By designing R/C shells we can easily have membrane forces in almost the entire structure except in some regions, for instance close to the constraints. Therefore, having assigned the loads and their position as well as the constraints, there are a great number of membrane shapes that can solve the design problem, both with normal internal forces only in compression, and in compression and tension. On the other hand, given loads and constraints, by using suitable algorithms and/or physical models, tension structures may be designed in order to find their shape with membrane tensile forces and minimal area. By taking into account tension structures properties as well as those of natural membranes, and after in-depth and pioneering studies in optimum design, Sergio Musmeci - a well known designer of bridges and concrete shell roofs of the second half of the past century - studied how to design R/C shells with minimal area. By using physical models, he shaped some of his shell constructions as a tension structure with the same loads and constraints, as well as the same normal internal forces but with the opposite sign. His design tools were empirical analysis, physical models, and mathematical analysis, which he used with a bright structural intuition. Nowadays these methods can be supported by modern heuristic and evolutionary algorithms. In this paper we analyse the “shaping” as well as the “form finding” of R/C shells by following Musmeci’s design method coupled with an heuristic algorithm, the “simulated annealing”. With progressive iterations, we search for stiffer shells with minimal area and only membrane compressive forces. The algorithm simulates the progressive elimination of defects on a crystal structure, that is obtained by reheating before cooling at a lower rate, namely through the annealing process. A number of applications are proposed; firstly we test the algorithm to find the shape of the shell of the famous Musmeci’s bridge on the Basento river in Potenza, and successively, by using the same design method, we shape a R/C pedestrian crossing of a deep canyon in an urban context.

### A method of shaping R/C shells with heuristic algorithms and with reference to Musmeci’s work

#### Abstract

By designing R/C shells we can easily have membrane forces in almost the entire structure except in some regions, for instance close to the constraints. Therefore, having assigned the loads and their position as well as the constraints, there are a great number of membrane shapes that can solve the design problem, both with normal internal forces only in compression, and in compression and tension. On the other hand, given loads and constraints, by using suitable algorithms and/or physical models, tension structures may be designed in order to find their shape with membrane tensile forces and minimal area. By taking into account tension structures properties as well as those of natural membranes, and after in-depth and pioneering studies in optimum design, Sergio Musmeci - a well known designer of bridges and concrete shell roofs of the second half of the past century - studied how to design R/C shells with minimal area. By using physical models, he shaped some of his shell constructions as a tension structure with the same loads and constraints, as well as the same normal internal forces but with the opposite sign. His design tools were empirical analysis, physical models, and mathematical analysis, which he used with a bright structural intuition. Nowadays these methods can be supported by modern heuristic and evolutionary algorithms. In this paper we analyse the “shaping” as well as the “form finding” of R/C shells by following Musmeci’s design method coupled with an heuristic algorithm, the “simulated annealing”. With progressive iterations, we search for stiffer shells with minimal area and only membrane compressive forces. The algorithm simulates the progressive elimination of defects on a crystal structure, that is obtained by reheating before cooling at a lower rate, namely through the annealing process. A number of applications are proposed; firstly we test the algorithm to find the shape of the shell of the famous Musmeci’s bridge on the Basento river in Potenza, and successively, by using the same design method, we shape a R/C pedestrian crossing of a deep canyon in an urban context.
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2005
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11584/21283`
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