Analytical Determination of Reactive Forces for Curvilinear Bars with a Flat Axis of Arbitrary Shape / Аналітичне визначення реактивних зусиль для криволінійних брусів із плоскою віссю довільної форми

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Ковальчук, Станіслав Богданович
Горик, Олексій Володимирович
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For most tasks of the mechanics dealing with the deformation of rod structural elements, the necessary basic data are the distribution of full loads on its surfaces, consisting of an active load and the reaction of fixations. The active component is usually known, the reactive one needs to be determined, which is one of the first steps of solving any problem of strength and stiffness of the bar. In cases when the load of the bar is represented by concentrated forces and moments, the determination of the reaction of support blocks, as a rule, is not a problem. However, for a curvilinear bar, even normal or tangential loads make it difficult to apply the equilibrium conditions known in theoretical mechanics. The purpose of this paper is to develop a generalized approach to determining the intensity of reactive loads for a statically determinable curvilinear bar with a flat axis of an arbitrary shape, which is under the influence of the system of normal and tangential loads on longitudinal cylindrical surfaces and ends. On the basis of the relations for the internal force factors obtained by the authors in the previous work, generalized relations for the components of resultants of active and reactive loads were developed. Together with the conditions of static equilibrium of the plane system of forces and the relations for modeling of concentrated and localized loads, the constructed dependences form the basis of the analytical method for determining the reactive forces of statically determinable curvilinear bars. The obtained relations are tested using the example of determining the reactions of support blocks of a hinged bar with a constant cross-section with an axis in the form of a parabola under the action of concentrated and distributed loads. The proposed analytical method of static calculation of curvilinear bars, in addition to obtaining the numerical values of reactive loads, enables to establish functional relationships between the intensity of active and reactive forces, the coordinates of their application points and the geometry of the bar, which opens wide possibilities for the analysis of the design model of a curvilinear bar for the purpose of its optimization.
curvilinear bar, natural coordinate system, active load, reactive forces, static equilibrium, криволінійний брус, природна система координат, активне навантаження, реактивні зусилля, статична рівновага, криволинейный брус, естественная система координат, активная нагрузка, реактивные усилия, статическое равновесие