Response spectrum analysis

The Modal Response Spectrum Analysis (also known as a dynamic analysis) more accurately depicts the response of the structure to the earthquake. This is done by considering the response of multiple modes instead of just the first one (as is done in the ELF). Whereas the use of a static analysis assumes that a load is applied relatively slowly, a dynamic analysis should be used if the application of the load is faster than the response of the structure. For this reason a dynamic analysis is mainly... 

For non symmetric buildings, two different pushover analysis should be performed for each seismic input direction, in the positive and negative directions. For structures that are torsionally flexible, ECS suggests to account for the torsional effects by following a simplified procedure where the frame displacements are increases based on a modal response spectrum analysis. This approach is based on the modified N2 procedure (Fajfar et al, 2005). 

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). 

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... 

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. 

Adaptive pushover analysis is an alternative to conventional pushover analysis. In force-based adaptive pushover analysis, the load vectors are gradually updated due to the damage occurring to the structure, which affects the mode shapes. One of the first procedures for the adaptive lateral load for pushover analysis was proposed by Bracci et al. (1997). Many different procedures for force-based adaptive pushover analysis followed. Most approaches involve response spectrum analysis which is performed for the different modal characters of the structure which are associated with selected stages of the pushover analysis. However, Aydinoglu (2003) has argued that the load patterns should be based on an inelastic rather than an elastic response spectrum. It was soon realized that force-based adaptive pushover analysis offers only a relatively minor advantage in comparison with conventional pushover analysis. As a result of such an observation, a displacement-based adaptive pushover procedure was proposed (Antoniou and Pinho 2004), which. 

In the 2003 NEHRP Recommended Provisions (BSSC 2004) for buildings with passive dampers, and for the equivalent lateral force (ELF) analysis (linear static analysis) specifically, the response is defined by two modes the fundamental mode and the residual mode, which is used to approximate the combined effects of higher modes. For response spectrum analysis, higher modes are... 

Response Spectrum Procedure Where the ELF procedure is not permitted, it is often permissible to use the response spectrum procedure for design. In this procedure internal forces and deformations are computed using response spectrum analysis, as described by Chopra (2007), among others. In this procedure, the natural frequencies and modes of vibrations of the isolated building are computed in the usual way, and demands are calculated through linear combination of these modes weighted by their spectral ordinates at each natural frequency. The results obtained from response spectrum analysis are not permitted to exceed those computed from the ELF procedure. 

If the process is repeated for every return period of interest, then design spectra for different hazard levels can be constructed, as shown in Fig. 12. If the aforementioned procedure is continued for many earthquake records, the result is a complete UHS that can be used in a simplified form in seismic norms (see Fig. 10). Such multiple spectra can be used in response spectrum analysis of a structure within a performance-based design... 

Response Spectrum Analysis of Structures Subjected to Seismic Actions... 

In many seismic codes, the equivalent static lateral force V is used as a reference value of the total seismic design base shear. For instance, the base shear calculated using the modal response spectrum analysis should not be less than 80 % or 90 % of the equivalent lateral base shear. This minimum base shear is provided because the computed period of vibration may be the result of an overly flexible (incorrect) analytical model. 

Linear static and response spectrum analysis methods for design are accepted for regular... 

The simplified analysis procedure provides an elastic-static method for calculation of the design demand of an MDOF system with MR dampers. The simplified analysis procedure utilizing the response spectrum analysis (RSA) method is summarized in Figs. 4 and 5. 

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