AN ADAPTIVE PUSHOVER ANALYSIS CONSIDERING TORSIONAL EFFECTS

Development of performance-based structural design during the last decade, has led to extensive research into nonlinear static (pushover) procedures. Since nonlinear dynamic methods are time consuming, impractical and also dicult to interpret, in spite of their high accuracy in seismic response estimation of the structures, they cannot be used in everyday engineering work. In contrast to dynamic procedures, pushover methods are simple, practical and easy to understand. Based on these facts, pushover methods have been the main subject of much research conducted during recent years. As an introduction to performance-based structural design, ATC-40 and FEMA-356 have introduced the capacity spectrum method (CSM) and the displacement coecient method (DCM), respectively. Since, in these methods, the lateral force distribution is assumed to be constant and is calculated based on the fundamental vibration mode of the elastic structure, they can provide accurate seismic demand estimates only for low and medium-rise buildings, where the contribution of higher modes in seismic responses is negligible. In order to improve the capability of these conventional procedures, dierent methods have been presented by researchers. Following these eorts, in the present study, an innovative adaptive pushover analysis considering torsional eects (APAT) has been developed. APAT is a single stage procedure which uses an equivalent adaptive load pattern. In order to consider the eects of higher modes, especially rotational modes in 3D structures with noticeable torsional eects, and due to the known drawbacks in common combination methods, such as square root of the sum of the squares (SRSS), herein, an eective modal mass combination (EMMC) rule for multi-story buildings is used. In the EMMC method, load vectors are combined based on determined coecients for each mode. These coecients are de ned using eective modal mass proportions. The equivalent load pattern in the present study is obtained through a combination of dierent modal shapes based on the EMMC rule. In order to capture the torsional eect, a three dimensional energy-based formulation is used which transforms the MDOF structure to an equivalent SDOF model. In the three dimensional energy based formulation, work undertaken by both translational and rotational forces is taken into account. The accuracy of the proposed procedure is evaluated for a series of asymmetric structures. The parametric study shows that the proposed method could predict seismic responses precisely, even in structures with signi cant torsional eects.