Modelling the Variability of Bending Strength in Structural Timber - Length and Load Configuration Effects
Abstract: The load carrying capacity of a beam of structural timber is dependent both on the span of the beam and the type of loading. The longer the beam and the more uniform the moment distribution, the lower the load carrying capacity. This phenomenon is due to the variability of material properties within a piece of timber. This variability is, in turn, due to the presence of knots, the slope of grain and other abnormalities in the timber. The Swedish building code does not take into account the dependence on length and load, while the Eurocode includes the effect of length. The scope of this study was to investigate the variability of bending strength within and between members of structural timber and to find a way of modelling this variability. Using the model, the effect of length and type of loading on the load carrying capacity of a beam has been investigated. The experimental tests were performed on Norway Spruce (Picea Abies). The first part of this thesis presents a description of timber as a structural material, the Weibull theory on length and load configuration effects and reliability- based analysis of the length and load configuration effects. The next part deals with the experimental investigation, preceded by a section on the non-destructive grading of timber, including both visual and machine stress grading. The grading parameters are essential tools when deciding how and where to test the timber. In total, 673 sections distributed over 132 beams were tested successfully in several weak sections within a beam. The tests were performed using a newly developed test set-up. Comparative tests were performed using the test arrangement prescribed in the European code. No significant differences between the results from the different set-ups were found. Furthermore, the grading parameters were compared with the actual strength. A non-parametric study of the length and load configuration effect using only the test data gave a shape factor of 0.1 in the Weibull distribution. The length and load configuration effects were, in general, quite small. The simulation of tests of bending strength according to the European, North American and Australian codes gave small differences, although the codes differ as to where on a timber the test should be performed. A model of the variation of bending strength within and between timber members was developed. The model is based on stochastic variables such as the distance between weak sections, length of weak sections, strength of weak sections and strength between weak sections. Several alternative inputs were investigated. The thesis is concluded with the presentation of a study on length and load configuration effects using the statistical model of the variation in bending strength. The effect was studied using direct comparison of strengths (Weibull theory), reliability-based methods (level II) and a calibration using the Swedish code format. The results from the latter could be introduced in a code. Compared with today's design, the strength of a beam could be increased by 10 % (depending on the length and type of loading).
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