Stability of Built-Up Timber Beams and Columns: Accounting for Modulus of Elasticity Variability

Built-up beams and columns comprised of dimension lumber fastened with nails, bolts or lag screws, are common in construction. Current design practice for stability checks is to use the lower-tail modulus of elasticity $\left(E_{\text{min}}\right)$ value tabulated for dimension lumber; however, this ignores the averaging effect on $E_{\text{min}}$ that occurs when the mechanically fastened laminations are constrained to deflect in unison. In this paper, we propose a method for checking stability of these assemblies that is based on established statistical theory. A factor $\left(C_s\right)$ is proposed to adjust $E_{\text{min}}$ value used in column and beam stability calculations to account for the reduced variability of $E$ when the laminations are constrained to deflect together. Using $C_s$ to account for the reduction of $E_{\text{min}}$ variability produces more efficient designs with respect to stability. Two examples are provided and each results in larger design capacities compared to current design methods for built-up beams and columns.