Damage prognosis by means of modal residual force and static deflections obtained by modal flexibility based on the diagonalization method

In this paper, two effective damage detection methods for localizing and quantifying structural damage in shear frames are presented. Both of them are based on the diagonalization of the stiffness matrix of shear frames. The first method is devoted to estimating structural damage by the modification of modal residual force while the second method is based on the computation of the static displacements under a unique static force by using only a few modes. The most important feature of the presented methods is their simplicity in the computation of damage. The proposed algorithms have been numerically applied to two shear frames to show that they can successfully detect and quantify damage in these structures. Also, the efficiency of the presented methods has been demonstrated through damage simulations when the modal data have been contaminated with noise. Finally, the applicability of the presented methods has been demonstrated by studying a five-story shear frame on a shaking table. All of the obtained results emphasize the robustness and good performance of the presented methods in the damage diagnosis of shear frames. (Some figures may appear in colour only in the online journal)