Minimum bracing stiffness for multi-column systems: theory (2011)
A method that determines the minimum bracing stiffness required by a multi-column elastic system to achieve non-sway buckling conditions is proposed. Equations that evaluate the required minimum stiffness of the lateral and torsional bracings and the corresponding “braced” critical buckling load for each column of the story level are derived using the modified stability functions. The following effects are included: 1) the types of end connections (rigid, semirigid, and simple); 2) the blueprint layout of the columns (i.e., the cross section orientation and location of the centroid of each column); 3) shear deformations along each column using the modified method initially proposed by Haringx in 1948; and 4) axial load distribution among the columns (i.e., load pattern). The effects of axial deformations and warping torsion are not included. The proposed method is applicable to 2D and 3D framed structures with rigid, semi-rigid, and simple connections. The formulation presented in this paper is based on a pre vious work presented by Aristizabal-Ochoa in 2007. It is shown that the minimum stiffness of lateral and torsional bracings required by a multi-column system depend on: 1) the blueprint layout of the columns; 2) the variation in heights and cross sectional properties among the columns; 3) the flexural and shear stiffness of each column; 4) the load pattern on the multi-column system; 5) the lack of symmetry (in the loading pattern, column layout, column sizes, and heights) that cause the combined torsion-sway buckling all of which reduce the buckling capacity of the frame as a whole; and 6) the support conditions and restraints at the top end of the columns. The proposed method is limited to multi-column systems with elastic and orthotropic columns with doubly symmetrical cross sections (i.e., with a shear center coinciding with the centroid) oriented in any direction with respect to the global axes. Four comprehensive examples are presented in detail in a companion paper that shows the effectiveness and simplicity of the proposed method.