Model for Stress Analysis and Strength Prediction of Lumber

A mathematical model has been developed that can predict the elastic and strength behavior of a section of a structural lumber member containing a knot and cross grain. The model, embodied in the computer program KMESHI, accounts for the presence of a knot, the associated grain deviations, and global cross grain, and can define localized stresses and displacements anywhere within the member. These capabilities are illustrated here through an examination of maximum stress concentrations for varying knot locations. The results point out the severe stress concentration that can be caused by an edge knot as opposed to a similar size center knot. An "effective section technique" is presented as a strength prediction procedure that uses Program KMESHI and a maximum stress failure theory. Unlike other strength prediction methods, this procedure recognizes that a progressive failure sequence leads to the ultimate member load. Through calculation of stresses and strains, and a predicted progressive failure sequence, the effective section technique was shown to be quite accurate in predicting the strength for two example pieces of lumber.