Accuracy of spectral combination techniques

ABSTRACT CQC method included in the most of Earthquake Resistant Design Codes has a basic usage. This is because of the assumptions of the method. CQC method considers the closeness of the successive natural frequencies of the analysing structure unlike its former SRSS. The considerations are made by the cross correlation coefficients which depend on the ratios of the natural frequencies and the damping of the structure. Once these coefficients have been determined, any type of the response is combined by using same coefficients. Hence, some error depending on the response types occur in the method. A computer program is coded which is capable of making time history and spectral analyses of structures including frames and panels. The program may use the modified earthquake records. Parametric studies have been realized. In this study, the relative errors arising from combining the shear forces in columns in the same direction with the earthquake analyzed. These types of errors result from the eccentricities as a distance between the mass and rigidity centres in a floor plan in the three dimensional structures. The relative error is defined as a difference between the errors belonging to two states of same structure including and not including the eccentricity, respectively. A relation between the relative error in combined shear forces of columns in the considered earthquake direction when CQC used and the participation masses of the modes rather than the closeness of the successive natural frequencies of the structure are realized. A relation between the relative error and a new ratio (Q) considering the participating masses of modes is obtained. Apart from that, combining the shear forces in columns in orthogonal direction to the earthquake by adding them together with their signs produced less varying errors than CQC method does. Furthermore, a modification has been proposed on the usage of CQC method. A condition for considering a structure to behave as a lateral-torsional coupling structure in analyses under earthquake loads has been given. This condition depends on the ratio Q, eccentricity between the mass and rigidity centres and the lateral stiffness ratios of the two orthogonal directions of the structure. Keywords: Natural Modes, Spectral Analysis, Combination Techniques, Lateral-torsional coupling, Accuracy. xn