Incremental dynamic analysis

One of the methods developed for the seismic risk evaluation of structures is the SAC-FEMA method, which enables probability assessment in closed form (Cornell et al. 2002), and represents a part of a broader PEER probabilistic framework (Deierlein 2004). Within the framework of SAC-FEMA method, the relationship between the seismic intensity measure and the engineering demand parameter is usually determined by Incremental Dynamic Analysis (IDA) developed by Vamvatsikos Cornell (2002). IDA is a powerful tool for estimation of seismic demand and capacity for multiple levels of intensity. However, it requires a large number of inelastic time-history analyses (and corresponding detailed data on ground motion time-histories and hysteretic behavior of structural elements) and is thus very time-consuming. Often it is possible to create summarized IDA curves with less input data, with less effort, but with still acceptable accuracy. One possible approach is to determine seismic demand for multiple levels... 

Vamvatsikos, D. Cornell, C.A. 2002. Incremental Dynamic Analysis. Earthquake Engineering and Structural Dynamics 31 491-514. 

The design base acceleration for the site is ag = 0.15g. Five incremental dynamic analysis are performed with ag = 0.15g, 0.12 g, 0.09 g, 0.06 g and 0.03 g. The shear strength is checked using the Eurocode 2 (2005), which uses the modified field theory. The results are represented in Figure 15. The bent are numbered from the left to the right from 1 to 14. 

Determination of fragility necessitates a wide-range assessment of stmctural response at multiple levels of intensity. There are several ways to organize the execution of nonlinear dynamic analyses, mainly differing in the manner of postprocessing and in how they can employ grotmd motion selection and scaling. The main candidates are three (Jalayer and Cornell 2009) cloud analysis, stripe analysis, and incremental dynamic analysis (IDA). 

Incremental dynamic analysis (IDA) is based on scaling and scaling only (Vamvatsikos and Cornell 2002). Its focus is on individual records, each of which is scaled to several levels of intensify, typically until collapse is reached. Although closely related to stripe analysis, its main advantage is that the IM levels of the different records do not need to match. Instead, a fixed number of nmilinear dynamic analyses can be utilized for... 

The process is repeated for different earthquake input sets, and a statistical estimate of q, is established for this type of building, design procedure, and performance criteria. The method suffers from the drawback that the performance indices do not depend linearly on the PGA (Kappos 1991) however, it has been commonly used since q is obtained at the expense of only one initial structural design and model formulation. This method falls closely with the application of the incremental dynamic analysis method (IDA) proposed by Vamvatsikos and Cornell (2003) for evaluating existing structural systems. 

UBC (1988) Uniform building code. International Conference of Building Officials, Washington, DC Vamvatsikos D, Cornell CA (2003) Applied incremental dynamic analysis. Earthquake Spectra 20(2) 525-533 Veletsos A, Newmark NM (1960) Effect of inelastic behaviour on the response of simple systems to... 

Incremental Dynamic Analysis, Fig. 4 Thirty IDA curves, 30 limit-state capacity points and the corresponding EDP and IM capacity distributions for the 9-story steel frame (From Vamvatsikos 2013)... 

Vamvatsikos D (2011) Performing incremental dynamic analysis in parallel. Comput Stract 89(1-2) 170-180 Vamvatsikos D (2013) Derivation of new SAC/FEMA performance evaluation solutions with second-order hazard approximation. Earthq Eng Struct Dyn 42 1171-1188... 

Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthq Eng Stract Dyn 31(3) 491-514 Vamvatsikos D, Cornell CA (2004) Applied incremental dynamic analysis. Earthq Spectra 20(2) 523-553 Vamvatsikos D, Cornell CA (2005) Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information. Earthq Eng Struct Dyn 34 1573-1600 Veletsos AS, Newmaik NM (1960) Effect of inelastic behavior on the resptmse of simple systems to earthquake motions. In Proceedings of the 2nd world conference on earthquake enginetaing, vol 2. Japan, PP 895-912... 

Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthq Eng Struct Dyn 31 491-514... 

Vamvatsikos D, Fragiadakis M (2010) Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty. Earthq Eng Stmct Dyn 39 141-163... 

Dolsek M (2009) Incremental dynamic analysis with consideration of modeling uncertainties. Earthq Eng Struct Dyn 38(6) 805-825... 

Prentice Hall, Upper Saddle River Lagaros ND (2010) Multicomponent incremental dynamic analysis considering variable incident angle. J Struct Infrastract Eng 6(l-2) 77-94 Lxypez OA, Torres R (1997) The critical angle of seismic incidence and the maximum structural response. Earthq Eng Stmct Dyn 26 881-894 Lopez OA, Chopra AK, Hernandez JJ (2000) Critical response of stmctures to multicomponent earthquake excitation. Earthq Eng Stmct Dyn 29 1759-1778 MacRae GA, Mattheis J (2000) Three-dimensional steel building response to near-fault motions. J Stmct Eng 126(1) 117-126... 

Penzien J, Watabe M (1975) Characteristics of 3-dimensional earthquake ground motions. Earthq Eng Stmct Dyn 3(4) 365-373 Rigato AB, Medina RA (2007) Influence of angle of incidence on seismic demands for inelastic singlestorey stmctures subjected to bi-directional ground motions. Eng Stmct 29(10) 2593-2601 Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthq Eng Stmct Dyn 31(3) 491-514 Wilson EL, Farhoomand I, Bathe KJ (1973) Nonlinear dynamic analysis of complex stmctures. Earthq Eng Struct Dyn 1 241-252... 

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