Admissible geometrical domains to evaluate constitutive elements of structural robustness
Geometrical domains characterising the degrees of freedom of a structural system within the context of Maxwell’s reciprocal representation of force and geometry are likely to provide indicators of the constitutive elements of structural robustness. Structural robustness is defined as the “insensitivity to local failure”. This definition emphasises the structure’s capacity for force redistribution and the possibility of finding alternative load paths in a structure. Features linked to resistance and the redistribution of forces are likely to be modelled by load path, struts and ties or thrust lines, close to geometrical thinking. Since most methods proposed today for assessing the robustness of structures are based on probabilistic approaches, they are of limited interest for the design phase. Of the few approaches that have adopted a deterministic formulation, all provide a type of survey that is based on an in-depth analysis of the structure once it has been designed, according to specific scenarios. A central challenge should be to manage the issue of robustness earlier during the design process, or even to be able to interact with a model of the future structure in order to adjust the features of robustness. This paper explores the ability of geometrical domains to assess some of the relevant elements of structural robustness in terms of design in order to characterise the capacity of structures to redistribute forces. It compares indicators linked to the area of these domains. Based on case studies, this quantification of the structural provision is then compared with indices of deterministic and energetic criteria currently proposed in literature to quantify structural robustness.