Within the framework of sustainable development we strive for structures with a minimum volume of material. When we only consider criteria on resistance and buckling, Samyn and Latteur prove that even at the stage of conceptual design a clear hierarchy among the different truss typologies can be established. Up to now, stiffness constraints -such as the upper limit on static displacements -were not considered. However, an optimum obtained by minimising the volume, only considering the strength criterion, often results in solutions which violate the stiffness constraint(s). To avoid large displacements a stress level reduction can be imposed. However, this comes at the cost of a significant volume increase. With an optimisation process that involves the stiffness constraints at the stage of conceptual design, an optimum can be obtained without the necessity to alter the structure drastically afterwards, which partly annihilates the main objective of minimal use of material. This approach compares the different truss types on a new priority scale, generating new optima. This implicates a non-negligible change in the truss choice at conceptual design stage. The solutions are logically depended on the displacement criterions. This approach forms a first step to a new design philosophy that considers all the stiffness constraints (static displacements, resonance, local and global buckling) at conceptual design stage and is called design for stiffness.
La présente étude compare le poids propre des arcs funiculaires paraboliques ou en chaînette, à partir d'une nouvelle approche basée sur la définition d'indicateurs morphologiques. Ces nombres sans dimension permettent de réduire le nombre de paramètres qui entrent en jeu dans le processus d'optimisation et de produire des courbes universelles propres à une famille d'arcs donnée, utiles au stade de la conception d'un projet. Ces courbes, baptisées « courbes d'efficience », permettent de prédimensionner les arcs, mais aussi d'optimiser et de comparer leur poids propre et de définir leurs élancements optimaux, indépendamment du type de matériau, de sections, de leur portée ou de la valeur des charges appliquées.ABSTRACT. This survey compares the self weight of funicular arches. The comparison is based on a new approach which deals with morphological indicators. Those dimensionless numbers allow to reduce the number of parameters during the process of optimization and to draw universal curves related to a given family of arches, useful at the stage of conception of a project. Those curves, named "curves of efficiency", allow to design arches, but also to optimize and compare their self weight and to define their optimum geometrical slenderness, irrespective of the material, the type of sections, the span or the value of the loads.
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