Invariant torsion properties of multistorey asymmetric buildings

Abstract

In this paper significant invariant torsion properties of multistorey asymmetric diaphragm systems are presented and investigated, which do not depend on certain special characteristics of the structural system, but only on the vertical distribution of the lateral loading. The analytical study includes generalization of the application of existing formulas for finding the exact location of the optimum torsion axis, verification for its uniqueness, evaluation of the principal torsion directions for any position of the loading axis, and especially for the position of the optimum torsion axis. It also provides quantitative criteria to ascertain whether the diaphragm rotations in general are sufficiently small, when static analysis procedures of calculating the seismic response are going to be applied. Several numerical examples demonstrate the applicability of the proposed methodology, which helps to a better understanding of the torsional behaviour of multistorey buildings. Copyright © 2007 John Wiley & Sons, Ltd.

Analysing the Critical Orientation of Seismic Loading in 3D Buildings: Preliminary Results for Constant Lateral Forces

“…Since the elastic axis is a very good descriptor of a building and allows the determination of its static behaviour independently of the external loading (Makarios and Anastassiadis 1998), studies have been dedicated to extend and generalize its concept for general multi-storey buildings. Two different methodologies can be found in the literature that deal with the approximation of the elastic axis for multi-storey buildings (Makarios and Anastassiadis 1998;Marino and Rossi 2004;Doudoumis and Athanatopoulou 2008). The advancement of the proposed methodology with exploitation of these concepts constitutes an area of future research.…”

Predicting displacement demand of multi-storey asymmetric buildings by nonlinear static analysis and corrective eccentricities

“…Out of the methods available in literature [57][58][59][60][61][62], the one proposed by Makarios and Anastassiadis [60,61] is used for the determination of the uncoupled torsional to lateral frequency ratios. According to this method, the uncoupled ratios X hy and X hx , corresponding to the seismic force acting along the y-and x-direction, respectively, are calculated as the ratios of the rigidity radii of gyration r kx and r ky to the mass radius of gyration r m .…”

In Plan Distribution of Isolators Effective Stiffness for Minimizing the Torsional Response of Base Isolated Buildings

“…The isolators' damping was taken equal to 30% for both the buildings. The distribution of the above three types of isolators in plan was chosen so as the optimum torsion axis (OTA) of the structures [11,12] to coincide with the vertical mass axis. Moreover, note that the total horizontal and torsional stiffness of the isolators should remain approximately constant between the cases (b) and (c).…”

“…For the determination of the OTA the methodology proposed by Marino and Rossi [11] was used. Then the principal directions under lateral loading were determined using the methodology presented in [12]. According to the aforementioned studies [11,12] the process of determining the OTA is as follows: Let there be N-storey building system with horizontal rigid floor diaphragms at the floor levels, in a Cartesian global coordinate system Oxyz with a vertical Oz axis (figure 1).…”

“…Then the principal directions under lateral loading were determined using the methodology presented in [12]. According to the aforementioned studies [11,12] the process of determining the OTA is as follows: Let there be N-storey building system with horizontal rigid floor diaphragms at the floor levels, in a Cartesian global coordinate system Oxyz with a vertical Oz axis (figure 1). Considering as degrees of freedom of the i th floor level the diaphragm rotation θ zi and the horizontal displacements u xi and u yi of a point on the diaphragm, the displacement state of the diaphragms can be characterized by the N-column vectors:…”