Elastic equations for a cylindrical section of a tree |
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| Institution: | 1. Department of Forest Resource Management, University of British Columbia, 2424 Main Mall, Vancouver, BC, Canada V6T-1Z4;2. Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA;3. Department of Forest Engineering, Oregon State University, Corvallis, OR 97331, USA;1. School of Resources and Safety Engineering, Central South University, Changsha, 410083, China;2. Hunan Key Laboratory of Resources Exploitation and Hazard Control for Deep Metal Mines, Central South University, Changsha, 410083, China;3. Institute of Mechanics for Engineering Materials, Advanced Research Center, Central South University, Changsha, 410083, China;1. Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi University, Nanning, 530004, China;2. Guangxi Provincial Engineering Research Center of Water Security Intelligent Control for Karst Region, Guangxi University, Nanning, 530004, China;3. Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, Guangxi University, Nanning, 530004, China;4. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China;1. Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mine, University of Science and Technology Beijing, Beijing 100083, China;2. Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China |
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| Abstract: | Considering a cylindrical section of a tree subjected to loads independent of x3 as a relaxed Saint-Venant's problem, it was shown that plane sections remain plane. Since plane sections remain plane, the displacement equations for the neutral fiber derived using either the relaxed Saint-Venant's problem or elementary beam theory are equivalent. The stresses in the plane of the transverse cross-section were found to equal to zero. Therefore, it is appropriate to use elementary beam theory to estimate the three-dimensional stress functions when the wood is considered to be homogeneous. In addition the three-dimensional displacement equations allow the required elastic coefficients in cylindrical coordinates to be measured from full size samples. |
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