Vol. 58 (2017) No. 4

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Dec 4, 2017 - by project-specific CAD plugins. These allow an algorithmic generation of the component geometries and the. CNC ISO6983 G-code for the ...

JOURNAL OF THE INTERNATIONAL ASSOCIATION Vol. 58 (2017) No. 4

FOR SHELL AND SPATIAL STRUCTURES Prof. D. h-C Eng. E. TORROJA, founder

December n. 194

international association for shell and spatial structures

Vol. 58 (2017) No. 4 December n. 194 ISSN: 1028-365X

28/12/04 07:06:09

Journal contents

VOL. 58 (2017) No. 4

n. 194 December

Annual Letter from the President S. Pellegrino

255

Memorial to Klaus W. Linkwitz M. Kawaguchi and E. Ramm

257

Memorial Statement

Tsuboi Proceedings Award Paper for 2016 Structural Design of a Building with Shell and Flat Slab Hybrids K. Noda and Y. Kanebako

259

Hangai Prize Papers for 2017 Parametric Study of Masonry Shells Form-Found for Seismic Loading T. Michiels, S. Adriaenssens and J.J. Jorquera-Lucerga

267

Non-Standard Patterns for Gridshell Structures: Fabrication and Structural Optimization R. Mesnil, C. Douthe and O. Baverel

277

Tunable Frequency Band Structure of Origami-Based Mechanical Metamaterials H. Yasuda and J. Yang

287

Théâtre Vidy Lausanne - A Double-Layered Timber Folded Plate Structure C. Robeller, J.Gamerro and Y. Weinand

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Upcoming Events

315

Reviewers of Papers

316

Technical Papers

COVER: Figures from paper by K. Noda and Y. Kanebako

IASS Secretariat: CEDEX-Laboratorio Central de Estructuras y Materiales Alfonso XII, 3; 28014 Madrid, Spain Tel: 34 91 3357491; Fax: 34 91 3357422; [email protected]; http://www.iass-structures.org Printed by SODEGRAF ISSN: 1028-365X Depósito legal: M. 1444-1960

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

THÉÂTRE VIDY LAUSANNE – A DOUBLE-LAYERED TIMBER FOLDED PLATE STRUCTURE CHRISTOPHER ROBELLER, JULIEN GAMERRO and YVES WEINAND Laboratory of Timber Construction IBOIS, EPFL Lausanne [email protected], [email protected], [email protected] Editor’s Note: Manuscript submitted 5 February 2017; revision received 30 September; accepted 8 November 2017. This paper is open for written discussion, which should be submitted to the IASS Secretariat no later than June 2018. DOI: https://doi.org/10.20898/j.iass.2017.194.864

ABSTRACT This article describes the first full-scale realization of a double-layered, folded plate structure (DLFP), for a new hall for the Théâtre Vidy Lausanne. (Fig. 1). Enabled by a novel double-tenon connection technology, the shape of the components simultaneously serves as a joining aid for rapid and precise assembly, as well as for a direct transfer of the forces between the plates and in between the two layers of the construction. This is made possible by project-specific CAD plugins. These allow an algorithmic generation of the component geometries and the CNC ISO6983 G-code for the fully automatic 5-axis simultaneous machining. Keywords: Integral Attachment, Folded Plate Structures, Origami, Digital Fabrication

Figure 1: Interior View of the Théâtre Vidy during the construction phase in December 2016

1. BACKGROUND Folded plate structures combine different loadbearing functions in their form. Due to the rigid combination of several oblique surfaces along their edges, the elements function simultaneously as a plate, slab and frame. [1] The resulting stiffness makes it possible to span larger distances without intermediate support. The majority of such constructions were realized with concrete in the 1960s and 1970s, the plates being folded in only one direction (so-called prismatic folding).

