Efficiency-based design of bending-active tied arches

Abstract

Active bending is recently attracting considerable attention as a new paradigm to build lightweight structures both in research and practice. While there are many references dealing with form-finding methods for bending-active structures, the literature on their performance in relation to their shape and member proportioning is still scarce. This paper addresses the relationship between configuration finding and structural performance in bending-active tied arches: planar arches composed of a bent (active) rod, lower spanning cables and secondary struts that are joined to the rod and act as cable deviators. This simple bending-active arrangement allows to state key relationships between shape, proportion and performance. Starting from the fact that rod segments between struts behave as elastica segments, and selecting the mechanical slenderness of the rod as key parameter, scale-independent relationships between rise-to-span ratio, rod slenderness and stresses after activation have been established for a three-strut tied arch. The limitations posed by keeping stresses in cables after the activation within an acceptable range have been also addressed. Span-deflection ratios corresponding to Eurocode loads for the serviceability limit state have been obtained for a set of three-strut configurations using a non-linear structural model. Results have been represented in terms of rod slenderness, cable slenderness and rise-to-span ratio. The same procedure has been used to determine and represent proper utilization ratios for rod cross-sections in ultimate limit state. All the results have been combined to show the design space corresponding to the given constraints and to exemplify how to extract from it a suitable structural configuration. Finally, we explain how to extend the proposed method to design bending-active tied arches with an arbitrary number and proportion of deviators.