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 (σ_T), and compression strength (σ_C). 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, σ_T, and σ_C? 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.