Flexural buckling of laced column with serpentine lattice

Abstract

Unlike the technique accepted in existing design specifications, the buckling problem of a laced column with a serpentine lattice is formulated as a stability problem of a statically indeterminate structure. The problem is reduced to a two-point boundary value problem for a system of recurrence dependences relating the deformation parameters of column cross-sections passing through the lattice joints. These relations are derived by using the initial value method for solving differential equations of column chord equilibrium. For columns with any degree of static indeterminacy, the critical force is determined as the smallest eigenvalue of the fourth-order system of homogeneous linear algebraic equations. The obtained mode shapes have the form of irregular curves with many points of inflection and disprove a concept that the stability problem of a laced column can be reduced to the analogous problem for an ‘equivalent’ continuous solid column based on Engesser's assumption. Euler critical forces calculated for a column as a statically indeterminate system are compared with the critical forces from Engesser's equivalent solid column. The phenomenon which is similar to the Boobnov effect can occur for the serpentine column: it can lose stability so that panels of one of the chords are buckled as isolated simply supported bars. This type of buckling is possible when the lattice rigidity of the column exceeds a specific limit. For columns with identical chords, the critical force is a function of the number of sub-panels and the special lattice rigidity parameter. The relationships between the critical force and the lattice rigidity parameter for columns with a varied number of sub-panels can be applied in designing steel-laced columns.