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. | Kayumov R.A. – doctor of physical-mathematical sciences, professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Shakirzyanov F.R. – candidate of physical-mathematical sciences E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazan state university of architecture and engineering The organization address: 420043, Russia, Kazan, Zelenaya st., 1 Ahmetzyanov R.I. – engineer E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it LTD «Tatgrazhdanproekt» The organization address: 420140, Russia, Kazan, Y. Fuchika st., 98А |
| Title of the article | Modeling of the process of deformation and evaluation of the life of a reinforced beam |
| Abstract. | Problem statement. The problem of the bending of a reinforced beam under transverse loading is considered. It is believed that the total deformation consists of an elastic part and a creep deformation. The elastic part is connected with the stresses by Hooke’s law. The variants of the connection of stresses and deformations of creep in the form of the laws of flow and hardening are investigated. To estimate the life of the beam, the parameter of Rabotnov’s damage, connected with the stresses by a differential relation, is introduced. The deformation of the fibers along the height of the beam during bending is assumed linear according to the Bernoulli hypothesis. For the closure of the system, equilibrium equations are added in the form of a connection in the section of stresses with normal force and a bending moment. The system of equations under consideration is solved by the method of finite time differences. On the longitudinal coordinate at each time step we obtain an algebraic equation with respect to the curvature of the beam. Results. The dependence of the distribution of stresses on the height of the beam section for different values of time is determined. Durability is determined from the condition that the parameter of damage is a unit value. The solution of the problem is carried out for various variants of mechanical characteristics. The results are presented in the form of graphs. Conclusions. The significance of the results obtained for the construction industry is that this calculation technique makes it possible to evaluate the durability of the reinforced beam. |
| Keywords. | finite difference method, durability, creep, hardening law, stress, deformation. |
| For citations: | Kayumov R.A., Shakirzyanov F.R., Ahmetzyanov R.I. Modeling of the process of deformation and evaluation of the life of a reinforced beam // Izvestiya KGASU. 2017. №4(42) P.174-181. |
