Load-Bearing Capacity of Roof Trusses

In structural timber elements the strength and stiffness will vary randomly along the elements due to the natural variability in timber strength. For example the bending strength can be modeled by a sequence of strong and weak cross sections with random strength and stiffness and with random length of the strong sections. In structural systems made of timber beams a systems effect can be expected due to the following two reasons. First, it is unlikely that the maximum load effects occur at cross-sections with very low strength. Secondly, there is a redistribution of load effects such that cross-sections with low strength and stiffness will generally not have large load effects. Further, there can be system effects due to non-linear material behavior. In this paper a stochastic model is established for the bending strength and stiffness of timber beams. Next, stochastic models for typical timber structural systems such as roof trusses are established and statistical characteristics of the load bearing capacity are determined. The results show that there is a significant increase in the characteristic (nominal) value and a reduction in the coefficient of variation (COV) for typical loads such as permanent, snow and imposed loads. The results have been implemented in the Danish code for timber structures.