This requires the definition of damage indicators, which are able to quantify the arising structural damage. As in present design, it applies nonlinear quasistatic (pushover) concepts due to code provisions as simplified dynamic design tools. Substituting so nonlinear time-history analyses, seismic low-cycle fatigue of RC structures is approximated in similar manner. The treatment will be embedded into a finite element environment, and the tangential stiffness matrix in tangential subspaces then is identified as the most general entry for structural damage information. Its spectra of eigenvalues or natural frequencies of the structure serve to derive damage indicators , applicable to quasistatic evaluation of seismic damage. Because det denotes structural failure, such damage indicators range from virgin situation to failure and thus correspond with FEMA proposals on performance-based seismic design. Finally, the developed concept is checked by reanalyses of two experimentally investigated RC frames.