Probabilistic System Effects in Timber Structures
Abstract: The main purpose of the performed research presented in this thesis is to increase the understanding of the effect of variability of strength properties on the reliability of timber structural systems. Compared to other structural materials such as steel and concrete, structural timber has a considerably higher variability of strength both within and between members. The advantage of the low probability that high stresses coincide with low strengths is however not accounted for and may give an extra safety margin. The strength of timber members will, due to their inhomogeneous nature, be dependent on both the length of the member and the type of loading. For structures with pronounced moment peaks such as roof trusses, an important increase in safety could therefore be expected. This can be quantified with a system effect factor defined as a multiplier on the single member strength. A statistical model by Isaksson (1999) was used to model the strength variability between but also within timber members of spruce (Picea Abies). Two different types of common timber structural systems were studied namely the W-truss and a parallel, sheathed timber system. The probabilistic system effect was simulated for a roof truss using both a linear elastic model and a non-linear elastic model for the joints. The engineering practice where the bending strength is increased at moment peaks was concluded to be on the safe side. The system effect for this system was found to be in the range 8% to 25% dependent on the assumptions. It was also concluded that the introduction of non-linear behaviour of the joints apparently does not influence the system effect factor, at least not for the studied roof truss. A sheathed parallel timber beam structure was simulated and the system effect was determined. The failure load for the system was calculated for the weakest T-section in the system as well as the system failure load. At 5th percentile (characteristic) level the ratio between the failure load of the system and the weakest T-section in the system was calculated. The ratio was found to be in the range 1.19 to 1.30 depending on the studied parameters. The COV of the system strength was found to be around 10% compared to the COV of the bending strength of single beams of around 20%. A new method to evaluate the system reliability was suggested which reduces the effect of the system size. The system effect factor that can be introduced in deterministic calculation is the ratio between the load factor of the single element and the load factor that is applied on the system. The system effect factor was found in the range 1.17 to 1.27 for the input data studied.
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