Interesting studies on folded plate cylinder vaults, in which the plates were folded in two directions, were examined in the 1970s built from glass-fiber reinforced plastic plates (GFRP). This plate material, which was new at the time, was well suited for such lightweight surface supports because of its good ratio of weight and strength. [2] The construction of such a fold with the material of wood, which in addition to the excellent ratio of weight and strength also allows for sustainable constructions, was only possible with the introduction of cross-laminated timber plates (CLT) and structural laminated veneer lumber (LVL). A first example of such a construction, inspired by Japanese origami paper folds, is found in the Chapel of St-Loup. [3] The first prototypes with plywood plates were fabricated and assembled with the help of custom made templates. [3] An experimental folded plate barrel vault made of a total of 144 elements could be built using analogue manufacturing technology in the form of a circular saw that could be tilted for angular cuts. However, as a result of manufacturing and joining with templates and guides, it was necessary to work with repetitive plate geometries, in order to minimize the required templates and guides. The prototype was built using 8

Copyright © 2017 by Christopher Robeller, Julien Gamerro and Yves Weinand. Published by the International Association for Shell and Spatial Structures (IASS) with permission.

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geometrically different elements, with which only singly-curved folded surface structures could be realized. 1.1.

Integral Attachment of Timber Plates

More complex, double-corrugated, folded surface structures, consisting of a large number of differently shaped components, have recently been achieved using integral attachment techniques [4] [5] [6]. This oldest principle of joining technology uses the form of components to transfer forces between them. A transfer of traditional wood panel connections from the carpentry sector was demonstrated in a research project. The integral dovetail tines served not only to transmit the forces, but above all also as a joining aid for a fast and precise assembly of a large number of differently shaped components. Dovetail joints belong to the group of the so-called prismatic, single-degree of freedom connections. The shape of such connectors allows only one insertion direction, which allows one to embed the only possible, correct positioning of the components in the final construction in the prefabricated connection. Thus, a complex, doublecurved overall shape of the load-bearing structure was made possible by means of the joining technique. The deflections on this double-curved folded plate structure were up to 40% less than in a comparable singly curved variant. [4] A further development with which the number of differently shaped edge connections was once again significantly increased are two-layered folding structures (DLFP) made of wood panels. A novel connection technology with double penetrating tenon connectors allows for a complete integral connection of both layers. For example, all four panels can be joined directly along folded edges, the double tenons also serving as spacers between

the two layers and absorbing shear forces [5] [6]. With a comparison of previous prototypes and buildings with the new pavilion for the Théâtre Vidy Lausanne, Table 1 illustrates the increasing relevance of integrated joining aids. 2. THE THÉÂTRE VIDY The Théâtre Vidy is an open space for everybody and dedicated to contemporary creation, a meeting place between art and people. The theater, located in a building designed and built by architect Max Bill for the National Exhibition in 1964, enjoys an exceptional location on the edge of Lake Geneva. Creation Centre of French Theater in the heart of French-speaking Switzerland, the Théâtre Vidy in the unique location of the Vaud capital, at the crossroads of Europe, is an open place in the world where dialogue of Latin theatrical culture and Germanic art is possible. The theater currently has three permanent buildings and a temporary room, located under a tent set up in the adjoining park. The temporary solution of the heated tent should now be replaced. With the permission of the City of Lausanne, a permanent solution in the form of a thermally insulated pavilion, with the ability to be dismantled in the future, if necessary, was planned as a collaboration of the Timber Construction Laboratory IBOIS at the Swiss Federal Institute of Technology Lausanne EPFL and the Bureau d'Études Weinand, who were the responsible architects and engineers. The construction of the Théâtre Vidy pavilion allows for the implementation of a novel type of load-bearing structure, exclusively made of wood panels. The double-corrugated, antiprismatic folded plate structure achieves its mechanical performance through the rigidity of the joints. All plates are joined by innovative wood-wood connections.

Table 1: Increasing relevance of integrated joining aids for the assembly of folded surface structure

Project Origami Folded Plate, 2006 [3] Chappelle St-Loup, 2010 [3] Interlocking Folded Plate, 2014 [4] Théâtre Vidy Lausanne, 2017

296

Number of plates Differently shaped plates 144 8 39 39 107 107 304 304

Differently shaped edge joints 4 67 239 456

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

The objective of this project was to further develop and implement the knowledge gained through recent research at the EPFL IBOIS laboratory. These innovative wood-wood connections will be applied to the scale of a building for the first time. The wood-timber connector’s peculiarity is that they are an integral part of the panels. This construction therefore requires a customized prefabrication: connectors are cut in the factory together with the panels in a single operation. Once assembled, these wood panels ensure the building structure solely, and minimize the need for metal connectors. 2.1.

