Comparison of exact IDA and approximate MPA-based IDA for reinforced concrete frames

Recent decade has witnessed the improvement of performance-based earthquake engineering (PBEE) methods. Therefore, procedures to estimate performance levels of structures have developed in accuracy as well as simplification in practice. Incremental dynamic analysis (IDA) and modal pushover analysis are probably the most important methods in this aspect. IDA was identified as the state-of-the-art method to assess the performance level of structures by FEMA-350 but is a computational demanding technique. On the other hand, modal pushover analysis -despite its inherent approximate nature- is broadly used as the simplified nonlinear static method to evaluate seismic demands of structures. Recently these two methods have combined and constituted a more advanced method called MPA-based IDA which possesses the advantages of the two methods. In this paper, a comparative study is carried out to evaluate the reliability of MPA-based approximate method for regular and irregular RC plane frames. Results show that MPA-based IDA procedure is satisfactory for structural demands with a huge reduction in computational effort for regular buildings. Various types of the analysis of structures for seismic design are linear static, linear dynamic, nonlinear static and finally nonlinear dynamic. The use of linear static analysis for seismic design of structures is often questioned among researchers. Although nonlinear static analysis under monotonically increasing lateral load (pushover analysis) has been gaining momentum of dynamic analysis and also exhibits simplified version of analysis, but it suffers from its approximate nature and cannot yield to an accurate estimation of seismic behavior of structures. A state-of-the-art method to assess the performance level of structures is Incremental dynamic analysis which based on nonlinear time history analysis (Vamvatsikos and Cornell 2002, 2004). This method is an extended procedure of pushover analysis that considers strength and stiffness degradation and also ground motion characteristics. In the other words, IDA is the most accurate procedure to evaluate seismic behavior of structures. The most important drawback of this procedure is its time consuming nature especially with considering full nonlinear analysis (material and geometrical nonlinearity) and strength deterioration and stiffness degradation. In section 3, a brief review of this procedure is given. As indicated above, Pushover is an alternative method for seismic analysis of structures. In this method, lateral static loads are gradually imposed on the structure. This requires consideration of inelasticity under increasing lateral loading. The pushover procedure has been evaluated in several studies. (Gulkan and Sozen 1974) are probably the first researchers who suggested pushover for representing the response of multi-degree of freedom system by a single degree of freedom equivalent. (Saiidi and Sozen 1981) introduced a simple analytical model to estimate the displacement histories of multi-storey reinforced concrete structures subjected to strong ground motions. In developing this model they made two major simplifications. First, they replaced a multi-degree-of- freedom (MDOF) model of a structure by a single degree-of-freedom (SDOF) oscillator. Secondly they approximated the variation of incremental stiffness properties of the whole structure by a single nonlinear spring. The specifications of SDOF oscillator were determined based on a calculated relationship between base moment and lateral displacement under monotonically increasing load. These researchers compared