Analytical cracking load estimation of Laminated Veneer Lumber (LVL) beams with holes

Predicting the load-carrying capacity of timber beams with holes cannot be performed by usual analysis methods if the failure of the beam is governed by the crack
initiation and propagation around the hole at low load
levels. Predicting the cracking load is an important design issue because it corresponds to the load-carrying capacity of the timber beam before the crack propagation. One of the models that can be used for the fracture formulation is
that of a beam on elastic foundation. In this model a part of the beam is assumed to follow the conditions of beam with elastic foundation which has spring stiffness equal to the fracture properties of the material in the crack surface. Based on beam on elastic foundation model, the cracking load prediction is the target of the paper. Some closed form
solutions for the beam with hole are presented. The formulation has been derived for two cases of pure shear and pure bending moment. Finally a semi-empirical formulation for combination of shear and bending moment in the section is presented. The model predictions are compared with the results of an experimental program showing good correlation. The analytical model can therefore be proposed for future revisions of codes of practice such as the Eurocode 5.