Text adapted from the IASS 2024 article Performance-Based Design of a Bending Active Hardwood  Glulam Beam-String: a Form-Finding Paradox written by João Tavares PINI and Hélio OLGA.

Read the full paper below:

(PDF) Performance-Based Design of a Bending Active Hardwood Glulam Beam-String: a Form-Finding Paradox

The project aimed to develop an efficient, simple, and clear structural solution in tropical hardwood timber that could compete with typical steel or precast concrete industrial sheds in the context of the global south. Early studies of trussed arrangements showed that they required numerous tensile connections, which led the research toward a lenticular beam-string that would reduce the number of critical nodes to two. While demonstrating very low material consumption, lenticular beams typically rely on curved members which depend on non-automated fabrication methods.

This led to a new hypothesis: a bending-active beam-string composed entirely of straight glulam chords bent into shape during pre-assembly. In this approach, the form-finding process gained complexity: the relationship between post heights and chord inertia would determine the structural form through pre-assembly deformation.

While the found structure resulted in extremely low timber consumption of 0.024 m³/m², the major outcome lies in the connection design. The shallow curvature of the upper chord and the greater width of the lower chord create a long contact region, allowing internal forces to be transferred with screws only, resulting in a minimal usage of 0.1kg/m² of steel.

A full-scale prototype validated the analytical predictions and the imposed-curvature concept. After automated gluing and machining, two carpenters pre-assembled two beam-strings per day. On-site installation of the first unit was completed in three weeks by a team of three.

By integrating geometry, material behavior, and production constraints from the outset, this design generated a lightweight, low-carbon, low-cost tropical hardwood solution capable of competing with steel and concrete alternatives. The form-finding algorithm enables adaptation to different spans and loads, making the solution scalable and appropriate for the context of the global south.

Documentary  THE STRENGTH OF FORM – bending-active hardwood beam-string  presents the research conducted in the search for a lightweight, efficient structural solution compatible with the Brazilian context, especially for small and medium-sized industrial buildings, traditionally built with prefabricated steel or precast concrete structures.

It features testimonials from internationally renowned professionals such as Erick Karsh (Equilibrium), Evy Slabbinck (Design-to-Production) Stefan Rick (SJB Kempter Fitze), Hélio Olga and João Pini (ITA Engenharia em Madeira). They discuss the technical implications of the research and the parallels with projects of great global relevance, including Wisdom Stockholm.

The design process was structured around an integrated computational workflow. Parametric geometry was developed in Grasshopper. It allowed key dimensions and cross-sections to remain variable and adaptable throughout the study. This geometry was then analyzed using Karamba3D for finite element analysis (FEA), enabling continuous structural evaluation.

Structural safety checks according to Eurocode 5 were performed using Beaver, which is fully integrated with Karamba3D. Beaver provided automated Ultimate Limit State (ULS) and Serviceability Limit State (SLS) verifications, along with detailed design ratio reports and failure mode visualizations.

Beaver is a timber engineering framework for Karamba3D users that brings transparent Eurocode 5 timber verification directly into Grasshopper. It allows designers to evaluate timber members and connections within the same parametric workflow used for modelling and structural analysis, reducing the gap between geometry generation, FEA, and code compliance. Rather than acting only as a final checking tool, Beaver supports iterative and performance-based timber design by exposing the governing checks, load cases, and parameters behind each result. A fully refactored version of Beaver, with deeper Karamba3D integration and a new user interface, used to develop this work, will be released soon on Food4Rhino.

The research explored timber beam-strings as an alternative structural system aimed at minimizing nodes and simplifying fabrication and transport constraints. An algorithm was developed to generate multiple beam-string configurations based on three primary parameters: structural height, span subdivision, and cross-sections.

Given the climatic context and lightweight roof system, wind was identified as the governing load case. A timber lower chord was selected instead of a steel cable to accommodate compression forces while maintaining material consistency and environmental performance. To reduce material consumption, simple vertical posts were preferred over diagonal bracing, provided overall stability could be ensured. Posts and lateral bracing were aligned with secondary structural elements to reduce unnecessary bending effects and improve overall efficiency.

To increase the algorithm’s complexity, the geometric definition of the beam-string system was expanded to account for bending-active behavior. Because the deformation of two beams bent toward each other is proportional to their rigidity, a preliminary analytical model was developed to simulate proportional imposed deformations following parabolic curves corresponding to post lengths. The resulting deformed configuration became the geometric basis for the beam-string chords.

The analytical model further incorporated the fact that these curves originate from straight members bent during assembly. In Karamba3D, this was achieved using an approach analogous to bending-active gridshell analysis, adapted to reflect the specific interaction between the beams.

In parallel with structural limit checks performed in Beaver, additional geometric constraints were introduced for construction efficiency. To maintain compatibility with a flat thermoacoustic roof tile used across the building complex, curvature in the upper chord was restricted. Although allowing unrestricted deformation would improve structural performance, limiting curvature ensured material standardization and cost-effectiveness.

To accelerate the form-finding process, parabolic curvatures were initially used as the geometric basis for the preliminary analytical model. These curvatures were introduced as imposed displacements corresponding to post heights, and the resulting beam deformations defined the overall beam-string geometry.

However, analysis of the bending moment diagrams revealed peak moments near the first posts at the supports. This indicated that parabolic curves were not optimal for distributing the concentrated forces introduced by the posts. As a result, a secondary form-finding phase was undertaken to refine the curvature geometry while maintaining the defined cross-sections and subdivisions.

By optimizing the curvature profile, the pre-assembly bending effects were reduced, leading to a measurable increase in structural safety at the Ultimate Limit State without additional material or fabrication complexity.