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Transforming a Cantilever with Fixed Joints into Trussed Configurations: A Case Study in Creative Design Thinking & Prototyping

Günther H. Filz

Günther H. Filz

University of Innsbruck, Faculty of Architecture, Lightweight Structures Unit (LSU)Innsbruck, Austria
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Filz, Günther H.
, 
Robert Eberle

Robert Eberle

University of Innsbruck, Faculty of Engineering Sciences, Engineering MathematicsInnsbruck, Austria
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Eberle, Robert
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Pia V. Nagl

Pia V. Nagl

University of Innsbruck, Faculty of Architecture, Lightweight Structures Unit (LSU)Innsbruck, Austria
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Nagl, Pia V.
 und 
Thomas Weinold

Thomas Weinold

University of Innsbruck, Faculty of Engineering Sciences, Geometry and SurveyingInnsbruck, Austria
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Weinold, Thomas
  
10. Mai 2025
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Online veröffentlicht: 10. Mai 2025
Seitenbereich: 113 - 128
Eingereicht: 24. Juni 2024
Akzeptiert: 03. Jan. 2025
DOI: https://doi.org/10.2478/acee-2025-0009
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© 2025 Günther H. Filz et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Realized T1 configuration of the Y-shaped, cantilever arm assembled from standardized beech wood profiles and bespoke, 3D printed joints
Realized T1 configuration of the Y-shaped, cantilever arm assembled from standardized beech wood profiles and bespoke, 3D printed joints

Figure 2.

Left: Benchmark Y-shaped, polyhedral cantilever with fixed joints in side and top view. Right: T1 with coordinates, and indication of node 10 (load point c10), node 23 (load point c23), and node 15 (0/0/0 = c0)
Left: Benchmark Y-shaped, polyhedral cantilever with fixed joints in side and top view. Right: T1 with coordinates, and indication of node 10 (load point c10), node 23 (load point c23), and node 15 (0/0/0 = c0)

Figure 3.

Y-shaped, polyhedral cantilever with fixed joints as benchmark versus configurations T1-T5. The arrows indicate the differences between the individual configurations
Y-shaped, polyhedral cantilever with fixed joints as benchmark versus configurations T1-T5. The arrows indicate the differences between the individual configurations

Figure 4.

Optimized cross-sections for beech wood (color coded) for configurations T1 to T5. Dimensions of standardized circular profile cross-sections in 2, 2.2, 2.5, 3, 3.5, 4, 4.5, 5, and 6 cm in diameter
Optimized cross-sections for beech wood (color coded) for configurations T1 to T5. Dimensions of standardized circular profile cross-sections in 2, 2.2, 2.5, 3, 3.5, 4, 4.5, 5, and 6 cm in diameter

Figure 5.

Configuration T1 and its displacements as simulated in Karamba3D. The cantilever was loaded by self-weight and vertical loads of 0.5 kN to both nodes 10 and 23
Configuration T1 and its displacements as simulated in Karamba3D. The cantilever was loaded by self-weight and vertical loads of 0.5 kN to both nodes 10 and 23

Figure 6.

Left: Resultant force replacing concentrical tension rods in multi-arm nodes by use of graphic statics. Center: 3D printing Node 11 including two through-the-joint-mounted fittings (also see Figure 8) by PrusaSlicer, Prusa i3 MK3 and PLA NX2. Right: 3D printed joints ready for T1 assembly
Left: Resultant force replacing concentrical tension rods in multi-arm nodes by use of graphic statics. Center: 3D printing Node 11 including two through-the-joint-mounted fittings (also see Figure 8) by PrusaSlicer, Prusa i3 MK3 and PLA NX2. Right: 3D printed joints ready for T1 assembly

Figure 7.

Left: Two point-clouds from laser-scan with local coordinate system, target balls and reconstructed cylinders. Center: Scans from unloaded (green) and loaded (red) structure. Right: Example of reconstructed cylinder from approximately 1300 scanned points
Left: Two point-clouds from laser-scan with local coordinate system, target balls and reconstructed cylinders. Center: Scans from unloaded (green) and loaded (red) structure. Right: Example of reconstructed cylinder from approximately 1300 scanned points

Figure 8.

Top: Overview of nodes. Bottom left: Node 19 with six wooden members and one threated tension rod. Bottom center: Node 19 in the realized structure. Bottom Right: Identical point c→19 {\vec {\rm c}_{19}} (blue dot) of the joint i=19 with six wooden members
Top: Overview of nodes. Bottom left: Node 19 with six wooden members and one threated tension rod. Bottom center: Node 19 in the realized structure. Bottom Right: Identical point c→19 {\vec {\rm c}_{19}} (blue dot) of the joint i=19 with six wooden members

Results of the computational comparison between the different configurations at the two load points

load point c→10 {{\rm{\vec c}}_{{\rm{10}}}} load point c→23 {{\rm{\vec c}}_{{\rm{23}}}}
Difference vector Δc→i {\rm{\Delta }}{{\rm{\vec c}}_i} : Δx [cm]: 3.21 1.39
Δy [cm]: 0.52 1.84
Δz: [cm]: 3.60 3.57
Euclidian norm Δc→i \left\| {{\rm{\Delta }}{{{\rm{\vec c}}}_i}} \right\| [cm]: 4.85 4.25
Directional angle αi [°]: 0.1 0.4
initial configuration end configuration initial configuration end configuration
elevation to the horizontal plane βi [°]: 40.43 39.69 27.41 26.79
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