Maximum load factors corresponding to a slightly asymmetric bifurcation point

Explicit formulations are derived for quantitative evaluation of imperfection sensitivity of critical load factors corresponding to a slightly asymmetric bifurcation point; i.e. the perfect system itself has slight asymmetry. The load factor corresponding to local minimum or maximum along the fundamental equilibrium path and the complementary path are simultaneously obtained as functions of the imperfection parameter. The upper bound of the imperfection parameter is also derived for existence of critical points along the fundamental equilibrium path. This way, interpolation formulas are presented between symmetric and asymmetric systems. The accuracy of the proposed formulas is verified by the examples of rods supported by translational and rotational springs.