An optimum reinforcement solution for a torsionless grillage with given minimum strength

Abstract

The paper presents the minimum reinforcement solution for a simply-supported square torsionless grillage, with beams parallel to the sides of the square, for specified uniformly distributed transverse load at collapse, for the case where a minimum proportion of reinforcement (and therefore a minimum bending strength) must be provided at every point. The optimal design collapses in a mode satisfying certain conditions on curvature, and the corresponding moment field is developed using lines of load transfer (with finite jumps in moment) for concentrated forces, and the equation of bimoments for finite grillage segments. A solution is obtained only for a limited range of load magnitudes (up to about twice what may be carried with the specified minimum bending strength alone). However, the minimum volume of reinforcement is not much less than that for a simple practical design, with crossed uniform bands of extra reinforcement near midspan, which can cope with any magnitude of load.