Elasticas and Buckling Loads of Shear Deformable Tapered Columns

This paper deals with the geometrical nonlinear analyses of buckled columns. Differential equations governing the elasticas of buckled columns are derived, in which both the effects of taper type and shear deformation are included. Three kinds of taper types are considered, i.e. breadth, depth and square tapers. Differential equations are solved numerically to obtain the deflection of elasticas and the buckling loads of such columns. Both clamped ends and hinged ends are considered. The effects of shear deformation on the deflection of elasticas of buckled columns and on the buckling loads of columns are investigated extensively. The buckling load equations for uniform columns are expressed as a function of the implicit shear effect. Experimental studies are presented that complement the theoretical results of nonlinear responses of the elasticas.