Implementation and propagation of prestress forces in pin-jointed and tensegrity structures

Abstract

The implementation of targeted prestress forces in pin-jointed structures, such as tensegrity structures, is often elusive since the activation of a prestressing device in a single cable or strut propagates forces into all other structural elements. Simultaneously controlling the internal forces and the shape of the structure through an appropriate set of length variations imposed by the devices, referred to as prestress scenario herein, has been a focus of research for over three decades. Overall, this article proposes a pedagogical state-of-the-art on the topic of prestressing and presents an alternative to the force sensitivity matrix, a commonly used method to anticipate the forces in all elements due to the unit length variation imposed on each element. Contrary to this element-to-element approach, a modal paradigm is presented here to simplify the mathematical complexity of a prestressing problem and provide a more intuitive understanding of the propagation phenomenon. Key concepts introduced in the article include the modal scenario, stiffness matrix of the self-stress modes, and propagation matrix. The propagation matrix quantifies the propagation of self-stress levels from one mode to another and offers a valuable design tool to plan the prestressing stages at each construction step or to correct errors observed in the self-stress levels. The article also introduces the self-stress scenario, which anticipates the elastic deformations caused by prestressing to achieve exact targeted forces and geometry while avoiding the propagation of prestress forces. Two examples of the application of the proposed concepts are given.