Calculation and design of hybrid wooden beams

The problem of determining the stress-strain state and designing hybrid wooden beams is considered. In general, the bar is a rod consisting of several layers. In principle, the number of layers is not unlimited. Each layer can be made of different materials. The geometry of the cross section of a layer may vary a lot. The cross-section of the rod can be either constant or variable in length. The rod experiences a straight transverse bending with stretching-compression. The physical nonlinearity, as well as the different material resistance to stretching and compression are taken into account. The deformations and displacements of the rod are considered to be small values, and it allows one to write the equilibrium equations for the undeformed state. We accept a valid theory of Bernoulli flat sections and a simplified expression for the curvature of a plane curve. The determination of the stress-strain state of the rod is reduced to solving a system of two nonlinear algebraic equations of the third order. To solve it, the load is divided into a number of steps in accordance with the loading history, which allows to linearize the system of resolving equations. Much attention is paid to the design of hybrid beams. Both parametric and functional designs are considered. Based on the calculation examples, it is shown that the use of the criterion of the equal strength in combination with the principles of hybrid design allows to significantly reduce the material consumption of the structure. Also a strong effect of different materials resistance during stretching and compression is shown on the transverse dimensions of the bars obtained during the design. The possibility of latent destruction is demonstrated, when the limiting state is reached in the inner layers of the beam.