This paper presents a numerical method for damage identification based on orthogonality conditions sensitivity methods based on stiffness modification index. Determination of dam-age severity is main objective of this article. Hence, the general eigenvalue problem and stiffness-orthogonality conditions sensitivity methods are developed to determine the damage severity index. In this study, the variation of stiffness matrices are introduced as damage in-dex and based on its changes the eigenvalue problem and stiffness-orthogonality condition of damaged structure are expanded to determine the damage quantification. To achieve the damage detection algorithm, the initial physical properties of intact structures such as the mass and stiffness matrices as well as modal parameters consist of natural frequencies and mode shapes must be utilized. For damage assessment, two numerical structures as discrete and continuous dynamic systems are modeled. First, the extent of induced damage is estimated in a simple 6-story shear building. Then, a 15-bar planner truss is modled and dam-age assessment methods are evaluated. Numerical results indicate that proposed damage quantification methods including the general eigenvalue problem and stiffness-orthogonality condition sensitivity methods can provide reliable tools to accurately determine the multiple structural damage quantification.

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