Estimation of crack-length density functions of measured cracks in glulam beams and in boards

Sammanfattning: The main purpose of this thesis is to estimate the density functions for crack lengths of glulam beams. I consider some different methods to estimate each function, hence probability density function. In some sense I also estimate the parameters of the estimates. We focus mainly on the crack length; the straight distance of the crack, not curvature.
The glulam beams of this work had different treatments, in order to see which was preferred. Each category, from a total of seven categories with a specific treatment, consisted of five beams in this investigation. The beams had been outdoors in a field test for 4 years. Cracks had been measured every summer, both manually and using photos.
The data differ for the South and North side of the beams. Overall the South side had more cracks than the North. The length and area was larger for the South side, except for the combined treatment of white paint and impregnation (pine). This category seemed to have a similar crack development between North and South. If we compare this treatment with glazing paint and impregnated pine, the white paint is preferred. The worst treatment was the combination of oil and impregnation (pine). If we measure the total crack length of different treatments, the best (shortest total length) were beams with red alkyd oil-painted spruce. If we consider the area (total for the North and South side), the best treatment was beams of red alkyd-based stain-painted spruce.
For the glulam beams, I found that the gamma PDF (probability density function) could be used for the individual crack lengths. Also, some tendencies about further development of the cracks could be seen. The PDF changed, so prediction of crack development is possible if the initial PDF is known with a high degree of accuracy. Owing to difficulties in measuring crack length (and area) in beams, I also investigated kiln-dried boards of pine. I wanted to see if I could get an appropriate PDF for crack length. The total crack length PDF for the boards seemed to be exponential, even if we could also use gamma PDF. For the boards this more precise estimate of PDF could be found because of crack development in even conditions. The measurement might also be easier if total crack length is considered. If we have the crack-length density function, it might be possible to see some tendency of crack development in the future. This means if the crack-length distribution has evolved, it might be possible to predict the distribution in the future. For future prediction, if we have a high precision means of measuring cracks, the SLAP (Stochastic Life Approach) could be used.