Asymptotic theory for static behavior of elastic anisotropic I-beam

End e}ects for prismatic anisotropic beams with thin!walled\ open cross!sections are analyzed by the variational!asymptotic method[ The decay rates for disturbances at the ends of prismatic beams are evaluatedand the most in~uential end disturbances are incorporated into a re_ned beam theory[ Thus\ the foundations of Vlasov|s theory\ as well as restrictions on its applicability\ are obtained from the variational!asymptotic point of view[ Vlasov|s theory is proved to be asymptotically correct for isotropic I!beams[ The asymptotically correct generalization of Vlasov|s theory for static behavior of anisotropic beams is presented[ In light of this development\ various published generalizations of Vlasov|s theory for thin!walled anisotropic beams are discussed[ Comparisons with a numerical 2!D analysis are provided\ showing that the present approach gives the closest agreement of all published theories[ The procedure can be applied to any thin!walled beam with open cross!sections[