# 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

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**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 |

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**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