Weight optimization of the postbuckled integrally stiffened wide column

Abstract

An optimum stress equation for an integrally stiffened wide column is developed which parallels the buckle resistant simultaneous mode analysis but which also holds for postbuckling design. Coupling between the local failure and Euler buckling stress is accounted for by a parabolic fit interaction equation where failure stress is computed using an empirically modified effective width theory. It is shown that the ratio of applied stress to local buckling stress can be considered an optimized parameter. Specific numerical results for aluminum and titanium demonstrate that at sufficiently low values of the load index, the postbuckled design can represent a weight savings. It is shown that these index values correspond to applied stresses approximately one half the respective proportional limits. The analysis is limited to optimum values of the ratio of applied stress to local buckling stress which do not exceed 1.55 due to limitations on the interaction equation. Therefore, the postbuckling weight advantage cannot be fully explored at the lower index range. The determination of the upper bound load index where postbuckling design ceases to represent a weight advantage is well within the applicability of the interaction equation and is the principal conclusion of this investigation. Cer = E = K = L = Nf = PT = r, = /. = j — Nomenclature distance between stiffeners stiffener web height failure stress equation coefficient for the i\h element of the cross section equivalent coefficient for the total cross section modulus of elasticity coupled local buckling coefficient column length distributed load (Ib/iri.) total failure load of representative width bw/bs tjt. skin thickness web thickness weight effective thickness (cross-sectional area per unit width) e = efficiency factor in the efficiency equation Tj7- = plasticity correction (ET/E) i/vc = slack variable equal to the ratio O-A/O-CC \!/E = slack variable equal to the ratio =s a function of material parameters and rb and rt with the dimensions of stress