Incremental Response Spectrum Analysis

An alternative nonlinear static procedure was proposed by Aydinoglu (2003). The procedure, called Incremental Response Spectrum Analysis (IRSA) does not properly belong to the pushover methods. The procedure is displacement-based, it uses the equal displacement rule and the structure nonlinear behavior is modeled as piece-wise linear. The initial modes are computed and the elastic response spectrum for the initial structure is carried out. In the first stop the spectral ordinates are scaled to the formation of the first plastic hinge, which corresponds in the piece-wise linear capacity curve, to the first change of stiffness. The updated modal quantities are computed and additional spectral ordinates are computed up to the formation of the second plastic hinge. The procedure continues until the entire spectral ordinates are applied. The method does not require any transformation to an equivalent SDOE system. 

Aydinoglu, M.N. 2003. An Incremental Response Spectrum Analysis Procedure Based on Inelastic Spectral Deformation for Multi-Mode Seismic Performance Evaluation, Bulletin of... 

Nonlinear performance assessment of bridges with Incremental Response Spectrum Analysis (IRSA) procedure... 

Multi-mode pushover analysis procedure IRSA (Incremental Response Spectrum Analysis) has been introduced by the first author to enable the two and three dimensional nonlinear analyses of buildings and bridges (Aydmoglu 2003). The practical version of the procedure (Aydmoglu 2004, 2007) works directly with smoothed elastic response spectrum and makes use of the well-known equal displacement rule to scale modal displacement increments at each piecewise linear step of an incremental application of linear Response Spectrum Analysis (RSA). In this paper, main steps of IRSA are summarized and its performance is evaluated on two example bridges under three different ground motions. 

Incremental Response Spectrum Analysis (IRSA) is a multi-mode pushover procedure, in which the incremental response is assumed piecewise linear at each pushover step in between the formation of two consecutive plastic hinges. The key point in IRSA is modal scaling, which is applied at each step to modal displacement increments, to identify their proportions in different modes (Aydmoglu 2003, 2007). 

Based on limited observations made above, it appears that approximate Incremental Response Spectrum Analysis (IRSA) procedure, which is the natural extension of the traditional Response Spectrum Analysis (RSA), proves to be a reliable analysis tool for deformation-based seismic assessment and design of bridges in the general framework of performance-based design. 

Aydinoglu, M.N. 2003. An incremental response spectrum analysis based on inelastic spectral displacements for multi-mode seismic performance evaluation. Bulletin of Earthquake Engineering l(l) 3-36. 

Aydinoglu, M.N. 2004. An improved pushover procedure for engineering practice Incremental Response Spectrum Analysis (IRSA). International Workshop on Performance-based Seismic Design Concepts and Implementation . Bled, Slovenia.PEER Report 2004/05 345-356. 

Aydinoglu, M.N. 2007. A Response Spectrum-Based Nonlinear Assessment Tool for Practice Incremental Response Spectrum Analysis (IRSA). Special Issue Response Spectra (Guest Editor M.D. Trifunac), ISET Journal of Earthquake Technology 44(1), No. 481. 

A standard linear response spectrum analysis (RSA) is performed at each (i) th incremental pushover step for the unit value of the unknown incremental scale factor = 1) by considering instantaneous mode shapes that are compatible with the current distribution of plastic hinges and the initial elastic spectral displacements taken as seismic input. Such a linear response spectrum analysis (RSA) effectively corresponds to adaptive pushover analyses, which are simultaneously performed in each mode followed by the application of an appropriate modal combination rule. Thus, any response quantity of interest, which is represented by a generic response quantity, r, is obtained for the unit value of the unknown incremental scale factor. Now, the increment of the generic response quantity, Ar, is expressed as... 

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