Progressive Incremental Dynamic Analysis for First-Mode Dominated Structures Alireza Azarbakht 1 and Matjaž Dolšek 2 Abstract: Incremental dynamic analysis (IDA) is a widely used method for assessing structural performance under earthquake excitations. It enables direct evaluation of the record-to-record variability in structural response through a set of ground-motion records. If the number of ground-motion records is large then, the method becomes computationally demanding. To facilitate its practical application, a precedence list of ground-motion records has been introduced, aiming at selecting the most representative ground-motion records for IDA analysis. In progressive IDA analysis, the IDA curves are computed progressively, starting from the first ground-motion record in the precedence list. After an acceptable tolerance has been achieved, the analysis is terminated. This approach may significantly reduce the computational effort for first-mode-dominated structures, since the seismic response can be computed only for a certain number of ground-motion records from the precedence list to achieve an acceptable level of confidence in the prediction of the summarized (16th, 50th, and 84th fractiles) IDA curves. The proposed implementation of incremental dynamic analysis, which is demonstrated using an example of a 4-story reinforced concrete frame, can also be used for the selection of ground-motion records from a very large set of records, provided that all the records properly represent the seismic scenario for a given site. DOI: 10.1061/(ASCE)ST.1943-541X.0000282. © 2011 American Society of Civil Engineers. CE Database subject headings: Ground motion; Earthquakes; Seismic response; Optimization; Frames; Concrete; Nonlinear analysis; Dynamic analysis. Author keywords: Ground motion; Earthquakes; Seismic response; Optimization; Building frames; Concrete; Nonlinear analysis. Introduction Determination of demand and collapse capacity attributable to earthquakes is an important issue in performance-based earthquake engineering. Many different methods and procedures for assessing seismic structural performance have emerged during the develop- ment of performance-based earthquake engineering. For example, methods for assessing structural collapse capacity to protect life vary from the simplest methods, which can be based on the response of a simple single-degree-of-freedom (SDOF) model, to complex nonlinear dynamic analyses performed for a structural model, which is analyzed for a set of ground-motion records (Villaverde 2007). One of the methods commonly used in recent years is IDA (Vamvatsikos and Cornell 2002). It involves subject- ing a structural model to a number of ground-motion records, each scaled to multiple levels of intensities. Although such an approach requires a large number of inelastic time history analyses, it has been used by several researchers for different applications (Zareian and Krawinkler 2007; Liao et al. 2007; Tagawa et al. 2008). Differ- ent approximate methods have also emerged, aiming at reducing computational effort. The approximate methods for IDA analysis usually involve the replacement of nonlinear dynamic analysis by a combination of the pushover analysis of a structural model and the dynamic analysis of a simple model, e.g., SDOF model (Vamvatsikos and Cornell 2005a; Dolšek and Fajfar 2005; Han and Chopra 2006). However, if the seismic response of a structure must be predicted with maximum accuracy using nonlinear dynamic analysis, then the practical application of incremental dynamic analysis is limited. This is attributable to the computa- tional effort needed to perform incremental dynamic analysis, but also owing to the definition of the seismic loading, which in this case, is defined by a set of ground-motion records. Different questions arise in the process of selecting the ground-motion records for the incremental dynamic analysis. It is important that the selected set of ground-motion records reflects the seismic haz- ard of the particular site and that the scaling of records is legitimate (see Luco and Bazzurro 2007). When these two conditions are not satisfied, a bias in the structural response can occur (Baker and Cornell 2006; Luco and Bazzurro 2007). The scaling of records is legitimate if the ratio between the median seismic response parameter to scaled records and the median seismic response parameters to unscaled records (bias) is in the range of the defined tolerable interval. However, careful selection of ground-motion records can reduce the bias in the structural response (Shome et al. 1998; Iervolino and Cornell 2005). On the other hand, many researchers have tried to reduce the dispersion in nonlinear response by introducing the improved intensity mea- sures (Tothong and Luco 2007; Luco and Cornell 2007; Baker and Cornell 2006; Vamvatsikos and Cornell 2005b). The most exten- sive study for evaluation of ground-motion selection and modifica- tion methods was recently prepared by the Ground Motion and Modification Working Group of the Pacific Earthquake Engineer- ing Research (PEER) Center (Haselton 2009). The progressive incremental dynamic analysis, which involves a precedence list of ground-motion records, and is proposed in this 1 Associate Professor, Dept. of Civil Engineering, Faculty of Engineer- ing, Arak Univ., Arak, Iran, P.O. Box 38156-88359. E-mail: a-azarbakht@ araku.ac.ir 2 Assistant Professor, Faculty of Civil and Geodetic Engineering, Univ. of Ljubljana, Slovenia. E-mail: mdolsek@ikpir.fgg.uni-lj.si Note. This manuscript was submitted on June 17, 2008; approved on July 2, 2010; published online on July 16, 2010. Discussion period open until August 1, 2011; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural Engineer- ing, Vol. 137, No. 3, March 1, 2011. ©ASCE, ISSN 0733-9445/2011/3- 445–455/$25.00. JOURNAL OF STRUCTURAL ENGINEERING © ASCE / MARCH 2011 / 445 Downloaded 04 Mar 2011 to 130.54.110.32. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org