R-FUNICULARITY : A NEW CONCEPT FOR EVALUATING THE BEHAVIOR OF FORM-FOUND SHELL STRUCTURES

Abstract

Shells have a structural behavior characterized by their curved geometry. They are generally designed pursuing criteria of structural efficiency and minimization of the employed material. Among efficient and optimized structural systems, funicular ones adopt the “right” shape in accordance with the applied load and are ideally able to resist external loads using membrane forces only, without introducing bending. To find the “right” shape, many form finding techniques have been developed and used by designers. However due to multiple design constraints, an ideal funicular behavior is sometimes impossible to achieve. When this is the case and bending moments cannot be avoided, a shell structure can still be considered “more or less funicular”. In fact, a quantification of the funicularity may contribute to selection of the most appropriate and efficient shell shape. This dissertation presents an effective and easy-to-read method to study and quantify the funicularity, named Relaxed Funicularity Ellipse Method. In order to formulate the new method, the classical funicularity concept has been extended and the definition of Relaxed Funicularity (R Funicularity or RF) introduced. The parameter used to define the funicularity is the eccentricity and a structural shell is called R-Funicular when the eccentricity is included into an admissibility interval. The new method has been applied to structural shells obtained using a form finding approach, and analyzed under different static loads. During the shell form finding process, gravity loads are considered, while the role of horizontal loading is ignored. Today shells with complex geometries are being designed and built, and are used to shelter people during extreme events such as earthquakes, but the dynamic behavior of civil thin shells has always been subjected to limited research. In response to this issue, this dissertation investigates the effects of dynamic loading on the behavior of civil thin shells form-found under gravity loads. A two-phased methodology is presented. In the first phase a modal analysis of the shell is performed and the RF- Ellipse Method is applied to the modal stress distribution obtained to observe which modes show a more funicular behavior. In the second phase, the structure is analyzed performing a time-history analysis under multi frequencies spectrum defined using ad hoc functions based on the outputs of phase one. The results of such a phased approach applied to benchmark studies, show that the frequency content of the different areas of the shell can give insights onto its membrane behavior. Moreover the form-found shell is analyzed under the action of the L’Aquila Earthquake (Italy, 2009) to prove how the methodology proposed can help to identify the vulnerable area of a shell form-found under gravity loading under a real seismic event. Finally, to allow a quick and accessible application of the RF-Ellipse Method, and consequently of the proposed two-phased methodology, a new Matlab-based software named r-Fun integrated with a Finite Element analysis package has been implemented.