Predicting strength of wood beams with tension end notches

Abstract

An equation for predicting the strength of wood beams with tension end notches (TEN) was derived using a critical fillet hoop stress (CFHS) theory. The equation is a simplified description of the results of hundreds of finite element (FE) analyses of TEN beams with varied geometries (total of 690 configurations). It accounts for the effects of loading type and beam and notch geometry variables, such as beam height, fractional notch depth, radius and notch location. The effect of span-to-depth ratio is implicitly incorporated in the formulation of the model. Notched beam strength is represented by a material parameter, K, which was found to be related to specific gravity. A simple equation for predicting K from specific gravity was derived from experimental results.

The CFHS equation is applicable to both filleted and sharp-cornered notches. An effective radius, R, which models the effect of a sharp-cornered notch, was determined and confirmed for two wood materials. A method of determining R, for other materials was established. The CFHS equation was compared with other models and notch equations currently recommended in design codes and significant differences were noted. Chief among them is the sensitivity of notched beam strength to notch location (or the ratio M/V). This is not currently considered by “notch factor"-based design equations. Stiffness of TEN wood beams was experimentally found to be influenced by fractional notch depth and notch location, M/V. The effect of end notching on beam stiffness has not been seriously addressed before and theoretical analysis does not predict the reduction.