Stochastic Model for Simulating the Distribution of Modulus of Elasticity Values in Samples of MSR Lumber

A stochastic model of the machine-stress-rated (MSR) lumber grading system is described. Pieces of lumber are represented in the model by their associated average modulus of elasticity (E). The model simulates the flow of mill-run E values through the grading system; the machine sorting of these values into discrete E classes; and the final sorting of pieces into lumber grade categories by human graders. Files of E values are generated which simulate the distribution of E in MSR lumber-grade categories. These can be used as input to subsequent Monte Carlo analyses of building components that utilize MSR lumber, e.g. trusses or glued laminated beams. The model also provides insight into the MSR grading system itself. The flow of E values through the grading system is simulated by drawing values at random according to a probability density function which has been defined to represent the mill-run distribution of E for the particular system being modeled. Visual grading is simulated by means of a probability matrix, each element of which is the conditional probability that a piece previously determined to belong in the E class represented by the element’s row will have visual characteristics that will result in the piece being sorted into the lumber grade represented by the element’s column.

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