Manish Kumar

IITB Logo Manish Kumar
Assistant Professor

Department of Civil Engineering
Indian Institute of Technology Bombay, Mumbai



Incremental Dynamic Analysis

In contrast to the pushover analysis, where a load pattern is applied to the structure and increased statically from an initial value till the failure of the structure to find the force and displacement capacity of the structure, in Incremental Dynamic Analysis(IDA), a selected ground motion is applied with increasing amplitude till the structure fails at a particular amplitude of the motion. Pushover Analysis is a nonlinear static analysis, Incremental Dynamic Analysis is a nonlinear dynamic analysis. An IDA curve typically shows a spectral response on the ordinate and displacement of rotation on abscissa. A typical behavior of IDA curve is shown below.


Figure taken from Vamvatsikos et al(2002), EESD

IDA is highly dependent on the characteristic of ground motion. Two ground motion with same peak ground motion can result in completely different nature of IDA curve. Hence a single ground motion can not represent the nonlinear dynamic behavior of the structure completely and in order to characterize the structural behavior large number of ground motions should be used for analysis. It can be argued that IDA represents "failure" of the structure more appropriately compared to pushover curve, but uncertainty lies in the fact that it is very difficult to define a "failure" point on IDA curve. Although values are specified by different codes for taking failure point like 2 percent inter storey drift(FEMA), this value can not be relied upon on IDA curve due to very erratic nature of IDA curve supplemented by phenomenon like "resurrection" of IDA curve etc. Resurrection is the phenomenon in which it seems that structures has yielded at particular amplitude of ground motion indicated by flatter response, but a steeper response appears again with increasing amplitude of ground motion. Figure below shows the erratic nature of IDA curves.

IDA Curve

Figure taken from Vamvatsikos et al(2002), EESD

Considering the uncertainly in deciding a failure point on the curve a probabilistic approach is taken where a fragility curve is plotted with probability of failure on ordinate and spectral acceleration on abscissa.

Incremental dynamic analysis is a very exhaustive procedure where one might have to do hundreds to nonlinear dynamic analysis to get some meaningful results, nevertheless it provides very useful information on dynamic behavior of the structure.


Useful References:

  1. Vamvatsikos et al(2002), EESD

  2. FEMA P695/June 2009: Quantification of Building Seismic Performance Factors(ATC-63)