Construction System

The construction system for the Théâtre Vidy Lausanne represents a consistent development on the basis of the previous prototypes. The two-layer construction explicitly uses the possibility of the

integral connection technology to join particularly thin plate cross sections. This allows the structure to span a distance of 16 to 20 meters without intermediate supports, with a plate thickness of only 45mm. The distance between the two layers is 300 millimeters from the upper side of the outer plate layer to the lower side (simultaneously the visible side) of the inner plate layer. The hollow interspace with a depth of 210 millimeters is also used for the insulation, which is blown in through the holes in the upper plate layer on site. Thus, the double-ply construction offers, in addition to the static properties, a decisive advantage over a single-layer construction with thicker plates. The latter requires, of course, a less demanding geometry generation and joining, but a significantly more complex solid-state insulation, which can only be realized on such a folded-roof roofing at high expense.

Figure 2: Ground plan of the Théâtre Vidy Lausanne

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The load-bearing timber construction of the theater is constructed in 11 building segments between the 12 main axes (figure 2). Each segment between two axes is prefabricated in 3 parts, two wall elements and one roof element. On site, the wall segments are connected to the respective neighboring wall segment, afterwards the roof segment is placed on top of them. There are thus 18 joining steps for each of the 11 building segments, 17 of which are prefabricated and one on the construction site. In the two-layer joining technique used, there are four different steps, each with different tenon shapes, as shown in figure 4, depending on the respective position of the folding edge in the construction. A general distinction is made between two situations in which either one segment is connected to one adjacent segment (figure 4, steps 1 and 2), or the case where one segment is simultaneously connected to two neighboring segments (figure 4, step 3 and 4). While in the first two cases the tenons are oriented at right angles to the edge, the two other cases require a rotation of the tenons within the plate plane, so that the insertion direction of all the tenons of the plate is parallel.

.

Figure 3: Double-layered folded plate assembly principle

A special case is illustrated in figure 4, step 4. Here, plates with slots must be connected to multiple neighbors with tenons at the same time. The insertion of this plate is only possible, if the tenons on the other 4 plates all are parallel. However, since these plates are located on differently oriented planes, there is only one possible insertion direction for the plate with the slots to be inserted. This direction is found along the intersection of the two planes of the two adjacent segments, which we obtain from the cross product of their two normal vectors.

Figure 4: Assembling an axis segment. In steps 1 and 2, a segment is connected to an adjacent segment, the ports are perpendicular to the edge. In steps 3 and 4, the tenons are rotated to allow a parallel slide-in. Step 5 does not take place in the prefabrication, but on the construction site

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2.2.

Structural Analysis of the plate joints

The global mechanical behavior of the Théâtre Vidy is complex, especially with the anisotropic characteristics of wood materials and the folded shape. For this reason, various experimental tests have been carried out to examine the strength of the compounds, taking into account various parameters, in order to determine the most suitable wood-based panels. In previous studies on the strength of integral tine and tenon joints, only Laminated Veneer Lumber panels (LVL) were used, which have a very homogeneous structure due to the many crosslinked layers, each only 3 mm thick [8] [9]. For the project of the Théâtre Vidy, Cross Laminated Timber (CLT) panels were for the first time also considered for an integral connection. One of the reasons for this was the special sustainability, since in this case regional Swiss wood could be used. A special feature of the Swiss panels, which are examined in the following section, is the additional lateral gluing of the board layers. This results in a more homogeneous behavior, which is of great importance for the integral connections.

150 millimeters, and the fiber direction of the plate cover layer was respectively along the orientation of the tenon like in the real project.

Figure 5: A simplified, single-layered finite element model was used for initial examinations of the expected bending forces

The focus of the investigations was on the behavior of the double-tenon and single-tenon joints under bending stress. This stress is decisive in folded wooden structures. Figure 5 shows a simplified, single-layered finite element model with the help of which the greatest expected bending moments were determined (highlighted area in figure 6). 2.3.

