Optimal Design of Portal Frames Against Buckling

Abstract

ABSTRACT ABSTRACT Portal frames subjected only to axial column forces usually fail by buckling into a sidesway mode. For a prescribed volume, the load parameter associated with this mode may be maximized. However, the optimal structure so obtained exhibits a hinge in each column and beam and can be demonstrated to buckle without sway, under a load parameter which is always smaller. Inverting the process by designing the structure for optimal swayless buckling is equally fruitless, in that it leads to sharply reduced resistance against sidesway buckling. These questions are explored, and it is shown that the correct optimal solution is based on a double eigenvalue associated simultaneously with both a sidesway and a swayless buckling mode. The relevant equations are developed and an analytical solution is obtained for the case of a symmetric portal frame under symmetric loading for various height-to-span ratios. As expected, and in conformity with the known solution to the fixed-fixed column problem, the c...