# Elements of a Timber Lamella Structure: Analysis and Systematization of Joints

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geometry and Characteristics of Timber Lamellae

## 3. Types of Joints for Timber Lamellae

#### 3.1. The Zollinger Joint and Its Modification

#### 3.2. Wood Joint for Lamellae

#### 3.3. Lamellae Joints with Steel Plates

#### 3.4. The Joint by Scheer and Purnomo

## 4. Systematization of the Existing Joints for Timber Lamellae

- the eccentricity,
- load capacity,
- number of elements/complexity of the joint,
- ease of manufacturing and assembly,
- adaptability to the cylindrical surface,

## 5. Discussion on the Analyzed Timber Lamellae Joints

## 6. Proposition of a Timber Lamellae Joint for a Prototype

_{v,Rk}= 0.5 f

_{h,α,k}t d

_{v,Rk}= 1.15 (2 M

_{y,Rk}f

_{h,α,k}d)

^{0.5}

- f
_{h,α,k}is the characteristic embedment strength in the timber member, - M
_{y,Rk}is the characteristic yield moment of the fastener, - t is the plate thickness and,
- d is the diameter of the fastener.

_{h,α,k}= f

_{h,0,k}/(k

_{90}sin

^{2}α + cos

^{2}α)

_{h,0,k}is the characteristic embedment strength parallel to the wood fiber calculated as

_{h,0,k}= 0.082 (1 − 0.01 d) ρ

_{k}

_{k}= 450 kg/m

^{3}and k

_{90}= 1.53, the angle between the resulting force and the grain direction is α = 5.83° according to the formula:

_{2}/N

_{1}) = arctg (1.79/17.5)

_{h,0,k}= 32.295 N/mm

^{2}.

_{u,k}= 560 N/mm

^{2}and is calculated as:

_{y,Rk}= 0.30 f

_{u,k}d

^{2.6}= 107,443.6 N/mm

^{2}

_{v,Rk}= 0.5 f

_{h,α,k}t d = 11,626.12 N

_{v,Rk}= 1.15 (2 M

_{y,Rk}f

_{h,α,k}d)

