Dynamic behavior of form-found shell structures according to Modal and Dynamic Funicularity

Civil thin shell structures are generally designed with the objective to achieve an ideal membrane behavior and pursuing criteria of structural efficiency and minimization of the material used. 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 earth- quakes, but the dynamic behavior of civil thin shells has always been subjected to limited research. This paper 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 R- Funicularity 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 single and multi frequencies spectra 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. Finally the form-found shell is analyzed under the action of the L’Aquila Earthquakes (Italy, 2009) to prove how the methodology proposed can help to identify the vulnerable area of a shell under a real seismic event.