Calculation of multilayer wood panels using the theory of composite rods
DOI:
https://doi.org/10.36910/6775-2410-6208-2025-14(24)-01Keywords:
CLT panel, roller shear, rod approximation, composite rods, wooden structures, Fourier series.Abstract
Abstract. The article proposes a method for calculating CLT panels using the theory of composite rods and rod approximation. It is shown that, unlike existing approaches, the panel operation is considered in two directions, and not as a beam system. First, the stiffness characteristics of the panel are determined in each direction, taking into account the shear. Then the plate is calculated as an orthotropic plate with different stiffness characteristics in mutually perpendicular directions. In this case, such a calculation is performed either as an orthotropic solid plate or as a cross-rod system. The theory of composite rods was used to determine the stiffness characteristics in each direction, taking into account the shear of the boards in the transverse direction. Taking into account the boundary conditions, the system of differential equations is reduced to a system of algebraic equations by expanding the unknowns and the external load into Fourier series. It is shown that taking into account the shear of the transverse boards significantly affects the final result of the maximum displacements in the middle of the span of the CLT panel. Calculation according to the theory of composite rods with proposals for the use of Fourier series for solving a system of differential equations allows us to determine the stiffness characteristics in two mutually perpendicular directions of the CLT panel. It is shown that the advantage of using the theory of composite rods is that it can be used to calculate panels with any number of layers. In addition, the theory of composite rods allows us to take into account different stiffnesses in the joints between the composite rods, different thicknesses of boards in the layers of the CLT panel. The article shows that today CLT panels are calculated according to the beam theory, although the floor panel works in two directions and its work differs from the beam one. The use of the rod approximation proposed by the authors of this article for calculating the CLT panels allows us to calculate them taking into account the work in two directions. The rod approximation allows solving the problem of correct modeling of the slab and eliminating the complexity of taking into account the ifferent thickness of the slab in two directions.
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