Proposed correction to the Gamma method for estimating the bending stiffness of CLT panels

Abstract

Engineered wood products, such as Cross Laminated Timber (CLT), have been widely used in civil construction. Standard calculation methods, like the Gamma method commonly used in structural design, estimate the bending stiffness of elements. However, these methods are based on one-dimensional solids (bar elements), which can be limiting. This limitation may result in inaccurate estimates, especially when the panel's dimensions, measured in the median plane, significantly differ by an order of magnitude. In this research, a parametric study was carried out using the finite element method (three-dimensional approach), varying the panel's dimensions (width and length), the layers' thickness, and the number of layers (cross-section height), and adopting elastic properties considering either the wood's orthotropy or the rolling shear estimation (108 numerical simulations in all). Based on the parameterization, multiple variable regression models were used to establish a correction coefficient to be incorporated into the Gamma method to improve its accuracy in estimating bending stiffness. Therefore, the single adjusted equation (considering the wood's orthotropy) showed values closer to the numerical ones (MAPE = 0.95 %, RMSE = 2.96 × 1011 N⋅mm2, and CV = 1.60 %) than those obtained by the Gamma method (MAPE = 2.13 %, RMSE = 7.47 × 1011 N⋅mm2, and CV = 4.04 %).