Analytical Study of Unstiffened Elements

An equation for the elastic local buckling stress of unstiffened compression elements is derived using an approximate wave form for the solution of small deflection equation of plates subject to membrane stresses. Von Karman's fourth-order partial differential equations for large deflection of thin plates with initial out-of-plane imperfections are solved, using the approximate wave form, to study the post-buckling behavior. The elastic and inelastic local buckling and post-buckling solutions obtained from the analytical study are compared with test results of members with unstiffened compression elements. Simple equation for the post-buckling effective width is derived through a parameter study.