Comparison of different plate types

The first series of tests was carried out by means of a single-layer tenon-hole connection between two plates at an angle of 90 °. The tenon width here was

Figure 6: The picture shows the position of the plate and the edge with the highest bending load which was used as the basis for comparison

Table 2: Overview of the three tested wood-based panels, 13-ply LVL compared to 3-ply and 5-ply CLT

CLT 40

CLT 45

LVL 39 (KERTO-Q)

tplate (mm)

40

45

39

Composition

I–I

I–I–I

II–III–III–II

tlayers

12.5mm / 15mm / 12.5mm

5 x 9 mm

13 x 3mm

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In order to obtain a comparison of different woodbased panels, two different CLT panels were tested (with side-glued boards) and a LVL panel (see Table 2). In addition, four series of different geometries and properties were tested for a total of 12 specimens per panel type. With the aid of this experiment, the influence of the tenon rotation along the folding edge could be investigated. This is important because the folding angles in the theater roof are different and require such rotation θ of the tenons. It was found that there is no difference in the bending stiffness between a rotation of θ = 0 ° and a rotation of θ = 15°.

boards. The 45mm thick CLT with the 5-ply structure is the best solution for several reasons: -

Higher stiffness compared to 40 mm BSP

-

Higher yield moment

-

Allows larger rotation in elastic part compared to 40 mm CLT

-

Ultimate moment almost twice higher than 40 mm CLT

-

Homogeneous behavior even with oblique tenons (examined at 0 and 15 °)

The influence of an additional screw connection was also investigated. The test results were more homogeneous with the screw connection, since an ideal initial position of the plates is ensured. In the average, this resulted in a higher bending stiffness of approximately 10%. Figure 7 shows the bending test setup for the singlelayer joint. A 20 kN cylinder, which presses on a steel lever arm, transmits the rotary motion to the horizontal plate with the tenon hole, while the vertical plate with the tenon is fixed rigidly by means of 4 bolts. The lever arm ensures that the force input to the horizontal plate is always perpendicular. The angle of rotation and the forces were detected by 2 inclination captors and 4 force measuring cells. During these tests, the rotation was limited to 30◦. A joint with larger strain is structurally useless and doesn’t enable to satisfy the service limit state of current European standards.

Figure 7: Rotational stiffness setup for single-layer tenonslot wood connection

At the slot plate (see Fig. 7), a protrusion comprises the tenon. The length of the protrusion in the test specimen and final structure is identical to the plate thickness. In the region of the tenon, this block cannot follow the bending of the outer regions. First, there is a fracture of the longitudinally oriented covering layer of the plate while the underlying transverse layer is still intact. In the case of a further bending, the rolling shear in the transverse position becomes too great and a break occurs. The investigations with the single-layered connections with different types of plates have shown that, for the specific integral tenon joints used in this project, CLT panels showed better mechanical properties under bending than LVL

300

Figure 8: Moment as function of rotation for all materials used

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

2.4.

Double-layered experimental testing

Following the investigation of the single-layer tenon joints and the selection of the 45mm CLT panel as the most suitable material, bending tests were conducted with the actual two-layer structure. In this case, the upper layer of the test sample is connected to a single tenon while the two lower layers penetrate each other with a double tenon and are subsequently connected to the upper layer. The experimentally examined configuration of the tenons shown in Figure 9 is a special case in which one of the four connecting lines is not integrally joined. This special case occurs with the in-situ connections in which the prefabricated roof part is placed on the prefabricated wall segments. Here, all four connection lines must be joined in a concurrently executed step. In the figure, the connection points of this connection line are shown in red. This particular compound was chosen because it obtained the highest bending moments in the finite element model (see Fig. 5).

Figure 9: Test specimens for the investigation of the bending load at two-layered corners, folding angles 90 ° and 110 °. The red points show additional screw connections which ensure the position of the components during assembly. (in the final building, only the top screws were put)

Tests showed a considerable increase in the mechanical efficiency due to the two-layer design. In principle, the connection behaves as the singlelayered variant: in order to compensate the bending moment, two opposing forces act, the intensity of which is proportional to the lever arm. In the case of a single-layer construction, there is no lever arm. With the two-layer construction, the value increases to 250mm. As a result, the forces compared to the single-layer variant are reduced to one-fifth.

