Assessment of probabilistic system effects on the reliability of timber trusses

In structural engineering the system effect is known as the possibility of transversal collaboration among parallel load-bearing elements due to mechanical load sharing. The statistical system effect, related to the variation of strength within structural timber elements, is investigated in this paper. The system investigated is a roof truss of W-type. The strength variation within and between timber members is described with a statistical model based on stochastic variables representing position of weak sections and length of weak regions, strength of weak sections and strength between weak sections. With the statistical model, the cumulative distribution of a Combined Stress Index (CSI), which is a measure of the stress levels in the truss, is determined with Monte Carlo simulations. The results from the simulations are used to determine the reliability level of the truss considering the effect of within member variation of the timber strength. It is shown that the load bearing capacity of a truss is increased significantly for a given reliability level, since the probability is low that sections with locally high stresses will coincide with weak sections. The increase in the estimated load bearing capacity for a W-truss is of the order 15-20% for spruce of Scandinavian origin and 30-35% for Radiata Pine.