# Modul Uprugosti Pri Izgibe

The aim of this work is to establish the variation of the elasticity modulus of elasticity along the height of a tree trunk in static bending. The change in the elasticity modulus of a growing tree along its height has not virtually been studied. The authors have attempted to do this in three ways: along a growing birch, along a freshly felled trunk and along a freshly felled trunk cut into pieces. To make a geometric description of a trunk profile the approximation formula has been used. Using the measurements of birch trunks their models have been developed. In addition, the authors have developed and described some methods of measuring a tree trunk and those of quantitative determination of its deflection, produced in three ways. The value of the elasticity modulus, in the first case, is distorted due to the influence of the tree root system deformation. But this method is the simplest one and it does not require cutting a tree. In the second method a freshly felled trunk was placed on two supports. Some static load was applied to it between them and its deflection was measured. The distance between the supports was

## modul uprugosti pri izgibe

discretely changed from the minimum value to the maximum one. The elasticity modulus was calculated by the formula derived by integrating the differential equation of an elastic line of a trunk axis. In the third method, to calculate the elasticity modulus of some birch trunk segments the trunks were cut into pieces by a length of respectively 20 and 25 cm. Then the experiment was carried out similarly to the second method with a constant span length of the beam. The results of the experiments allow us to note the following: first, with the increasing length of a chump, the elasticity modulus increases; secondly, its increase is non-linear in nature; thirdly, the rate of the above increase decreases with increasing a tested chump length.

7.Ivanov G.A., Kotov A.A. Izmenenie modulya uprugosti berezypo vysote [Change of the module of elasticity of a birch on height] Aktual'nye problemy razvitiya lesnogo kompleksa: materialy mezhduna-rodnoy nauchno-tehnicheskoy konferencii, 8-10 dekabrya 2009 g. [Actual problems of development of a forest complex: materials of the international scientific and technical conference, on December, 8-10, 2009.]. Vologda, VoGTU, 2010, pp. 152-155.

8.Ivanov, G.A., Kotov, A.A. Koyefficient zhestkosti kornevoy sistemy dereva pri staticheskom izgibe [Stiffness coefficient of root system of a tree at a static bend]. Moscow State Forest University Bulletin - Lesnoy Vestnik. 2011, no. 3, pp. 98-102.

9.Ivanov G.A., Kotov A.A. Priblizhennyy sposob opredeleniya modulya uprugosti drevesnykh stvolikov pri izgibe [Approximate method of determining the modulus of elasticity of tree trunks when bending]. Aktual'nye problemy razvitiya lesnogo kompleksa: materialy mezhduna-rodnoy nauchno-tehnicheskoy konferencii, 8-10 dekabrya 2009 g. [Actual problems of development of a forest complex: materials of the international scientific and technical conference, on December, 8-10, 2009.]. Vologda, VoGTU, 2010, pp. 155-159. 041b061a72