Probabilistic modelling of the tensile related material properties of timber boards and finger joint connections

Abstract

In the present paper a probabilistic approach for modelling the tensile strength and tensile stiffness properties of timber boards and finger joint connections is presented. The approach includes the geometrical setup of timber boards (the position of knot clusters) and a hierarchical representation of two strength and stiffness related indicators. One indicator to describe the mean material properties of timber boards and one indicator to describe the lengthwise variability due to knots. Based on the two indicators the tensile strength and tensile stiffness of timber board sections and finger joint connections are estimated using material models. The application of the approach is illustrated. For this purpose, finger joint connections and timber boards with different length are simulated and the material properties are compared with values proposed in the literature.

Probabilistic approach for modelling the load-bearing capacity of glued laminated timber

“…The prediction of material properties is associated to model uncertainties, expressed through the error term e. Due to the censored regression analysis (strength model) the model uncertainties are slightly underestimated. Thus a larger r e ¼ 0:2 was assumed (see [21]). To consider the correlation of the material properties within one timber board, the error term e was separated into two parts: one constant part for the uncertainty of the mean material properties ðe 1 Þ, and one part for the uncertainty of the strength and stiffness reduction of each particular WS (e 2 ).…”

“…The parameter for the probabilistic model [21] are summarized in Table 1. For both strength grades only marginal correlations between the parameter was identified; here the correlations are not considered.…”

“…However, in [21] the length of a WS was assumed to be constant (l WS ¼ 150 mm), thus the minimal distance between two adjacent WS is d min P 150 mm. Accordingly a shifted gamma distribution is used to describe d; m and k are the model parameter of the gamma distribution:…”

“…Timber boards are simulated using the probabilistic model introduced in [21]. The specific characteristic of this model is that the natural growth characteristics of timber is considered; i.e.…”

“…Under consideration of [41,28,12,38,5] the material model was extended for FJ [21]: The tensile stiffness ðE t;j Þ is assumed to be the mean stiffness of the two adjacent CWS (Eq. (6)).…”