This paper constitutes the second part of a study devoted to the 1D modeling of beam-like structures, of arbitrary cross-section with periodic properties along the axis. In the first part, the asymptotic expansion method has been described, and the equations involving the successive terms of the outer solution have been given. In particular, it has been shown that neither the leading term nor the full outer solution are able to satisfy arbitrary prescribed edge data. A specific study is thus necessary and it is presented in this paper. The method used is the decay analysis initially proposed for homogeneous plates by Gregory and Wan (J. Elast. 14 (1984) 27). This approach consists in deriving the appropriate set of boundary conditions for the outer expansion solution, for any arbitrary edge data (stress, displacement or mixed data). These boundary conditions are obtained from the solution of canonical beam problems, without computing any inner solution. The method is illustrated through numerical examples on a lattice structure. The results obtained prove the importance of a correct treatment of the edge effects, in order that the inclusion of higher-order terms in the beam model serves actually to increase the accuracy of the outer expansion solution.