Automated yield-line analysis of orthotropic slabs

The rigid-plastic yield-line analysis of orthotropically reinforced concrete slabs under uniformly distributed loading is developed as the lower-bound form of a linear programming formulation. The analysis is extended to consider geometric variation of chosen yield-line patterns by the technique of sequential linear programming. It is shown that the omission, within the iterations of the sequential linear programming process, of the effects of geometric variation on yield-line ultimate moments of resistance leads to a formulation which is, at best, inefficient, and can be divergent or converge to an erroneous solution. Accordingly, a formulation is developed which includes a linearized representation of the geometric sensitivities of the resistance moments within the iteration process. This formulation is shown to be both effective and efficient for the yield-line analysis of a number of example slabs which include a range of support conditions and boundary geometries.