Bracing requirements for multiple parallel nonidentical columns with initial curvature

For a system consisting of multiple columns, horizontal discrete braces are often used to increase the system’s strength by decreasing the effective length of columns. Since the bracing requirements for such systems in current design standards were developed based on the assumption of identical columns with pin-ends, an analytical method is proposed to evaluate the ideal brace stiffness and brace forces for multiple columns by accounting for the stiffness interaction among columns and braces. For systems with uniform column lateral stiffness, the explicit solution for the maximum brace force is derived, and a simple formula is subsequently proposed by fitting the analytical results. The proposed formula explicitly accounts for the influences of column initial curvature and semi-rigid end connections on the maximum brace force. The method is comprehensive and applicable to multi-column systems with nonuniform column lateral stiffness, which can result from differences in column sizes, end connections, or applied loads. The results obtained from the proposed formulae are verified against those of finite element analyses. The ideal brace stiffness and brace forces for a system containing a distinctive column with a greater moment of inertia than the other columns are investigated. The results show that the location of the distinctive column affects the magnitudes of the ideal brace stiffness and the maximum brace force, which is yet to be considered in current design standards.