Shape Generation of Bending-Active Braced Arches Based on Elastica Curves

The active bending concept provides a new perspective for a well-established structural type which has been used at various scales: the beam-string, consisting of a beam with an attached lower tie in tension and bracing struts balancing the forces between them. The idea goes back to the gutter beams of the Crystal Palace and has been widely used to the present for large-scale structures. When a slender beam is used, the tension in the tie induces curvature in the beam and increases the structural depth of the system; this opens new formal possibilities and results in lightweight structures at the expense of increasing their overall flexibility. Systems of this kind fall within the realm of active bending. We name them bending-active braced arches. The target shape of the system follows the tensioning process and needs to be pre-determined by means of a specific analysis, typically involving dynamic relaxation or optimization-based methods. In this paper, we propose an analytical method to generate shapes for bending-active braced arches. It assumes that each segment of the activated rod between deviators behaves as a segment of elastica; this enables the use of closed-form expressions to evaluate the shape and induced stress level in the active member. Taking advantage of this idea, it is possible to devise a procedure to carry out the shaping process in a sequential way by adequately choosing the design parameters. When alternative choices for the parameters are selected, the problem becomes non-linear and can be solved using suitable techniques. Some examples with different design constraints have been reproduced to illustrate the possibilities of the method.