PAPER • OPEN ACCESSCalculation of load-bearing capacity of prestressed reinforced concrete trusses by the finite element method Abstract. The technique of calculation of prestressed reinforced concrete trusses with taking into account geometrical and physical nonlinearity is considered. As a tool for solving the problem, the finite element method has been chosen. Basic design equations and methods for their solution are given. It is assumed that there are both a prestressed and nonprestressed reinforcement in the bars of the trusses. The prestress is modeled by setting the temperature effect on the reinforcement. The ways of taking into account the physical and geometrical nonlinearity for bars of reinforced concrete trusses are considered. An example of the analysis of a flat truss is given and the behavior of the truss on various stages of its loading up to destruction is analyzed. A program for the analysis of flat and spatial concrete trusses taking into account the nonlinear deformation is developed. The program is adapted to the computational complex PRINS. As a part of this complex it is available to a wide range of engineering, scientific and technical workers IntroductionThe design of prestressed reinforced concrete structures, including reinforced concrete trusses, is currently conducted using empirical and semi-empirical formulas [1]. These formulas do not take into account all the features of the work of prestressed systems associated with the nonlinearity of deformation, with loading, unloading and possible reloading (change in the direction of deformation) due to a sharp redistribution of forces in the event of failure of one or another element. Recommendations for accounting for the nonlinearity of the deformation of concrete and reinforcement [2], which are given in the building norms and acts and annexes to them, carry conventional character. In addition, the normative documents practically do not contain recommendations for taking into account the geometric nonlinearity. Therefore, the development of methods for analysis of prestressed reinforced concrete structures, taking into account physical and geometrical nonlinearity, which makes it possible to determine the load-bearing capacity of structures, is a vital task. This work is devoted to the analysis of prestressed reinforced concrete trusses taking into account the nonlinearity of deformation by the finite element method. A prerequisite for the successful solution of this problem is the general theory of truss analysis, the foundations of which were laid in the nineteenth century [3] and developed later in the works of domestic and foreign scientists [4][5][6][7][8].

Relevance. Buckling analysis is important in the design of buildings and structures. It is used in various fields of engineering - mechanical engineering, aircraft and shipbuilding, civil engineering, etc. Until the second half of the twentieth century, mainly analytical methods of buckling were applied in practice. With the appearance of computers, numerical methods, in particular, the finite element analysis, began to prevail. Buckling analysis was implemented in programs of finite element analysis, such as NASTRAN, ANSYS, ABAQUS, ADAMS, DIANA, and others. In view of great responsibility, buckling analysis of structure should be carried out using at least two different programs. However, due to the high cost of software products, not all project organizations are able to have a number of programs. An alternative is to develop programs that can complete buckling analysis using several methods. This would increase the reliability and quality of calculation results. The PRINS computer program has opportunity for buckling analysis using two methods - static and dynamic. The aims of the work - to show the theoretical aspects and practical implementation of the dynamic principle of buckling analysis in buildings and structures using finite element method, as well as to give the algorithm implemented in the PRINS program and the results of verification calculations confirming its reliability. Results. The algorithm presented in this article and implemented in the PRINS computer program allows to determine critical loads using a dynamic buckling criterion. On the basis of numerous verification calculations, it was established that the implemented algorithm was effective for determining critical loads in frame, thin-walled and ribbed plate structures. The use of the PRINS computer program enables to use an alternative method for determining critical loads for a wide class of engineering problems in addition to the classical (static) method.

An algorithm of physically and geometrically nonlinear static analysis of structures by the finite element method is described, the distinguishing feature of which is the use of a full nonlinear stiffness matrix. This matrix is represented as the sum of five terms, namely, the stiffness matrix of the zero, first and second order, as well as matrices of initial displacements and initial stresses. When using modified Lagrange coordinates, the matrix of the initial displacements becomes a zero matrix. The calculation is carried out by a step-by-step method. Features of the application of this technique in the calculation of reinforced concrete structures are considered. The examples of static nonlinear analysis of reinforced concrete structures with the aid of program PRINS are given.

143Для цитирования: Айдемиров К.Р., Агапов В.П. Исследование влияния трещин на несущую способность железобетонных плит с помощью вычислительного комплекса ПРИНС. Вестник Дагестанского государственного технического университета. Технические науки. 2019;46 (4):143-154. Резюме. Цель. В статье рассмотрена конечно-элементная методика определения несущей способности железобетонных плит с дефектами в виде трещин с целью определения остаточного запаса прочности. Метод. Методика основана на использовании алгоритмов расчета конструкций с учетом физической нелинейности, реализованных в программе ПРИНС. Эти алгоритмы предполагают использование одной и той же расчетнойсхемы в процессе решения задачи. Однако специфика поставленной задачи заключается в том, что расчетные схемы исходной конструкции и конструкции с трещинами различаются. Результат. С учетом этого обстоятельства алгоритмы нелинейного расчета конструкций по программе ПРИНС были дополнены опцией, позволяющей менять параметры расчетной схемы в процессе сквозного расчета. Для исследования несущей способности железобетонных плит используются многослойные конечные элементы, для каждого из которых задается определенный пакет материалов. Модернизация расчетной схемы в данном случае заключается в замене одного пакета материалов на другой. Входной файл программы ПРИНС дополняется описанием трещин с указанием мест их расположения и всех необходимых характеристик. Приводятся примеры определения несущей способности плиты с дефектами в виде трещин при различных граничных условиях. Вывод. Использование перестраиваемой расчетной схемы при сквозном расчете позволяет эффективно решать задачу по определению несущей способности железобетонных плит с дефектами в виде трещин. Это даст возможность эксплуатационным службам отслеживать изменение несущей способности зданий и сооружений, содержащих железобетонные плиты, при возникновении дефектов в виде трещин, определять работоспособность конструкций и принимать обоснованные решения в случае необходимости ремонта.Ключевые слова: строительные сооружения; плиты; метод конечных элементов; нелинейность; несущая способность; программное обеспечение Вестник Дагестанского государственного технического университета.

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