Optimum torsion axis in multistory buildings under earthquake excitation: A new criterion based on axis of twist

Abstract

The elastic axis is essential for the definition of structural eccentricity, which significantly affects the torsional behavior of buildings. However, it can be determined straight-forwardly in single-story and some special cases of multi-story buildings. Therefore, for the majority of multi-story buildings, the notion of optimum torsion axis has been introduced, according to which, the torsion of the building is considered optimum when the sum of squares of the floor torsional angles is minimum under horizontal forces passing through this axis. The existing determination procedures refer to the application of static horizontal forces and static torsional moments at each story. The present study proposes a new criterion, which approaches the optimum torsion axis by the prism of axis of twist and requires the sum of floor translational displacements of the axis to be minimal. The criterion can be applied under: i) static torsional moments imposed at each story or ii) torsional ground motion excitation. In the latter case, the term of dynamic optimum torsion axis is introduced. Mathematical formulae are provided for the application of the new criterion as well as for the determination of the location of the optimum torsion axis, static or dynamic. It is mathematically proved that the coordinates of the static optimum torsion axis depend on the distribution of torsional moments along the building’s height. However, the coordinates of the dynamic optimum torsion axis are independent of the torsional base excitation and depend only on the mass moments of inertia at each floor level. The proposed method can be easily implemented, as it is based on data given by any structural program, either in terms of structural characteristics or in terms of response.