^{0.5}= 10,494.45 N

_{v,Rk}/1.30 = 12,916.25 N

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Lan, T. Space Frame Structures. In Handbook of Structural Engineering; Chen, W.F., Ed.; CRC Press: London, UK, 1997; pp. 943–1001. [Google Scholar]
- Masarikova Kolonia at Simple Studio. Available online: http://www.simplestudio.sk/project-details.php?id=MASARYKOVA (accessed on 8 March 2023).
- Krovne konstrukcije at PiramidaSM. Available online: https://piramidasm.rs/krovne-konstrukcije/ (accessed on 8 March 2023).
- Makowski, Z.S. Analysis, Design and Construction of Braced Barrel Vaults; Elsevier: New York, NY, USA, 1985. [Google Scholar]
- Wolf, K. Rautennetze by Emil Hünnebeck—Steel lamella roofs of the interwar period. In Iron, Steel and Buildings: Proceedings of the Seventh Conference of the Construction History Society, Virtual, 12–13 April 2020; Construction History Society: Cambridge, UK, 2020; pp. 117–128. [Google Scholar]
- Tutsch, J.F. Weitgespannte Lamellendächer der Frühen Moderne: Konstruktionsgeschichte, Geometrie und Tragverhalten. Ph. D. Dissertation, Fakultät für Architektur, Technische Universität München, München, Germany, 2020. [Google Scholar]
- Weller, B.; Tasche, M.; Baatz, J. Lamella Roof Constructions by Hugo Junkers. In Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium, Valencia, Spain, 28 September–2 October 2009; Domingo, A., Lazaro, C., Eds.; Universidad Politecnica de Valencia: Valencia, Spain, 2009; pp. 1611–1621. [Google Scholar]
- Leslie, T. Form as Diagram of Forces: The Equiangular Spiral in the Work of Pier Luigi Nervi. J. Archit. Educ.
**2003**, 57, 45–54. [Google Scholar] [CrossRef] - Chiorino, M.A. Art and Science of Building in Concrete: The Work of Pier Luigi Nervi. International Exhibition and ACI Spring 2012 Convention. 2012. Available online: http://email.concrete.org/marketing/resources/ci3403chiorino.pdf (accessed on 25 August 2021).
- Nervi, P.L. Aesthetics and Technology in Building, The Charles Eliot Norton Lectures, 1961–1962; Harvard University Press: Cambridge, MA, USA, 1965. [Google Scholar]
- Zollinger, F. Space-Enclosing, Flat or Curved Components. German Patent DE387469C, 28 November 1923. [Google Scholar]
- Winter, K.; Rug, W. Innovationen im Holzbau—Die Zollinger-Bauweise. Bautechnik
**1992**, 69, 190–197. [Google Scholar] - Petrović, M.; Ilić, I.; Mijatović, S.; Šekularac, N. The Geometry of Timber Lamella Vaults: Prototype Analysis. Buildings
**2022**, 12, 1653. [Google Scholar] [CrossRef] - Tamke, M.; Riiber, J.; Jungjohann, H. Generated lamella. In LIFE in: Formation. On Responsive Information and Variations in Architecture, Proceedings of the 30th Annual Conference of the Association for Computer Aided Design in Architecture, New York, NY, USA, 21–24 October 2010; ACADIA: New York, NY, USA, 2010; pp. 340–347. [Google Scholar]
- Vestartas, P.; Weinand, Y. Joinery Solver for Whole Timber Structures. In Proceedings of the WCTE 2020 World Conference on Timber Engineering, Santiago, Chile, 24–27 August 2020. [Google Scholar]
- The 2030 Agenda for Sustainable Development. Available online: https://sustainabledevelopment.un.org/content/documents/21252030%20Agenda%20for%20Sustainable%20Development%20web.pdf (accessed on 5 March 2023).
- Abed, J.; Rayburg, S.; Rodwell, J.; Neave, M. A Review of the Performance and Benefits of Mass Timber as an Alternative to Concrete and Steel for Improving the Sustainability of Structures. Sustainability
**2022**, 14, 5570. [Google Scholar] [CrossRef] - Dickson, M.; Parker, D. Sustainable Timber Design; Routledge: New York, NY, USA, 2014. [Google Scholar]
- Petrović, M.; Ilić, I. Integration of new technologies into buildings made from CLT. In Proceedings of the 5th International Academic Conference on Places and Technologies 2018: Keeping up with New Technologies to Adapt Cities for Future Challenges, Copenhagen, Denmark, 22–24 July 2022; Krstić-Furundžić, A., Vukmirović, M., Vaništa Lazarević, E., Đukić, A., Eds.; University of Belgrade—Faculty of Architecture: Belgrade, Serbia, 2018; pp. 389–393. [Google Scholar]
- Ivanović-Šekularac, J. Drvo u Savremenoj Arhitekturi; University of Belgrade—Faculty of Architecture: Belgrade, Serbia, 2017. [Google Scholar]
- Franke, L.; Stahr, A.; Dijoux, C.; Heidenreich, C. How does the Zollinger Node really work? A Structural Experimental Investigation to a Better Understanding of the Nodal Behavior. In Proceedings of the IASS Annual Symposium 2017, Hamburg, Germany, 25–28 September 2017. [Google Scholar]
- Herzog, T.; Natterer, J.; Schweitzer, R.; Volz, M.; Winter, W. Timber Construction Manual; Detail: Munich, Germany, 2004. [Google Scholar]
- Peulić, Đ. Konstruktivni Elementi Zgrada; Croatiaknjiga: Zagreb, Croatia, 2002. [Google Scholar]
- BlogTO on Twitter. Available online: https://twitter.com/blogTO/status/1090708821083934722/photo/1 (accessed on 12 August 2022).
- Müller, C. Holzeimbau, Laminated Timber Construction; Birkhauser: Berlin, Germany, 2000. [Google Scholar]
- Löschke, H.; Stahr, A.; Schröder, T.H.; Schmidt-Kleespies, F.; Hallahan, R. Segmentation and assembly strategy for lamella roof shell structures. In Proceedings of the IASS Anual Symposium 2020/21, Guildford, UK, 23–27 August 2021; 2021; pp. 2800–2807. [Google Scholar]
- Bath Bespoke. Zollinger Roof. Available online: http://www.bathbespoke.co.uk/2019/06/07/zollinger-roof/ (accessed on 13 May 2022).
- Jirka, O.; Mikes, K. Semi-rigid joints of timber structures. Pollack Period.
**2010**, 5, 19–26. [Google Scholar] [CrossRef] - Sumiyoshi, T.; Matsui, G. Wood Joints in Classical Japanese Architecture; Kajima Institute Publishing, Co.: Tokyo, Japan, 1989. [Google Scholar]
- Johanides, M.; Lokaj, A.; Mikolasek, D.; Mynarcik, P.; Dobes, P.; Sucharda, O. Timber Semi-rigid Frame Connection with Improved Deformation Capacity and Ductility. Buildings
**2022**, 12, 583. [Google Scholar] [CrossRef] - Johanides, M.; Lokaj, A.; Dobes, P.; Mikolasek, D. Numerical and Experimental Analysis of the Rotational Stiffness of a Timber Semi-Rigid Dowel-Type Connection. Materials
**2022**, 15, 5622. [Google Scholar] [CrossRef] [PubMed] - Šmak, M.; Barnet, J.; Straka, B.; Kotásková, P.; Havírová, Z. Doweled joints in timber structures experiment-design-realisation. Wood Res.
**2016**, 61, 651–662. [Google Scholar] - Scheer, C.; Purnomo, J. Recent Research on Timber Lamella Barrel Vaults. In Analysis, Design and Construction of Braced Barrel Vaults; Makowski, Z.S., Ed.; Elsevier: New York, NY, USA, 1985; pp. 406–421. [Google Scholar]
- EN 1993-1-8; Eurocode 3: Design of Steel Structures—Part 1-8: Design of Joints [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]. European Committee for Standardisation: Brussels, Belgium, 2005.
- EN 1995-1-1; Eurocode 5: Design of Timber Structures—Part 1-1: General—Common Rules and Rules for Buildings [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]. European Committee for Standardisation: Brussels, Belgium, 2004.
- EN 1991-1-1; Eurocode 1: Actions on Structures—Part 1-1: General Actions—Densities, Self-Weight, Imposed Loads for Buildings [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC]. European Committee for Standardisation: Brussels, Belgium, 2002.

