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Incremental Spectrum Analysis (ARSA) method is a displacement-controlled pushover analysis method. In the method, the modal displacement increments are scaled according to the nonlinear spectral displacement value obtained according to the instantaneous dynamic characteristics of the structure. The basis of modal scaling in the ARSA method is based on the "equal displacement rule". According to this rule, assuming that nonlinear spectral displacement is equal to elastic spectral displacement, modal displacement increments are expressed as ratios of elastic spectral displacements of that mode. Therefore, in the first repulsion step (linear elastic case), the elastic spectral displacement of the nth mode will be calculated from S den (1) and the same value will be used in all other steps (i = 2,3….).
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The value of S aen (1) is the spectral acceleration value found for each vibration mode using Horizontal Elastic Design Response Spectrum . The figure below shows how the values of S aen (1) are found for 3 modes (n = 1, n = 2 and n = 3 for the third mode) as a representation. The S ae values, which are the equivalents of the periods obtained from the modal analysis results from the first impulse step in the horizontal elastic design spectrum, are found. In the term S aen (1), the index "n" indicates the mode in which and the index (1) indicates the step in which step is processed. The term S ae turns into the term S aen (1) in the ARSA method .
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As in the picture above any n-th initial curve of the jitter mode Elastic Response Spectrum 's if the pouch, said mode performance point of Elastic Response Spectrum ' is the point where the cut. In this case, there is no mention of a nonlinear behavior for the n'th vibration mode because the n'th vibration mode remains within the elastic boundaries. The contribution of the modes in which the n th vibration mode cuts the initial stiffness Elastic Response Spectrum is not considered after reaching the performance point.
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