Analytical solutions and optimization design for bending behavior of cross-laminated timber beams considering orthotropy and interface slip

The aim of this work was to propose analytical solutions and an optimization design method for the bending behavior of cross-laminated timber (CLT) beam, in which the orthotropy of timber and interface slip between the neighboring layers were considered simultaneously. The lamina layers of orthotropic woods were modeled based on the two-dimensional (2D) elasticity theory without transverse shear deformation assumption. By means of series expansion and solving differential equations, the general solutions for stresses and deformations in the beam were obtained with undetermined coefficients. The unknown coefficients were further determined by the transfer matrix method. The comparison study indicated the proposed solutions had higher accuracy than the Euler-Bernoulli beam solution and isotropic solution, since the proposed solutions renounced the transverse shear deformation assumption and considered the orthotropy of wood. Moreover, it was found that the interfacial stiffness has an economical upper bound above which no significant gain on the bending stiffness of CLT beam can be obtained, and an optimal configuration of geometry and material can achieve an increase of bending stiffness. We release our program for the proposed analytical solutions, at https://github.com/Njtpw/CLT-Beam.git.