Approximate Nonlinear Seismic Evaluation of Frame Buildings by Static and Dynamic Analysis Methods and Comparison with the Exact Solutions

Performance-based earthquake engineering requires accurate estimation of the seismic demand and capacity of structures. In recent years, various kinds of nonlinear static and dynamic analyses have been developed for the seismic evaluation of structures. Nonlinear dynamic time history analysis method is not only very time consuming, but also needs a proper skill and proficiency in order to interpret its results. For the performance evaluation of the structures, the speed and also the precision of conducting different analyses are very significant criteria. This issue has led to the creation of various new methods based on the principles of nonlinear and incremental static and dynamic analysis. One of the methods that has been proposed to tackle this task is incremental dynamic analysis (IDA). This procedure requires non-linear time history analyses (NL-THA) of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover a wide range of structural response; all the way from elastic behaviour to global instability. From the results of such computation, it is possible to determine structural capacities (or ground motion intensities) corresponding to various limit states; immediate occupancy (IO), life safety (LS), or collapse prevention (CP). Another approach to reduce the computational effort required for IDA is to estimate seismic demands for the practical structures by modal pushover analysis (MPA), an approximate procedure, instead of non-linear RHA. Thus, each of the many non-linear RHA required in IDA is replaced by a MPA. In addition, a more recent proposed method logically combines two different techniques, IDA and MPA is employed, presented by modal incremental dynamic analysis (MIDA). Using MIDA procedure, simple approximate curves that present a realistic linear and non-linear seismic behavior of the structure headed for the calculation of the damage measure (DM) due to the applied scaled level of earthquakes can easily be extracted. In this study, the capability, limitation and precision of MPA in comparison with NL-THA and also MIDA in comparison with IDA method are evaluated. For this purpose, two steel building models of 5 and 15-story with special moment resisting frame (MRF) in X direction and simple frame with X-bracing in Y direction has been designed. Furthermore, seven far field earthquake records are used for nonlinear analyses. In the current article, acceleration spectral intensity of the first mode of vibration with 5% damping, i.e. Sa(T1, %5) factor, are used as of intensity measure (IM). The story deflection and story drift are chosen as of the most important DM parameters to estimate the seismic vulnerability of structures in design practice. Comparison of the numerical results reveals that the MPA method has good accuracy in building seismic demands evaluation for 5-story frames (MRFs and braced frames) and 15-story MRF. However, no exact response is obtained for 15-story braced frame, considering the first three vibration modes of the structure. It is also shown that the results from MIDA simple method compares favorably to the IDA method. Thus, MIDA can be served by design engineers for seismic analysis in order to evaluate structural performance due to its relative simplicity and minimal computational effort.