Regarding calculation of flat concrete frames with rods variable rigidity using deformation method based on time factor

Abstract

Annotation. Aim. The aim of this work is to develop a method of calculating flat statically indeterminate reinforced concrete frames using deformation method with variable cross-section stiffness, considering time factor through the use of transformable strain diagrams of concrete. Tasks. The implementation of the algorithm for calculating the flat reinforced concrete frames using deformation method based on time factor based on the examples of statically indeterminate reinforced concrete frames with  П shaped and closed-loop to research the effect of short-term and long-term load. Methods. There are many approaches to solve the task. Many of them have their pros and cons. In our case, the most appropriate and logical method is to calculate frame structures by displacement using the deformation method with variable stiffness rods through the use of transformable strain diagrams of concrete. This method gives full freedom in solving the problem of redundancy and the direct calculation of elements section. Such approach helps to solve the problem despite the type of load and / or their combination. The unknown in solving the displacement method are the angles of rotation occurring in all nodes of rigid frame, and linear displacements, the number of which is determined by injection to all rigid nodes of the system, including reference, hinges, which ensures that the mobility of a mechanism is equal to the number of linear displacements. To calculate the frame with a constant stiffness of rods along their length, it is first of all necessary to solve ancillary questions on beam deformation under forced rotation of end sections at an angle equal to unit. The research, executed by the author of the study, taking into account the presence of the frame in the rods of up to 10 separate sections with various atrocities, made possible to determine the value of the above angles of rotation, as a function of the number of sites that are separated by the frame rods, application number, section number and sections rigidity. It was also discovered that the traditional values of individual nodal points of the frame using the displacement method can be expressed by the value of given angles of rotation, taking into account the frame rods breakdown into sections with individual rigidity. After determining the value of all the unknown forces in the frame structure using the displacement method in calculations taking into account the variable rigidity of the rods at a time moment Δt = 1, we move to the calculation of section, when we define new value of the curvature in the estimated sections and rigidity values at intermediate spots of frame rods. In order to calculate the flat frame in nonlinear installment by iterative method with adjusted variable rigidity in sections of crossbar and uprights we are using an algorithm for solving systems of nonlinear equations for concrete estimated sections equilibrium using the deformation method through the use of transformable strain diagrams of concrete. Conclusions. The developed method of calculation of flat frames using deformation method with a variable section rigidity taking into account time factor basing on the use of time convertible deformation diagrams of concrete allowed to establish a functional dependence of the coefficients of the system of canonical equations of displacements method on the determined angles rotation of the nodes of frame rods; to expand algorithm for solving system of nonlinear equations for concrete estimated sections equilibrium using the deformation method to take into account the time factor when calculating flat frames with variable rigidity basing on time convertible deformation diagrams of concrete; to calculate statically undefined frame structures of varying complexity with variable rigidity.