Determination of Slenderness Ratio for Laced and Battened Columns

Abstract

This article focuses on elastic stability analysis of battened columns and laced columns with crosswise, fir-shaped, and serpentine lattices. The columns are considered as static indeterminate systems. The buckling problem of the column is formulated as a two-point boundary-value problem for a system of recurrence relations between displacements of the column joint nodes. For columns with any degree of static indeterminacy, the Euler buckling load is determined as the least eigenvalue of the fourth-order system of homogeneous linear algebraic equations. A buckling-mode shape of the column is displayed as a superposition of the set of displacements of the column joint nodes and the curves describing the deflection of the column chords between the joint nodes. Two different combinations of the end boundary conditions are considered. The Euler buckling load of the laced columns depends significantly on the rigidity parameters of the column lacings, and the Euler buckling load of the battened column depends on the rigidity parameters of the batten plates. The use of computer programs developed to solve the buckling problem of the built-up column as a two-point boundary-value problem makes it possible to establish a relationship between the modified slenderness ratio of the built-up column and the rigidity parameter of its lattices or battened plates under various combinations of boundary conditions at the ends of the column. The result of the stability analyses of the considered columns disproves the statement that the rigidity characteristics of batten plates and lacings can be ignored in determining the modified slenderness ratio for the built-up columns.