Calculation of load-bearing capacity of prestressed reinforced concrete trusses by the finite element method

Abstract

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].

Realization of reinforced concrete structures analysis with the account of physical and geometrical nonlinearity in computer program PRINS

“…where ep C is the elasto-plastic matrix of material characteristics. Detail description of the methods of derivation of this matrix for one-and two-dimensional reinforced concrete structures, realized in the program PRINS, is given in the works [19,20].…”

Nonlinear Strength Calculation of Shell Structure of Arbitrary Shape Based on FEM

“…The formation of the stiffness matrix and the column of nodal loads in the quadrangular finite element at the loading step is carried out on the basis of the equality of external and internal forces at the possible movement [11][12]…”

Calculation of thin-walled axisymmetrically loaded structures of the AIC taking into account FEM-based physical nonlinearity

“…The theory of thin shells is widely used [1][2][3][4][5][6]. Due to difficulties in obtaining analytical solutions based on the theory of shells for the designed thin-walled elements, numerical methods have become widespread [7][8][9][10]. The action of external loads in the presence of shell meridian branching can cause plastic deformations.…”