Constrained Axial Buckling About Non-Principal Axes

When certain structural members are used in axial compression, framing considerations dictate the orientation of the cross section about the member's longitudinal axis. When a second member is framed to the first, a constraint is imposed which forces the member to buckle about a non-principal axis. The author investigates axial buckling for this case, and formulates equations for the compound buckling of axial compression members. Formulas are derived using the differential equations of classical structural stability mechanics. For the initial case analyzed, where a member is continuously supported about a non-principal axis, the author discovered that the classical Euler buckling equation holds, but the radius of gyration is calculated about the respective nonprincipal axis. Due to coupling from the product of inertia, a moment is induced about the orthogonal non-principal axis.