Serviceability and Strength of Concrete Floors and Bridge Decks: Grid Analogy

This paper analyzes bridge decks and two-way horizontal slabs with or without beams or drop panels using a grid analogy. The grid members are beams with a horizontal centroidal principal axis. The nodal displacements are a downward deflection, two rotations about Cartesian axes, and two translations along the Cartesian axes. The internal forces at a cross section of a grid member were a vertical shearing force, a twisting moment, a bending moment about horizontal principal centroidal axis, and a normal force at centroid. The model gives deflections in agreement with the solution of the differential equation of elastic deflection of thin plates. For ultimate strength design of sections and deflection calculation, it is recommended to use analysis of a grid with zero twisting moments. This can be done by setting a negligible value for the torsion constant for all members. Long-term curvatures and deflections are predicted using equations derived for beams.