About the authors
| First name, Middle name, Last name, Scientific degree, Scientific rank, Current position. Full and brief name of the organization, The organization address. | Murat N. Serazutdinov, Doctor of Physical and Mathematical Sciences, Professor. Kazan National Research Technological University, Kazan, Russian Federation Email: This e-mail address is being protected from spambots. You need JavaScript enabled to view it , ORCID: 0000-0001-7222-1935 |
| Title of the article | Determination of movements of a beam with a crack using the theory of rods |
| Abstract. | Problem statement. Currently, the relevance of studying the problems associated with the occurrence of damage in beams in the form of cracks is due to the need to predict the consequences of their occurrence in operated structures. The calculation of complex rod structures, using only the relations of the theory of elasticity, is associated with significant difficulties. In such cases, a rational research method consists of a combination of relatively easy-to-implement calculation methods and elasticity theory. The purpose of the work is to identify the main patterns of changes in the deformed state in rod systems during the formation of various defects and damages in them. The objective of the study is to develop a mathematical model and a method for calculating beams during bending, which allows determining the movements that occur when a crack appears. Results. A mathematical model of beam deformation during bending is constructed, which allows determining the movements when a crack occurs. The peculiarity of this model is that the part of the rod containing the crack is replaced by a section in which the cross-sectional dimensions are smaller than the initial value. General patterns of deformation of beams with damage have been revealed. In particular, it is shown that for cracks with the same relative depth, the calculated height of the cross-section of the weakened section is approximately the same for different cases of loading and fastening of the beam. Conclusions. The significance of the results obtained for the construction industry consists in improving the methods of calculating rod structures when cracks occur in operated structures. |
| Keywords. | crack, beam bending, mathematical model, deformed state, bending patterns |
| For citations: | Serazutdinov M.N. Determination of movements of a beam with a crack using the theory of rods // News KSUAE, 2024, № 2(68), p. 114-123, DOI: 10.48612/NewsKSUAE/68.10, EDN: JPGQMS |