3. AUTOMATIC GENERATION OF PLATE AND JOINT GEOMETRY The generation of all plate component geometry is done automatically using a CAD plugin that was custom built for the Théâtre Vidy project, developed with the software development kit (SDK) Rhino Commons and the programming language C#. The Grasshopper software is used as a user interface, in which the input parameters of the design can be edited and modified, including a realtime preview of the 3D components. The parameters of the project-specific DLFPgeneration CAD plugin are listed in table 3. The details are as follows: Table 3: Joint parameters. User defined inputs include insertion direction of the joints

No

Input

Output

1 2 3 4 5 6 7

DCEL mesh tplate toffset Joint type Fold type Vinsert,1 Vinsert,2

3D preview Vinsert,1 preview Vinsert,2 preview 3D poly out 3D BREPS out 2D matrix out

1. A single-layer polygon mesh with planar triangular surfaces for the roof elements, and planar quadrangular surfaces for the wall elements. (figure 11) Using this surface model, the identification numbers are managed for all components and edge connections. This is made possible through the use of a double-connected-edge-list (DCEL) data structure, which allows for neighborhood request. These requests are crucial for the automated geometry generation through the algorithmic tool. 2. the plate thickness tplate, which was set to 45mm for the final building components. 3. the total thickness of the double-layer elements. This offset starts at the bottom side of the lower plate, which lies exactly on the surfaces of the DCEL polygon mesh and ends at the upper side of the upper plate. It therefore includes the two plate thicknesses and is not influenced by changes of the tplate value. The toffset for the final project was to 300mm.

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4. The type of joints, managed through an Excel spreadsheet file (see table 4) containing data and overrides for the parameters which are assigned automatically by the algorithm. As illustrated in table 4, the joint type differentiates between regular joints and special joints, such as on naked edges like the ground plane (grnd), front and back end of the building (vend), and at the 10 vertical separaration planes between the prefab segments (vcon). A second column gives additional information on the location of assembly. The joints between the roof and wall elements are connected on site (in-situ), which is a special case with a special joint geometry. 5. The fold type indicates whether a joint is a positive or negative fold, considering all normals of the base polygon mesh facing outwards. Negative folds are treated differently by the algorithm.

adjusted, the geometry can be output into the CAD program through three switches for different representations.

Figure 10: DLFP-generator CAD plugin for the 3D plate geometry and 2D plate matrix for fabrication

6./7. Two insert vectors for each regular joint (see table 4, vins,1 and vins,2). These 3d vectors have been calculated with a separate algorithmic tool, which ensures that plates can be inserted. This requires that multiple edges per plate, which must be joined simultaneously, must share the same insertion vetor. These vectors must lie on the plane of the plate they belong to. They are perpendicular to the plate edge wherever it is possible, when two edges are joined at the same time, the bisector between the two edges is used. Additionally, the njoints parameter provided an override for the manual definition of the number of joints, separate for the inner and outer layer. Outputs include a 3d preview of the plate geometry including all joints, as well as a visualization of the insertion directions for each regular joint edge in the polygon mesh. Once the parameters are

Figure 11: Base geometry polygon mesh (DCEL mesh), Plate ID numbers are visualized in blue color, edge ID numbers are shown in black color

Table 4: Joint parameters. Values for edge IDs 1-8, taken from the Excel DLFP configuration spreadsheet

ID 000 001 002 003 004 005 006 007 008

302

type vend grnd regl regl vend regl grnd grnd regl

loc pref pref pref situ regl pref pref pref situ

fold pos pos pos pos pos pos pos pos pos

vins,1 x -0,412 0,000 0,000 0,118 0,061 -0,438 0,000 0,000 0,000

vins,1 y 0,911 0,000 0,000 0,854 -0,954 0,899 0,000 0,000 0,000

vins,1 z 0,000 0,000 1,000 0,507 -0,293 0,000 0,000 0,000 1,000

vins,2 x -0,412 0,000 -0,901 -0,361 0,061 -0,385 0,000 0,000 -0,901

vins,2 y -0,911 0,000 0,000 -0,907 0,954 -0,923 0,000 0,000 0,000

vins,2 z 0,000 0,000 -0,434 0,216 -0,293 0,000 0,000 0,000 -0,434

njoints,1 3 3 3 6 3 14 3 3 3

njoints,2 3 3 3 3 3 13 3 3 3

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

In addition to the 3d plate contours, boundary representation solids (BREPS) can be output, which was required for the evaluation of masses and visualisation purposes. Also, all plates can be sorted and layed out on the world XY plane, prepared for the fabrication. Here, each plate geometry is transformed from its own local base frame, to the world base frame. The dimensions of the grid are based on the maximum dimensions of the plates. 3.1.

