Herramienta de análisis en el plano para estructuras reticuladas

Abstract

In the present technological proposal, the development of an analysis tool using Matlab computer software is proposed, which makes it possible to systematize the method of stiffness applied to reticulated flat structures in order to obtain the internal forces in the bars and the displacements in the knots. Following the methodology of Extreme Programming, developed to guide the process of developing applications or software in a short period of time. Mainly, the needs of the clients were taken into account; visualize the matrices of global stiffness of the structure, and see the calculations made in the background to obtain the stresses and deformations in the structure that is entered. To comply with the users' requirements, a timeline with deadlines for each iteration is established, which serve to create and improve the graphic interface, functionality, or user - machine interaction, in order to make the graphic interface more efficient . At the end of the iterations the result is a complete graphical interface with all the necessary fields to analyze the reticular structure using the stiffness method. Once the definitive graphical interface for the proposed analysis tool has been defined, the procedure to be followed is explained in order to interactively model the reticulated structure formed by; knots, bars, supports, and joints; Also define and assign geometric properties to the elements type bars; area and inertia, modulus of elasticity and likewise enter point and distributed loads. The analysis tool allows to model lattice-like gantry structures, reinforcements and beams, with embedded or articulated elements, with or without displacements imposed on the supports, with point loads at the nodes and distributed trapezoidal loads on the bars, with or without displacements imposed in the supports and that are also on a plane parallel to the horizontal axis or inclined to it. Once the reticulated structure is modeled in the analysis tool, it is possible to choose the processes that the user wants to visualize, among these are included; local bar stiffness matrixes, transformation matrixes, global bar stiffness matrixes, global structure stiffness matrix, global knot load vectors, global bus load vectors, global displacement vectors, internal stresses of the bars and deformations in knots. These results are shown in the Matlab console that can later be exported to PDF format with the possibility of exporting the vectors and matrices obtained to a spreadsheet. After the tool executes the analysis to the structure, it allows to visualize the graphs of moment, shear, axial and displacements on the structure, in addition to the moment and shear equations that allow to obtain these efforts at a distance x from the start node of each modeled bar. Finally, to validate the results obtained by the analysis tool, it is compared with the results obtained by a commercial software that serves as a reference to obtain the percentage of error between both analyzes, giving confidence to the users that the results obtained by the proposed tool in this titling project they are practical and precise.