Probabilistic models for the modulus of elasticity and shear in serial and parallel acting timber elements

Elastic properties, like modulus of elasticity and shear, are basic design parameters. Besides calculation of deformations in serviceability limit state design, these properties are also applied to ultimate limit state design, considering stability analysis of columns and girders and the calculation of internal forces in statically indeterminate structures. However, analytical probabilistic models explicitly considering the stochastics of elastic properties in timber design and product modelling are scarce or even missing. Focus was put on elastic properties of structural timber and timber products, composed of face-by-face rigidly and continuously bonded timber members. Considering timber members as rigid composites of sub-elements in series and timber products as rigid composites of timber members as serial system of parallel sub-elements, probabilistic models for parallel and serial acting elements are obtained assuming linear elastic theory and lognormal distribution. Motivated by the material structure, a two-level hierarchical model was modelled explicitly considering within- and between-element variation and correlation. Parameter settings were defined for three timber qualities. The authors (1) investigated structural timber and timber products with and without finger joints and quantified the homogenization in dependence on input parameters, i.e. the coefficient of variation and the number of serial and/or parallel interacting elements and sub-elements, (2) compared the outcome with current regulations in European standards, e.g. EN 338:2009 and EN 14080:2013 and JCSS:2006, and (3) gave recommendations for revisions. Although not explicitly demonstrated, the probabilistic models have additional potential in calculating the stiffness of joints consisting of multiple fasteners, as well as of joint stiffness in flexible composites, e.g. mechanically jointed beams where the stiffness parameters are later used in shear analogy or gamma-method.