**Figure 1.**Friedrich Zollinger’s patent for a lamella roof shows the elements of the roof, its geometry, joints, and lamella shape [11].

**Figure 2.**The geometry of the curve for equal distances between the lamellae; a helix on the circular cylinder surface (

**left**). Three possible types of lamellae placement on a circular cylinder surface. Type (

**a**) shows a continual torsion of the lamellae, type (

**b**) are lamellae in discrete torsion, and type (

**c**) are vertically placed lamellae. This drawing presents lamella, with the length of one diamond in the pattern (

**right**) [4].

**Figure 3.**The lamellae for a timber lamella vault where all the axes of the lamellae intersect in the node. The curve of the lamellae axis is the same for all the lamellae, and the length differs on the perimeter (yellow lamellae). The colors of the lamella show the different types of lamellae.

**Figure 4.**The shape of one lamella in floor plan and elevation, with an arched shaped axis. This drawing presents one typical lamella for a timber lamella vault, where all the axes of the lamellae intersect and the lamella axis is a planar arch.

**Figure 6.**A modification of Zollinger’s joint, with steel plates and additional bolts. The axes of the lamellae intersect at the node.

**Figure 8.**The wood joint for a classical pitched roof with a lamella diamond pattern. The left photo shows the joint in plan, and the right shows the elevation with one connecting lamella in place [27].

**Figure 9.**(

**a**) Timber lamellae joint with bent steel plates nailed to the lamellae. (

**b**) Timber lamellae joint with horizontal steel plates let into slits and nailed. (

**c**) Timber lamellae joint with T-section steel plates dowelled to lamellae.

**Figure 10.**A complex joint with steel plates dowelled to the lamellae and connected to the central lamella with a threaded bolt.

