Load capacity ratios for structures

For a given structure made of a perfectly plastic material with a yield stress sYsY, we consider the load capacity ratio of the structure: the largest positive number C, depending only on the geometry of the structure, which satisfies the following property. For any loading distribution f   on the structure whose maximum is fmaxfmax, the structure will not undergo plastic collapse as long as fmax⩽sYCfmax⩽sYC, independently of the distribution of the load. The paper presents the mathematical aspects, related mechanical notions, algorithms and examples corresponding to load capacity ratios of structures.