Interactive graphic software for structural analysis of slabs using Grid Analogy with consideration of column’s stiffness

Resumo

For the dimensioning of reinforced concrete slabs, the appropriate determination of internal forces and
displacements is vital. These parameters are subject of structural analysis and, in the case of slabs, the equation
that mathematically describes such elements’ behavior is the Lagrange Differential Equation, which analytical
solution has a high degree of complexity, that increases considerably depending on the boundary conditions
involved. However, in modern days, thanks to the computational revolution, numerical solutions for this problem
have become more and more feasible and accessible, and are now widely used as basis for the structural analysis
of slabs. Among the several viable methodologies used with this purpose, this paper describes the use of the Grid
Analogy Method as the core method for developing a Python interactive-graphical software focused on the
structural analysis of concrete slabs. Furthermore, based on the observation that a solidarization process occurs in
the slab-column interface regions, the effect of the direct employment of the columns’ bending stiffnesses on the
stiffness matrix of the structural system is also analyzed. For verification matters, the recorded grid analogy results
are compared with data present in the Literature, while the influence of the columns’ stiffness is studied by
comparing the results of the analysis of the same structure with and without this consideration. The results were
very satisfactory, both numerically and regarding the graphical environment created, that can be used for handling
the structural model design and presenting the results of internal forces and displacements.