This article presents a design methodology based on a stiffness and volume optimization algorithm for three-dimensional nonlinear hyperstatic and pre-stressed structures composed of elements only subjected to axial forces, with a special emphasis on tensegrity structures. The algorithm is based on dimensionless numbers called morphological indicators that allow finding, within a given family of structures, the geometry related to a maximum stiffness or a minimum volume of materials or the best ratio between stiffness and volume. The algorithm takes into account the buckling of the struts and different materials for cables and struts. This article first demonstrates the optimization algorithm and then gives numerical confirmations and examples.

The architectural potential of tensegrity structures is proven. Yet, paradoxically, very few real construction projects have been built around the world. The main reasons are complex construction processes, lack of design and optimization guidelines, and excessive self-weight due to the prestress needed to guarantee stiffness and dynamic behavior. Hence, optimizing the stiffness and self-weight is a key aspect when designing a tensegrity footbridge. Previous research has demonstrated the validity of a design and optimization methodology, based on morphological indicators, that identifies geometry with a maximum stiffness and=or a minimum self-weight for a family of structures. In this paper, that methodology is applied to footbridges composed of tensegrity modules comprising simplex, quadruplex, pentaplex, and hexaplex types. A comparison of the stiffest and lightest structures is provided, a practical case study is developed, and the relevance and feasibility of such tensegrity footbridges are discussed. As a result, the study provides advice on optimum footbridge topologies with the following characteristics: excellent stiffness and dynamic behavior; efficient structures composed of simplex modules; and self-weight that is still rather high but similar to that of bended structures, although with potential to be reduced thanks to optimization of the prestress scenario.

<p>Tensegrity describes systems in which bars in compression seem to float inside cables in tension. This concept has inspired artists and designers for more than 60 years, however nowadays very few civil structures are built across the world. Although tensegrity structures seem visually light, there still remains a lack of rigorous and quantitative proofs about their structural efficiency in particular in terms of self-weight and stiffness. This article presents a 60m span tensegrity footbridge in steel composed of adapted simplex modules that contain one more cable than the classic simplex modules. The influence of this choice on the structural performances of the footbridge are here detailed. Eventually, the tensegrity footbridge is heavier and less stiff than traditional trusses but it is an aesthetic solution which offers the remarkable ability to deploy.</p>

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