Buckling by Constant Stiffness and Curvature-Deflection Resonance

The extensive use of plates and frames in construction regularly brings the engineer to confront buckling failure and its analysis and estimates of strength ;this makes it necessary to continue to explore easier ways of finding and verifying buckling solutions. Buckling by the constant initial elastic stiffness matrix is desirable but difficult to find in the literature ;the use of stability functions to modify the stiffness matrices is more readily found. By replacing the curvature in the Euler equation for buckling by its relative value, a successive approximation of steady state relative curvature -deflection ratio is, in-fact, found to be the buckling coefficient. In this way, a new practical buckling criterion is invoked as the resonant relative curvature-deflection ratio . Bars and rigid-frames are examined in this study.