Asymptotic theory for static behavior of elastic anisotropic I-beams

End effects 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 evaluated, and the most influential end disturbances are incorporated into a refined 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 3-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. (C) 1988 Elsevier Science Ltd. ell rights reserved.