Optimization matrix method for the determination of the real torsion axis orientation angle

• Published in: Engineering structures Vol. 286; p. 116133
• Main Author: Terzi, Vasiliki G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-07-2023
• Subjects: Matrix optimization; Orientation angle; Real torsion axis; Structural eccentricity; Orientation angle; Real torsion axis; Matrix optimization; Structural eccentricity
• ISSN: 0141-0296; 1873-7323
• DOI: 10.1016/j.engstruct.2023.116133

•An optimization matrix method is proposed in order to determine the orientation angle of the real elastic axis.•Three different criteria are proposed for characteristic values of the stiffness matrix, determined at the real elastic axis.•The optimization method is independent of any kind of applied loading.•The proposed procedure can be implemented in any programming language.•Numerical results are presented and the proposed method is compared with other researchers’ results.
The vertical axis of a multi-story building, at which the rigidity centers of the floors are aligned, is called real torsion axis. In particular, the real torsion axis is characterized as bending; twist; and shear axis, as well. If the local axes of the vertical structural elements are not aligned with the axes X and Y of the global orthogonal coordinate system (O,X,Y,Z), the principal horizontal axes, I and II of the coordinate system defined at the real torsion axis, present an angle, ao, which is usually determined according to axis X. The principal vertical axis III coincides with Z axis. The present paper proposes a new method for the determination of the orientation angle of the real torsion axis. The method refers to single-story and special classes of multi-story buildings, which possess a real torsion axis, in contrast with the majority of the multi-story buildings, at which an optimum torsion axis is usually sought. Firstly, the stiffness matrix of the building is determined at the location of the real torsion axis. Secondly, the rotation matrix around the vertical axis is determined and the rotated stiffness matrix is determined, as well. Three new criterions are proposed in order to define the critical rotation angle, at which the rotated stiffness matrix receives a diagonal form, and therefore, the critical angle defines the orientation of the two principal bending planes I,III and II,III. The optimization matrix method can be easily implemented in any programming language. Numerical examples are presented. Their results satisfy the three characteristic axis properties of the real torsion axis and are in complete agreement with the results of other researchers.