Load capacity ratios for structures

For a given structure made of a perfectly plastic material with a yield stress s Y , 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 f max , the structure will not undergo plastic collapse as long as f max ⩽ s Y C , 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.