Integral and differential relations for internal power factors in the bending of the bar with a curved flat axis of an arbitrary shape
Journal Title: Вісник Одеської державної академії будівництва та архітектури - Year 2018, Vol 1, Issue 70
Abstract
The work is dedicated to the theoretical study of internal power factors in a curved bar with a flat axis of an arbitrary shape, that is in a plane bending condition by a surface load of an arbitrary type. The natural curvilinear cylindrical orthogonal coordinates system associated with the structure of the bar and given by the characteristics of families of coordinate surfaces and Lame coefficients is used to describe the geometry of the bar and also the load distribution. The analysis of the equilibrium conditions of the elementary section of the bar made it possible to obtain integral relations between internal power factors and loads distributed on its longitudinal and end surfaces. The relations obtained were used to derive differential dependencies between internal power factors, that express the equilibrium conditions for the elementary section of a curved bar. Also, based on the equilibrium conditions of the bar cross-sections, integral relations between internal power factors and the stress state components were obtained. The presented integral and differential relations have a general form, invariant to the shape of the axis of the bar and allow to make a direct connection between loads and stresses. The results of the work can be used to solve theoretical and applied problems of a plane bending of curvilinear homogeneous and inhomogeneous bars with different types and combinations of external load.
Authors and Affiliations
S. B. , Kovalchuk, O. V. , Goryk
Keywords
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