Design of Lateral Braces for Columns Considering Critical Imperfection of Buckling

The present paper discusses the design of column-type structures, which are composed of columns and lateral braces attached perpendicular to the columns. Buckling of the braces of this kind of structures directly leads to global buckling of the columns. The brace-buckling modes are successfully detected by considering higher-order geometrically nonlinear relations and by introducing Green's strain into the total potential energy of the structure. Sensitivity analysis of the eigenvalues of the tangent stiffness matrix under fixed load condition is carried out with respect to imperfections of the nodal locations. Furthermore, the critical imperfection that most drastically reduces the eigenvalues are calculated and buckling loads of the imperfect systems are evaluated. The numerical results show that the second or higher eigenmode of the tangent stiffness matrix of the perfect system should be sometimes used for estimating the buckling load of the imperfect system. Design examples are presented using the proposed method, and they are compared with those in accordance with an allowable-stress design standard. The results show a possibility of reducing the sizes of the brace sections.