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Determination of Bending Moment and Deflection in Lumber Cross-Sections of Dahurian Larch from the Action of Initial Stresses

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V.N. Glukhikh,  A.Yu. Okhlopkova

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The article presents a solution to the problem of determining the bending moment from the action of initial stresses in sawn timber formed during the growth of Dahurian larch trees. We adopt the distribution of initial stresses along the stem volume using the law of the 14th degree paraboloid for the size of the core zone, characteristic of this tree species. The authors obtain the mathematical models for studying initial stresses and deflection of sawn timber from the action of initial stresses and own weight, which allow us to establish the size of the boards’ length when their resultant deflection is equal to zero. The magnitude of the resultant deflection depends on the position of annual growth layers in the board, and this is an objective evidence of initial stresses in it. Mathematical models of lumber deflection demonstrate the impact of the position of annual growth layers, which serves as a justification for a double measurement of the boards’ deflection (from the side of the outer and inner sawn face) during their machine stress grading. On that basis we should correct the method and improve the design of machines for stress grading of lumber taking into account the initial stresses in them formed during the tree growth. The results of the research allow defining the modulus of elasticity and initial stresses in lumber from Dahurian larch tree and other timber species, which are important when establishing the strength class in the process of stress machine grading. Due to the selection and rational arrangement of structural lumber in the glued building wood construction, taking into account the initial stresses in it, we can increase its load-bearing capacity. Lumber, naturally bent due to the presence of initial stresses, can be selected for producing elements of arches and vaults. The developed mathematical models can serve as a basis for creation of computer technologies for designing and manufacturing high-tenacity glued wooden building structures. The results of the research allow us at the stage of drawing up a scheme for cutting sawlog from Dahurian larch to determine natural sweep of boards appearing due to the action of initial stresses. This will improve the quality of larch lumber and reduce their losses due to twisting during kiln drying.


V.N. Glukhikh¹, Doctor of Engineering Sciences, Professor
A.Yu. Okhlopkova², QC Manager


¹Saint Petersburg State University of Architecture and Civil Engineering, Vtoraya Krasnoarmeyskaya ul., 4, Saint Petersburg, 190005, Russian Federation; e-mail:
2Woodworking Complex “Asia Les”, per. Oblachnyi, 78A, off. 11, Khabarovsk, 680030, Russian Federation; e-mail:


initial stress, bending moment, modulus of elasticity, deflection, own weight of lumber, Dahurian larch, mathematical model, strength class

For citation

Glukhikh V.N., Okhlopkova A.Yu. Determination of Bending Moment and Deflection in Lumber Cross-Sections of Dahurian Larch from the Action of Initial Stresses. Lesnoy zhurnal [Forestry journal], 2018, no. 1, pp. 89–98. DOI: 10.17238/issn0536-1036.2018.1.89


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Received on September 21, 2017

Determination of Bending Moment and Deflection in Lumber Cross-Sections of Dahurian Larch from the Action of Initial Stresses


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