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The Tsai-Wu strength theory for Douglas-fir laminated veneer

University of British Columbia

This study investigates the determincrtion and use of a multi-axial failure criterion for Douglas-fir lcrrninated veneer. Unlike previous studies on failure theories, this study treats strength parameters as random variables as opposed to detenninistic variables. Also, size effect has been incorporated in the failure theory implementation. A comparison has been made between four established orthotopic failure theories based on off-axis tensile test data to determine the most appropriate theory of the four considered; Tscd-Hill, Norris, Tscri-Wu and Tan-Cheng theories. The Tsai-Wu tensor polynomial theory has been shown to best predict the mean values of the off-axis data considering both practicality and accuracy of the strength criteria. A non-linear mirurnization technique has been developed considering the strength parameters of the Tscri-Wu criterion to be random variables to approximate the mean and standard deviation of the interaction parameter, F12. The same statistical approach has been used to approximate a size effect adjustment factor to account for the difference in stressed volumes between the shear block specimens and the off-axis specimens. A sensitivity analysis has been conducted on the interaction parameter, F12. This study indicates that the data from the 15 degree off-axis tensile tests is more reliable than that of the other angles tested, 30, 45 and 60 degrees, in establishing the most accurate value for F12. Also, the first and second quadrants of the stress space are found to be the least sensitive to variations in F12. That is, small inaccuracies in the data obtained from tests producing these stress combinations could lead to significant errors in the effectiveness of the Tscd-Wu criterion in the third and fourth quadrants. The Tsai-Wu failure criterion has been coupled with finite element analyses in a simulation procedure to estimate the cumulative probability distribution for failure load of 30 and 45 degree off-axis 3 point bending specimens. A load configuration effect has been included in the prediction model to account for the brittle strengths, tension parallel and perpendicular to grain and shear having been developed in a uniform stress configuration. Two approaches, using Weibull weakest link theory, have been investigated to incorporate the load configuration effect. Both models provide reasonable accuracy in predicting the off-axis failure load when compared to experimental results. An alternative, less versatile approach to predicting failure load for the off-axis bending application has also been studied. This approach entails using the Tsai-Wu failure criterion to first predict off-axis tensile strengths and then, using Weibull formulation, adjusting these tensile strengths to predict off-axis bending strengths. This prediction model is also corroborated by the experimental results.

Thesis/Dissertation

application/pdf

2009-02-03

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http://hdl.handle.net/2429/4154

Forestry

University of British Columbia

UBCV

DSpace