## 8 Incremental Dynamic Analysis (IDA)  
IDA [34], is an analysis method which can be used for more detailed seismic performance predictions of structures subjected to different seismic excitation levels. IDA involves numerous inelastic time history analyses performed using one or a set of ground motion record(s), each scaled (up or down) to study different seismic intensity levels. The IDA results are commonly presented using an intensity measure (IM) versus a damage measure (DM) of interest. IM is a non-negative scalable scalar, which is a function of the unscaled accelerogram, and is monotonically increased with a scale factor [34]. The 5% damped spectral acceleration at the structure's first-mode period (S\({}_{\text{a}}\) (T\({}_{1}\), 5%)) is often recommended and used as the IM parameter. The damage measure, DM, is defined as a non-negative scalar quantity that characterizes the response of the structure to seismic excitations and can be deduced from the output of the non-linear dynamic analysis. For bridges, the maximum drift ratio of the critical columns or the maximum ductility demand is typically used for the DM parameter. In using IDA, the post-peak (i.e., cap point) response of structural elements should be included in modelling. The most important factors in structural modelling for IDA are the plastic rotation capacity, \(\theta_{\text{cap}}\), and the post-capping rotation capacity, \(\theta_{\text{pc}}\)[26]. These parameters are used to define a component backbone curve, as shown in Figure 12.  
A study by [PERSON] and [PERSON] [11] provides some empirical equations to estimate the engineering demand parameters. These parameters include drift ratio, plastic rotation and strain in the longitudinal bars for circular bridge columns based on the properties of the columns including longitudinal and transverse steel ratio, axial load ratio, and geometry. In this research, the ultimate tensile strain in the steel bars corresponding to the bar buckling damage state from the empirical equations is used to compute the ultimate curvature of the columns and the corresponding drift and curvature ductility is defined as the point at which strength degradation begins (i.e., \(\theta_{\text{cap}}\) in Figure 12). Several damage states are considered in the seismic evaluation of the bridge under study including yielding, cover spalling, bar buckling and dynamic instability (regarded as collapse). The damage states in this study are predicted using empirical equations developed by [PERSON] and [PERSON] [11]. The serviceability damage state and bar-buckling damage state (shown by bar-buckling (Priestley)) are predicted based on the criteria given by [PERSON] et al. [7]. More detail regarding the determination of the damage states for the bridges under study is given by [PERSON] [12] and [PERSON] and [PERSON] [24]. The influence of using different types of record including artificial and natural records on the IDA results was investigated. IDA was performed for the regular and irregular bridge configurations considered in this research using different sets of artificial and natural records and the predictions including the IDA curves, percentiles and variability of the results were compared at different damage states. The IDA results for the transverse direction of the bridges were chosen to investigate the differences between the predictions from different record sets. The IDA curves obtained  
Figure 12: Backbone curve parameters (adapted from FEMA P695 [26]). from different record sets are summarized in Figure 13. It is clear from this figure that the use of artificial records resulted in lower variability in predictions, compared to the case of natural records. IDA curves were also obtained for different number of records, as presented in Figure 14, to investigate the sensitivity of the predictions to the number of records used in IDA. It is evident from this figure that for the case of SIMQKE and natural records the number of records did not have any important effect on the IDA results.