A Parametric Framework for Modelling the Influence of Semi-Rigid Connections on Timber Gridshell Behaviour
Linking connection behaviour to global structural performance
Article by : Kaj Hasenaar
Supervisors: Arjan Habraken, Joey Janssen
The environmental impact of construction is one of the major challenges facing contemporary structural engineering. The built environment is responsible for a large share of global CO₂ emissions, and material consumption in construction is expected to keep increasing in the coming decades. This creates a clear need for structural systems that are efficient, lightweight, and based on low-impact materials.
Timber is an important material in this transition. It is renewable, stores carbon, and can offer a significantly lower environmental impact than conventional steel or concrete structures. At the same time, timber design introduces its own challenges. Timber is anisotropic, meaning its behaviour depends strongly on grain direction, and timber connections often show complex stiffness behaviour that is difficult to capture in simplified structural models.
This research focuses on how the stiffness of semi-rigid steel–timber connections influences the global behaviour of timber gridshells. Gridshells are lightweight structural systems that use geometry as a source of stiffness. Instead of resisting loads mainly through bending, a well-designed gridshell can transfer a large part of the load through axial forces and membrane action. This allows large spans to be achieved with relatively slender members and limited material use.
In practice, however, gridshells are rarely shaped by structural optimisation alone. Their geometry is often influenced by architectural intent, fabrication limitations, transport constraints, connection detailing, and assembly logic. These constraints can lead to forms that deviate from structurally ideal geometries.
When this happens, the accuracy of the structural model becomes especially important. Small changes in stiffness can have a large effect on deformation, load distribution, second-order behaviour, and global stability.
A critical part of this modelling problem is the representation of connections. In many finite element models, joints are simplified as either pinned or fully rigid. For timber structures, this simplification can be problematic. Steel–timber connections generally behave in a semi-rigid way, with stiffness governed by embedment deformation, load direction relative to the grain, local geometry, and time-dependent effects.
Although design codes such as Eurocode 5 provide guidance for estimating joint stiffness, not all relevant geometric effects are fully captured. As a result, simplified models can lead to discrepancies between predicted and actual structural behaviour, especially in structures where connection stiffness plays a significant role in the global response.
Research Aim
This research investigates how the stiffness and load-bearing behaviour of steel–timber connections are influenced by geometric and material parameters, and how these variations affect the structural behaviour of unbraced quadrilateral timber gridshells.
The study aims to connect local connection design directly to global structural analysis. By doing so, it becomes possible to evaluate how changes in dowel diameter, bolt group layout, timber density, member geometry, and boundary conditions influence the stability and deformation of the entire gridshell.
The broader goal is to support more reliable and efficient timber gridshell design by making semi-rigid connection behaviour easier to include in computational design workflows. This is expressed with the main research question:
How do material and geometric parameters influence the stiffness of semi-rigid steel–timber connections, and how does this stiffness affect the form, structural performance, and fabrication strategies of timber gridshells?
To answer this question, the research is divided into several connected parts, each with its own conclusions and results:
- How can parametric workflows aid in establishing efficient models for the analysis and design of timber–steel connections?
- How does node stiffness affect gridshell behaviour?
- How can the rotational stiffness of steel–timber connections be determined based on geometric and material parameters?
- Does solid linear elastic finite element modelling provide an accurate prediction of rotational stiffness?
Methodology
To create a clear understanding of the effects of spring stiffness, this research approaches this issue from an analytical and numerical perspective. Applying both at a global and local scale. This should allow for the analysis and integration of both scales for the final case study.
Parameterising Connection Stiffness
To compare different stiffness conditions in a consistent way, the study introduces a dimensionless stiffness parameter. This parameter describes the relative stiffness of a connection or support condition, ranging from a pinned condition to a fully rigid one.
This approach makes it possible to compare different connection behaviours without being tied to one specific detail. The same stiffness concept can be applied to in-plane stiffness, out-of-plane stiffness, and axial boundary stiffness.
The parameterisation is based on simplified beam and arch behaviour. For rotational stiffness, a clamped beam is compared to a beam with rotational springs at its ends. For boundary stiffness, a similar normalised approach is used to describe the horizontal restraint of the gridshell supports.
Analytical Connection Modelling
At the connection level, the rotational stiffness of dowelled steel–timber connections is estimated using a beam-on-elastic-foundation approach.
In this model, the dowel is treated as a beam embedded in timber. The timber around the dowel is modelled as an elastic foundation, enabling the local embedment behaviour to be translated into an estimate of the connection stiffness.
This method makes it possible to study how stiffness changes with:
- Timber density
- Dowel diameter
- Embedment length
- Bolt group arrangement
- Dowel spacing
- Load direction relative to the timber grain
Because timber behaves differently parallel and perpendicular to the grain, the effective embedment stiffness depends on the direction of loading. Connections loaded more strongly perpendicular to the grain show reduced stiffness compared to those loaded parallel to the grain.
Several bolt group layouts are investigated, and these layouts are assessed under practical spacing conditions while accounting for splitting limitations.
The analytical model provides an estimate of the initial, non-damaged rotational stiffness of the connection. It does not include failure mechanisms such as splitting, plastic deformation of the fasteners, or compression failure in the timber fibres.
