Inclusion of diffusion effects due to in-plane forces in the grillage method

Abstract

The grillage method is often used for the structural analysis of concrete plates and slabs of bridges and buildings. As is well known, the grillage method allows for the study of bidimensional structural members subjected to loads normal to their mid-surface. However, the analysis of certain bidimensional members may require the consideration of inplane stresses and strains. This may be important in the analysis of prestressing provided by concentrated sets of tendons or hyperstatic structural systems with constrainde in-plane displacements combined with the effects due to the time dependent deformation of concrete. Those aspects exceed the capabilities of the conventional grillage method and are presently treated by means of the finite element method. which is in general more costly. The inclusion of in-plane effects in the grillage may be accounted for through the correct treatment of the compatibility of rotations at nodes, and by providing rigid links, representing finite nodes, in Timoshenko beams with shear strain as an additional rotation. In this paper, both the heoretical and the analytical bases for the extension of the grillage to in-plane effects in plates and slabs are presented. To ilustrate the possibilities of the proposed method, two examples consisting of a prestressed slab (belonging to a building structure), and a deep beam subjected toa concentrated load, are presented. In both cases, results obtained by means of extended grillage and also by finite elements are compared and discussed.