# Calibrating of a Simulation Model to Predict the Flexural Capacity of Pre-Stressed Concrete Beams
## 1 Introduction  
Modeling using the finite element method (FEM) is a key advance in the design of complex elements, as it allows the different designs of an element to be analyzed prior to manufacture, with the results for behavior closely fitting to those that the actual element will have. With these techniques, which are widely used in many sectors, the design, optimization and production processes of elements are streamlined, making it possible to have the final product available in less time, with corresponding economic savings for the manufacturer. In the field of structural concrete, classic theories of analysis, together with experience, have long been sufficient to provide a solution to simple construction elements. However, as technological and social development have advanced, new construction problems have appeared for which classic theories are unable to provide a reliable answer, and hence, many authors have proposed the use of the FEM to find a practical solution. Thus, applying the FEM to the modeling of the behavior of reinforced concrete has been, and continues to be, extensively studied by many authors. An excellent review on the literature on the application of FEM for linear and non-linear analysis of reinforced concrete structures was conducted by the American Society of Civil Engineers [1; 2; 3]. Numerical modeling of reinforced concrete beams has been studied by the scientific community since the 1980s [4], with research topics including constitutive relationships, steel-concrete bond models, material failure criteria and finite element technology [5; 6; 7]. The different studies suggest that the development of the constitutive models describing the behavior of materials and the non-linear solution of the physical problem yield numerical results that are substantially similar to those obtained in laboratory tests. Studies on the non-linear analysis of concrete focus on solving the cracking response in structural elements, such as beams, floors or walls, caused by tensile stresses. Thus, a multitude of specific models have been generated which advance the knowledge on the behavior of this heterogeneous material, with the responses provided now being very close to that of the real elements [8; 9]. The constitutive models used to describe the non-linear behavior of materials have a decisive impact on the structural response of the beam analyzed [10]. Thus, the beams analyzed by this author under distributed loading show that, depending on the constitutive model implemented, the load capacity and deflections of the numerical results differ from the results obtained experimentally. [PERSON] [7] studied the non-linear behavior of reinforced and pre-stressed concrete beams using the linear and volumetric elements of the commercial ANSYS program for the simulation of concrete and steel. [PERSON] [11] and [PERSON] [12] used the ANSYS program to analyze the influence of the non-linearity of materials on deflections of reinforced concrete beams, considering specifically the interaction between steel and concrete by means of a special finite element, obtaining interesting results with respect to beams tested in a laboratory. Finite element modeling has been used to study other aspects, such as the influence of longitudinal reinforcement on the flexural response of beams [13] or the application of concrete with steel fibers [14; 15; 16; 17]. The list of new experiments is constantly growing, underlining the importance of finite element modeling in the design of specific concrete elements and the knowledge of new situations where this material is applied. Calculation tools are now appearing, the operation of which integrates the main models, and research efforts are being concentrated on verifying the functionality of this implementation, comparing the analyses with actual experiments [18; 19]. Tools, such as ANSYS, ABAQUS and SOLIDWORKS, have emerged, with finite elements and constitutive models adapted to a greater or lesser extent to reproduce the behavior of reinforced concrete.