Capacity of timber roof trusses considering statistical system effects

For structural timber systems such as trusses, system effects related to strength variation within timber members has a significant effect on reliability. The system effect originates from the reduced probability that weak sections of timber coincide with the most stressed sections in the truss. In this paper, the strength variation within and between timber members is described with a statistical model earlier calibrated against data for Norway Spruce of Scandinavian origin. A method is presented to account for buckling effects when expressing the interaction between axial loading and bending in all sections of the truss members. The interaction is expressed in terms of a combined stress index, CSI, defined so that the failure criterion is CSI=1. For a given truss with given load, the cumulative distribution of CSI can be determined by Monte Carlo simulations based on the statistical model. By comparing the results with corresponding results obtained from deterministic engineering design, the statistical system effect is quantified. It is found that within member variability gives an extra capacity of 12% for Norway Spruce and 24% for Radiata Pine. Design rules proposed for Eurocode accounting for system effects in trusses give results slightly on the safe side compared to the results from the present study.