Flexural buckling of laced column with crosswise lattice

Abstract

Solving the flexural buckling problem of a laced column as a statically indeterminate system is reduced to the two-point boundary value problem for a difference equation system that comprises recurrence relations between the displacements and the force parameters of column cross-sections passing through the lattice joints. The critical force for a column with any degree of static indeterminacy is determined as the smallest eigenvalue of the fourth-order system of linear algebraic equations. The recurrence relations that have been established for the torsional buckling in the author's preceding study are extended to the case of flexural buckling of a laced column with a crosswise lattice, owing to the static-geometric analogy between the two kinds of buckling. The obtained deflection mode shapes show that the loss of stability of the laced column occurs as a result of the local buckling of column chords, and disprove a concept of the sine-shaped deflection mode shape, which is basic in design manuals for steel-laced columns (Engesser's assumption). Columns with a very rigid lattice can lose stability, so that joint cross-sections are not displaced, and the chord panels are buckled as isolated simply supported bars. For columns with identical chords, the critical force is a function of the number of panels and the special lattice rigidity parameter of the column. The plots of this function for a series of columns with a varied number of panels can be validly applied in designing steel-laced columns.