Computational analysis of concrete slabs subjected to perpendicular loads

Resumo

The objective of the present paper is the analysis of the behaviour of concrete slabs when subjected to
loads normal to the plane. The mathematical model is governed by the Lagrange’s Equation in the two-dimensional
plane. The differential equation is discretized by the Finite Difference Method in uniform grid with Neumann’s
boundary condition at the support positions. The system of algebraic equations is solved by the Gauss-Seidel
method. Two case studies with distinct geometry, boundary conditions and loading are carried out. The first
case is a simply supported triangular slab subject to uniformly distributed load. The second case simulates the
hydrostatic loading on a reservoir wall or the earth thrust on a retaining wall. Through the computational analysis
it was possible to capture displacements and internal forces (shear forces and bending moments) over the whole
slab domain, which is crucial for designing such structural element. Numerical results also showed excellent
agreement with analytical results extracted from the literature, validating the use of the proposed computational
code.