Parametric & Computational Workflow
A parametric workflow is developed to connect the connection design and global structural analysis.
Grasshopper is used to generate the gridshell geometry and define the connection parameters. RFEM6 is used for the global structural analysis. Through this workflow, changes in connection geometry or material properties can be translated into stiffness values and applied directly to the structural model.
The intention is to make advanced stiffness modelling more accessible during design. Instead of treating connection stiffness as a fixed assumption or a late-stage detail, the workflow allows it to become an active design parameter.
Initial Results
Global Influence of Connection Stiffness
The gridshell models are analysed using timber members with a cross-section of 128 × 64 mm. Rotational stiffness, in-plane stiffness, out-of-plane stiffness, and axial boundary stiffness are varied parametrically.
The results show that connection stiffness has a clear influence on global behaviour. This is particularly important for quadrilateral gridshells, where stability depends strongly on the combined effect of geometry, joint stiffness, and boundary restraint, especially when membrane action is limited.
The study uses Pareto fronts to identify combinations of stiffness parameters that result in stable structural behaviour. A configuration is considered feasible when it satisfies the global buckling criterion and remains within acceptable deformation limits. These Pareto fronts define a design space: combinations of stiffness parameters within this space lead to stable behaviour, while combinations outside it do not.
However, stability alone is not sufficient. As the boundary of the feasible design space is approached, deformations increase significantly, and bending stresses become more pronounced. This means that a gridshell may technically remain stable, while still being undesirable from a serviceability or stress perspective due to the increasing extensional behaviour.
The orthogonal grid has a much smaller feasible design space. In the study, the solution space for the orthogonal configuration is approximately 25% of that of the diagonal grid. This indicates that the orthogonal grid is far more sensitive to variations in connection and boundary stiffness.
The diagonal grid performs more robustly. Its geometry provides greater inherent stiffness, which makes it less dependent on high connection stiffness. This suggests that grid orientation can be a powerful design tool for improving the structural reliability of timber gridshells.
This result also highlights an important design principle: connection detailing and global geometry should not be treated separately. A more favourable grid layout can reduce the required connection stiffness, while a less favourable layout may demand much more from the joints and supports.
Behaviour of Local Connection Stiffness
The connection study shows that rotational stiffness is strongly affected by timber density, dowel diameter, embedment length, and bolt group arrangement, as illustrated by the ranges shown in the graphs.
Timber density and dowel diameter are the dominant parameters. Within the practical range of dowel diameters, the relationship between dowel diameter and stiffness is approximately linear.
Embedment length has a different type of influence. At small embedment lengths, increasing the length leads to a rapid increase in stiffness. Beyond a certain point, however, the effect begins to level off. In the analysed configurations, the influence of embedment length becomes less significant beyond approximately 100 mm.
The orientation of the load relative to the timber grain is also important. Loading perpendicular to the grain reduces embedment stiffness and therefore lowers the rotational stiffness of the connection.
Bolt group configuration has a significant influence as well. Larger or more widely distributed bolt groups generally increase rotational stiffness because the fasteners are positioned further away from the rotational centre. However, increasing stiffness can also increase local force concentrations, which means strength checks remain essential.
Comparison with Simplified Engineering Methods
The analytical stiffness model is compared with simplified engineering approaches such as those used in Eurocode 5.
Both approaches capture similar general trends. They both show the influence of dowel diameter, timber density, and bolt group layout on stiffness. However, the simplified method does not capture all geometric effects with the same level of refinement.
The engineering curves from Eurocode 5 appear to coincide with the lower limit of the bolt pattern results. This suggests that, for certain steel–timber connection designs, simplified design-code approaches may underestimate the available stiffness.
These differences become important when the global behaviour of the structure is sensitive to connection stiffness. In more conventional structures, simplified stiffness assumptions may be acceptable. In lightweight gridshells, however, especially near the boundary of the feasible design space, these discrepancies can lead to significant differences in predicted deformation or stability.
Discussion and Disclaimer
This research is still ongoing and is likely to be subject to changes. If you intend to use these methods or results, do so at your own risk!
The results show that semi-rigid connection behaviour is not just a local detailing issue. In timber gridshells, connection stiffness directly influences global stiffness, stability, deformation, and load distribution.
The study also confirms the importance of geometric stiffness. The diagonal grid performs significantly better than the orthogonal grid because its layout provides a more robust structural system. This means that global form and grid orientation can help reduce the sensitivity of the structure to uncertain or variable connection stiffness.
At the same time, connection design remains critical. Dowel diameter, timber density, embedment length, grain direction, and bolt group layout all influence the rotational stiffness of the joint. These local parameters can then affect the behaviour of the entire gridshell.
The findings suggest that reliable timber gridshell design requires a closer connection between architectural geometry, structural analysis, and connection detailing. A parametric workflow can support this by allowing designers to evaluate the effect of connection choices early in the design process.
However, the study is limited to linear elastic and initial stiffness behaviour. Failure mechanisms such as splitting, plastic deformation, progressive damage, and local buckling are not explicitly included. Time-dependent effects are considered through load amplification rather than by modifying material stiffness directly. These assumptions are suitable for a serviceability-focused stiffness study, but further work is needed to extend the approach toward full strength and failure assessment.
Conclusion
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