Damage Identification in Plane Multi-storey Reinforced Concrete Frame

Triantafyllos K. Makarios1, *
1 Institute of Structural Analysis and Dynamics of Structures, School of Civil Engineering, Faculty Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

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© 2023 Triantafyllos K. Makarios

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Institute of Structural Analysis and Dynamics of Structures, School of Civil Engineering, Faculty Engineering, Aristotle University of Thessaloniki 54124, Greece; E-mail:



In this paper, a new method for damage detection in reinforced concrete multi-storey frames is presented.


The proposed new methodology is a hybrid technique consisting of two parts. The first step involves determining the seismic pushover capacity curve of the structure, and the second step includes formulating the diagram of the instantaneous eigenfequencies of the structure in the nonlinear regime. With reference to this diagram, more details are given in the text. To estimate the equivalent target displacement defined at the top of the structure, which corresponds to the instantaneous eigenfrequencies of a structure with damage, the diagram of these eigenfrequencies is combined with the seismic pushover capacity curve of the structure. Thus, the target displacement at the top of the frame is calculated.


The advantage of the proposed methodology is that using this target displacement, the final picture of the damage in the structure is estimated from the two pushover analyses, with positive and negative signs of the floor lateral forces corresponding to triangular distribution in elevation. For clarification, an example of a three-storey R/C frame is presented as a paradigm.


Using the proposed methodology, the locations of damage in the structure are successfully identified, as well as the Damage Stiffness Matrix is estimated with high accuracy.

Keywords: Damage identification, Diagram of instantaneous eigenfrequencies, Pushover capacity curve, Identification of dynamic characteristics, Seismic target displacement, Nonlinear analysis of reinforced concrete frames, Plastic mechanism.