Simulation method to generate the strength of glulam using correlated random variables

Many reports have been published about designing the strength of glulam using simulation methods. In simulation methods, one of the most important problems is how to deal with correlations among strength factors, i.e., modulus of elasticity (MOE), modulus of rupture (MOR), tensile strength (σT), and compression strength (σC). For example, in the case that the MOR criteria of glulam is σ ni /f ni + σ bi /f bi ≥ 1 (where σ ni and σ bi are the axial stress and the bending stress of the i-th lamina respectively, and f ni and f bi are the axial strength and the bending strength of the i-th lamina respectively), a correlation between f ni and f bi exists. How can we account for this correlation when calculating the strength of glulam, bearing in mind that it is very difficult to measure the correlation coefficients among MOR, σT, and σC? We developed a method by which these problems could be solved, and, using random variables generated by this method, the strengths of glulam were simulated. The simulated values were almost the same as the experimental values. The results indicated the usefulness of the method.