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We present a continuous bi-rod structure composed of two flanges and a pleated web. The structure is characterised by an instability mechanism that couples axial contraction and twisting. In so doing, the latter can be controlled by the former. Moreover, a remarkable softening response is observed immediately after the critical state. A custom testing machine has been designed and manufactured in order to experimentally investigate the mechanical response of the continuous bi-rod. Full scale finite element simulations have been also performed to provide a deeper understanding of the relative contribution of the flanges and the pleated web to the observed mechanical response. The features exhibited by the continuous bi-rod pave the way for innovative technological applications in areas of growing interest (e.g., compliant mechanisms, morphing and deployable structures).