Modelling glulams

ThePrototype 1: Glulam blank modelproject takes the embedding of timber properties to the scale of architectural components and glulam blanks.

As such, the embedded information in the models changes from one of being purely material properties to also encompassing fabrication data and material specifications such as wood quality and type of manufacturing process. The established production processes of glulam blanks provide useful constraints that allow the glulam blank model to be abstracted into a lightweight geometric model with associated functions. The blank model incorporates a data structure that allows the referencing of individual lamellae, meaning that a link between light‐weight, architecturally scaled models and the lower‐level, discretized element models of individual timber planks is made possible.

Because of the production processes involved in the creation of a glulam blank, certain 3D modelling assumptions can be made. Sawing logs into lumber results in timber elements that resemble rectangular extrusions.

Indeed, the planar and parallel cuts in the sawmill ”crop” the log into nominally straight sections of rectangular profiles. Cut along the trunk of the tree, the longitudinal axis of the lumber element corresponds to the approximate longitudinal material orientation throughout its volume. As beams or columns, glulams follow a similar process: longitudinal extrusions of a rectangular cross‐section, with the longitudinal material orientation roughly parallel to the central axis of extrusion ‐ thecentreline curve. This is a convenient starting point for developing a constrained and light‐weight model of free‐form glulam blanks: a straight or curved extrusion axis, swept by a rectangular cross‐section that is, in turn, composed of smaller rectangular sections corresponding to the cross‐sections of the individual constituent lamellae.

The initial exploration into the modelling of free‐form glulam blanks takes place inProbe 2: IBT glulam workshop. Through a combination of digital modelling and physical prototyping, the bending limits of timber lamellae and overall fabrication feasibility of free‐form blanks is linked to computational rules and procedures. This leads to the first 3D models in this research that focus on the relationship between curvature and material specification, issues of orientation and consistency, and key aspects of the 3D model that distinguished free‐form glulams from other free‐form digital elements. In transferring the principles of glulam production to 3D modelling, the probe draws on advice from industrial partnersBlumer Lehmann AGandDesign‐to‐Production GmbH.

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Fig. 4.17:A free‐form element cut out of a single‐curved glulam blank.

The glulam blank (dashed outline) envelopes component RB_4_0 from Demonstrator: MBridge. Traces of each lamella leave their imprint on the final design geometry.

To begin with, free‐form curves are projected onto an undulating surface. A rectangular cross‐section is aligned with the start of the curves, and oriented so that it stands normal to the surface. Sweeping the cross‐section in this way results in a free‐form rectangular extrusion that is oriented on the surface. However, this does not result in consistent cross‐section dimensions along the sweep. A subsequent method instead distributes the cross‐section onto a series of planes perpendicular to the free‐form curves, which are then lofted together. This ensures that, at each cross‐section along the curve, the cross‐sectional dimensions are true.

Relating the material specification of the glulam to its centreline curve requires the translation of Eurocode bending limits into algebraic and modelling procedures. Referring back to Eurocode 5, the maximum allowable thickness for a timber lamella in a glulam is1/200^thof the minimum radius of its curvature. Implementing this rule consists of finding the largest curvature vector of the centreline curve by sampling the curve at regular, user‐specified intervals. The magnitude of this curvature vector (v⃗_k) is the maximum curvature (k_max) of the curve. Since the curvature and radius of curvature are inversely related, the maximum thickness (tmax) of the glulam lamella is easily found:

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Fig. 4.18:An introduction to modelling 3D glulams inProbe 2: IBT glulam workshop.

(a)The lamella thickness (20.3mm)exceeds the curvature limits of the glulam.

(b)The lamella thickness (10.2mm) is within the curvature limits of the glulam.

Fig. 4.19:Integrating fabrication and material bending constraints into 3D glulam modelling. A curvature graph (yellow) identifies the areas of greatest curvature on the glulam, allowing the minimum radius of curvature to be calculated (2060.4mm).

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wherer_minis the minimum radius of curvature of the glulam centreline curve. This radius must also be adjusted to account for half of the width or height of the glulam cross‐section, since the glulam face on the inside of the curve has a higher curvature than the centreline.

These two considerations ‐ the alignment and consistency of orientation cross‐sections on a free‐form centreline curve and the relationship between the maximum curvature of the centreline curve and the maximum allowable thickness of its lamellae ‐ are the primary modelling distillations from Probe 2: IBT glulam workshop. In addition, the straightness and planarity of the centreline curve ‐ not only as a driver of curvature but of fabrication complexity ‐ becomes a key ingredient in the glulam model. To explore how they can be deployed, the workshop uses these relationships to model four free‐form glulam blanks and fabricate them using hand tools, clamps, and simple jigs. These initial explorations help to identify key modelling principles that form the basis of theglulam blank modelwhich is further developed intoPrototype 1: Glulam blank model.

One particular driver for moving from an implementation of existing modelling tools to dedicated plug‐ins for modelling free‐form glulams is the high degree of involvement and organisational clutter in the modelling environment duringProbe 2: IBT glulam workshop. This entails a large amount of repetition of labour and increase in visual density within the modelling environment. Also, by having every modelling step explicitly exposed, it results in frequent errors and inconsistencies, especially when used by different designers in an ad hoc manner.

The implementation of these modelling principles ‐ cross‐section orientation along a free‐form centreline curve and the relationship of cross‐section specification to bending limits ‐ is therefore encapsulated in a software library (Fig. 4.20). The cross‐section specification dictates the sizing and count of lamellae and is therefore dependent on the curvature and type of centreline curve. This positions the modelling of different types of glulam blanks as a convergence of thecentreline curve,cross‐section orientation, andcross‐section material specification.

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(a)The node layout for modelling a glulam blank inProbe 2: IBT glulam workshop.

(b)Encapsulating of the procedures into a software library simplifies the modelling environment.

Fig. 4.20:Encapsulating a complex modelling process (a) by creating custom plug‐in components for modelling different types of glulams blanks (b).

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Fig. 4.21:The different glulam types derive from the same generic base class.