The Joint Author | Floor Plan ^{1} | 3D View ^{1} | Eccentricity ^{2} | Type of Connection ^{2} | Joint Elements | Advantages | Limitations |
---|---|---|---|---|---|---|---|

Zollinger | e = 3d, the joint can accept Me = F × e | hinge | bolts | Easy assembly, Simple joint elements, The lamellae are bevelled and drilled, no additional shaping is needed. | Eccentricity, Large displacement in the nodes, Small load capacity. | ||

Müller | e = 0 | hinge | bolts, bent steel plates | No eccentricity, Simple joint elements separated onto wood and steel, Symmetrical, Mounting of the joint elements only from the obtuse angle makes it simpler, The lamellae are bevelled and drilled, no additional shaping is needed. | Preparation of the bent steel plates. | ||

FLEX team | e = 1d, the joint can accept Me = F × e | hinge | screws | Small number of joint elements. | Eccentricity, Reduction of the cross-section area, The additional shaping of the lamellae, Long preparation for mounting of the lamellae. | ||

Bath Bespoke | e = 1d, the joint can accept Me = F × e | semi-rigid | / | The aesthetics of the joint. | Eccentricity, Reduction of the cross-section area, The lamellae must be prefabricated with the utmost precision not to form any gaps in the joint, The need for screws as reinforcement of the joint. | ||

Herzog et al.—nailed bent steel plates | e = 0 | semi-rigid | nails, bent steel plates | No eccentricity, No reduction of the cross-section area, The lamellae are bevelled and drilled, no additional shaping is needed. | Nails cannot be mounted at an acute angle unless the steel plates are larger. | ||

Herzog et al.—horizontal steel plates | e = 0 | moment | nails, steel plates | No eccentricity, The position of the steel plates dictates the direction of the lamellae, making the structure assembly simpler and faster. | Additional shaping of the lamellae for the horizontal plates. | ||

Herzog et al.—T section joint | e = 0 | semi-rigid | dowels, welded steel plates | No eccentricity, The position of the steel plates dictates the direction of the lamellae, making the assembly process simpler and faster. | This joint needs additional elements in order to be mounted onto the central lamella. | ||

C. Scheer and J. Purnomo | e = 0 | hinge | thread bolt, tube with internal thread, screws, steel plates, dowels | No eccentricity. | A large number of elements, Additional shaping of the lamellae, The small contact surface between the central and connecting lamellae, Complicated installation of the joint. |

^{1}The drawings are by the authors of this paper.

^{2}d—width of the lamella. F—axial force in the lamella.

number of bolts in a row parallel to grain (n) | 1 |

average distance (a_{1}) from the loaded edge | 12 |

number of rows | 2 |

the effective number of bolts parallel to grain (n_{ef}) | n^{0.9} (a_{1}/13d)^{1/4} = 0.9365 |

effective load capacity parallel to the grain | N n_{ef}/n = 12,096.25 N |

total load capacity parallel to the grain | 2 n_{ef} N = 24,192.5 N |

Total N: | 24.19 kN |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Petrović, M.; Pavićević, D.; Ilić, I.; Terzović, J.; Šekularac, N. Elements of a Timber Lamella Structure: Analysis and Systematization of Joints. *Buildings* **2023**, *13*, 885.
https://doi.org/10.3390/buildings13040885

**AMA Style**

Petrović M, Pavićević D, Ilić I, Terzović J, Šekularac N. Elements of a Timber Lamella Structure: Analysis and Systematization of Joints. *Buildings*. 2023; 13(4):885.
https://doi.org/10.3390/buildings13040885

**Chicago/Turabian Style**

Petrović, Milica, Darko Pavićević, Isidora Ilić, Jefto Terzović, and Nenad Šekularac. 2023. "Elements of a Timber Lamella Structure: Analysis and Systematization of Joints" *Buildings* 13, no. 4: 885.
https://doi.org/10.3390/buildings13040885