Design and Optimization of Hyperboloid Lattice Structures for Timber Towers: A Study on Stiffness and Material Efficiency

Abstract

The presented research aims to design and optimize a timber observation tower, with a primary focus being the influence of topological and curvature parameters on its stability and lateral stiffness in resistance to non-uniform wind load profiles.

Having recognised the environmental benefits and urgency to find other alternatives, there's a clear necessity to incorporate wood as the main construction material into the infrastructure projects, like observational towers. By conducting a study on hyperboloid towers implemented in the last 100 years, this project questions the necessity of in plane stiff platforms, flexurally stiff rings and continuous vertical members as being pivotal to the stability and lateral stiffness of the global structure when subjected to non-uniform wind loads. In addition, the study intends to investigate how the narrowness of the hyperboloid might affect the lateral stiffness of the structure. Thus, by utilizing parametric tools (Grasshopper, Karamba3D and Beaver plug-in), the study aims to design a timber tower structure comprised of fully segmented members as well as incorporation of circular (flexurally stiff) rings, aiming to address the questions raised. In terms of structural member arrangement, the study will investigate two topologies: one featuring a diagrid pattern that emulates a geometrical shape of an antiprism, and a custom pattern inspired by the post and beam approach, which resembles a regular prism shape. The study emphasizes the tower's multi-functionality and adaptability throughout its lifespan. Tower's main structural framework is a pivotal element in providing required stiffness and strength by excluding the need for in-plane reinforcement provided by arbitrarily placed platforms.

The key realisation of this research was the kinematic behaviour exhibited by the segmented, triangular tower, adversely impacting its stability characteristics. The study used a combination of analytical and graphic kinematics techniques, along with a physical mock-up model, to confirm the kinematic behavior of the tower given that even sided polygons for rings are incorporated. This revelation would have an impact on how a structure like that would perform as well the way it would be built. Further research unveils the strong influence of ring type on structural stiffness showing that segmented rings render tower structures less stiff than ones employing curved ring members, regardless of the pattern. In terms of the direct comparison between tower patterns, custom one demonstrated a more consistent and stable performance in general, particularly achieving higher stiffness levels when employing segmented rings. As regards the triangular pattern, the stiffest response against wind loads has been exhibited through the use of curved rings. In addition, the study validates that adopting a hyperboloid shape along with smaller shape factors for the global tower geometry yields more favorable lateral stiffness characteristics. Finally, the study navigates through the exploration of the most optimal connection design, illustrating how considerations related to detailing have necessitated a re-evaluation of the most optimal tower configuration, which initially was chosen to be a triangular one equipped with curved rings. A qualitative assessment of a potential joint within this specific tower variant has confirmed that designing such a connection is significantly more complex. This is due to the necessity of ensuring the continuous flow of the curved ring, emergence of a kink within the insertion of the plate and how that is needed to be addressed.

Alternatively, these considerations have motivated the design process to converge into a new hybrid design, integrating segmented rings with a curved top ring defined by the custom pattern. This choice has been made by conducting a separate parametric study of the new tower design and ensuring that the new connection design fulfills elastic slipping modulus and ultimate strength requirements. The final topology that showed higher stiffness metrics was the custom one. It's also highlighted that maintaining the top of the tower constrained leads to favorable effects on stability and stiffness, irrespective of the chosen topology. The resulting structure is optimized for mass by strategically reducing member cross-sections in accordance with connection scheming while adhering to both SLS and ULS criteria.