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Title: Integral and differential relations for internal power factors in the bending of the bar with a curved flat axis of an arbitrary shape
Other Titles: Інтегральні та диференціальні співвідношення для внутрішніх силових факторів при згині бруса з криволінійною плоскою віссю довільної форми
Интегральные и дифференциальные соотношения для внутренних силовых факторов при изгибе бруса с криволинейной плоской осью произвольной формы
Authors: Kovalchuk, Stanislav
Goryk, Oleksii
Keywords: curvilinear bar
plane bending
internal power factors
integral relations
differential dependencies
natural coordinates
криволінійний брус
плоский згин
внутрішні силові фактори
інтегральні співвідношення
диференціальні залежності
природна система координат
криволинейный брус
плоский изгиб
внутренние силовые факторы
интегральные соотношения
дифференциальные зависимости
естественная система координат
Issue Date: Mar-2018
Publisher: Odessa State Academy of Civil Engineering and Architecture
Series/Report no.: Bulletin of Odessa State Academy of Civil Engineering and Architecture;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 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.
ISSN: 2415-377Х
Appears in Collections:Фахові видання

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