Flexural buckling of laced column with fir-shaped lattice

Abstract

In contrast to the classical Engesser method of solving the buckling problem for laced columns in terms of an “equivalent” solid bar, the buckling problem of a column with a fir-shaped lattice is formulated as a stability problem of a statically indeterminate system of elastic bars. Solving this problem by conventional methods consists of the determination of a smallest eigenvalue for the linear algebraic system of a high order which depends upon the number of the column joints. The present approach requires analyzing only the fourth-order system for columns with any degree of static indeterminacy. The stability analysis is reduced to numerical solution of a two-point boundary value problem for a system of recurrence relations between deformation parameters of column cross-sections passing through the column joints. The critical force and the modified slenderness ratio for column with any number of panels and the fixed inclination of lattice diagonals are represented as a function of the lattice rigidity parameter. The obtained values of Euler's critical force are essentially higher than those obtained with Engesser's model. The distinctive feature which is similar to the Boobnov phenomenon occurs for the column with a fir-shaped lattice: the column loses stability so that joint cross-sections are not displaced and the chord panels are buckled as a simply-supported bar. This type of buckling is possible when the lattice rigidity exceeds a specific limit. The plots of the modified slenderness ratio as a function of the lattice rigidity can be applied in designing steel-laced columns with a fir-shaped lattice.