The paper presents an overview of the progress in research regarding seismic response of plan and vertically irregular building structures. Three areas of research are surveyed. The first is the study of the effects of plan-irregularity by means of single-storey and multi-storey building models. The second area encompasses passive control as a strategy to mitigate torsional effects, by means of base isolation and other types of devices. Lastly, the third area concerns vertically irregular structures and setback buildings. Although fewer papers have been published in this last area with respect to the former ones, this state-of-theart reports extensively on research efforts and progress into the seismic behaviour of irregular buildings in elevation to show the growing interest among specialists in the field.

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The increasing popularity of simplified nonlinear methods in seismic design has recently led to many proposals for procedures aimed at extending pushover analysis to plan asymmetric structures. In terms of practical applications, one particularly promising approach is based on combining pushover analysis of a 3D structural model with the results of linear (modal) dynamic analysis. The effectiveness of such procedure, however, is contingent on one fundamental requirement: the elastic prediction of the envelope of lateral displacements must be conservative with respect to the actual inelastic one.This paper aims at verifying the above assumption through an extensive parametric analysis conducted with simplified single-storey models. The main structural parameters influencing torsional response in the elastic and inelastic range of behaviour are varied, while devoting special attention to the system stiffness eccentricity and radius. The analysis clarifies the main features of inelastic torsional response of different types of building structures; in this manner, it is found that the above-mentioned method is generally suitable for structures characterized by moderate to large torsional stiffness, whereas it cannot be recommended for extremely torsionally stiff structures, as their inelastic torsional response almost always exceeds the elastic one. TORSION-INDUCED LATERAL DISPLACEMENTS FOR PUSHOVER ANALYSIS1371 displacements and the distribution of lateral forces for each resisting element; (2) a planar pushover analysis for each resisting element of interest (typically resisting elements located on the building perimeter), using the lateral force distribution and target displacement defined in step 1). However, although the procedure is convenient, in that it requires conducting only a small number of planar pushover analyses, it may be ineffective in the presence of significantly uneven distributions of stiffness and strength in buildings, since in such cases load distributions obtained simply through elastic analysis may differ considerably from the actual inelastic one [16].More recently, an important step towards incorporating torsional effects into pushover analysis has been made by Fajfar et al. [18,19]. They proposed combining the results obtained by pushover analysis of a 3D structural model based on the N2 method (i.e. the simple 2D nonlinear method developed in [2, 3]) with the results from a linear dynamic (modal) analysis. In particular, the N2 method controls the target displacement at the centre of mass and the distribution of deformations along the building height, whereas the linear dynamic analysis is used to define the plan-wise torsional amplifications of lateral displacements. The use of linear dynamic analysis is justified by the assumption that the elastic envelope of lateral displacements at the flexible edge is conservative with respect to the inelastic one [20,21]. According to their procedure, only amplifications due to torsion with respect to the target displacement at the mass centre are...

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