Relevance of fold angles in the structure

One of the most critical parameters for the fabrication is the cutting angles, at which the tool must be inclined to produce the plate components. This angle β results from the dihedral fold angles phi in the basic polygon mesh. If the dihedral angle is at phi=90 degrees, no alignment of the tool is required. Also such orthogonal folds are structurally beneficial. However, it is not possible or feasible to achieve the overall geometry without a deviation β from these orthogonal angles (see figure 12).

3.2. Optimization of fold angles and edge lengths The basic polygon mesh for the Théâtre Vidy was first designed to suit the architectural constraints and requirements of the building. The almost rectangular cross section in the XZ plane allows for an efficient use of the interior spaces, but it also results in a challenge for the folding system. The solution was to combine a prismatic fold for the wall elements with an antiprismatic fold for the roof elements. The joints between these two systems have the most obtuse fold angles in the building, which increase from the center of the structure to the front and end symmetrically.

Figure 12: The tool alignment angle β results from the fold angles deviation from 90°. Very obtuse or acute fold angles require a large inclination of the tool during cutting

Figure 13: Visualization of the tool alignment angle β. Inclinations larger than 55° require a slow cutting velocity, larger than 60° cannot be fabricated with the setup

On the CNC machine used for the cutting of the plates at the plate manufacturer and wood processing facilities, the maximum tool alignment angle was β =60 degrees. This allows for a maximum fold angle of 150 degrees. Taking into account the tool holder profile, in this case a slim thermo-shrink chuck, the required clamping length of the shank-type milling cutter can be calculated. This protrusion is to be kept as short as possible, because it makes the cutting prone to vibrations which reduce cutting speed and cut quality. Larger protrusions therefore require larger milling cutter diameters, however this increase in diameter would have a negative effect on the notches, which are required for the cutting of the concave corners in the plate contours (see section 4).

Following the initial design of the polygon mesh, the CAD plugin allowed to display all fold angles, as shown in the color coded Cad model in figure 13. Subsequently the mesh was modified for a more efficient fabrication, optimizing the maximum and average values for the length of edges (resp. max plate sizes for transport and machining), as well as the fold angles. In the optimized version of the CAD model, the edge lengths were reduced to a maximum of 12.2 meters and an average of 5.5 meters. The dihedral angles were reduced to a maximum of 148 degrees and an average of 125 degrees. This keeps the maximum tool alignment for regular cuts limited to a maximum of 58°. The average tool alignment of 35° allows for an efficient production.

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3.3.

Output of the plates for fabrication

Figure 14 shows the plates from one of the 11 axis segments of the building (in this case the segment No.1, between the axes 1 and 2, see Figure 2), prepared for the production data. Each axis segment consists of three prefabricated components: two wall elements, shown in red color in figure 15, and one roof element, shown in blue color. The wall elements are attached to the base and the adjacent axis segment on site, then the roofing element consisting of a total of 20 prefabricated plate components is placed on the wall elements. This insitu tenon connection is also designed as a double tenon connection, but with some adjustments for easier on-site attachment. Normally, as shown in figure 3, the lower plate in the double-layer connection is inserted along a vector on its own plane (regular insertion), while the upper plate is inserted along a vector that lies on the plane of its counterpart (inverted assembly). This creates an interlocking assembly, where the two parts of a neighboring segment cannot be removed along the same direction, as their insertion directions are at a large angle away from each other. A disassembly is only possible one plate after another. For the in-situ joints in between the prefabricated wall and roof segments, this assembly principle could not be applied, since the two plates of the wall cannot be inserted separately, because the entire wall segments were prefabricated including insulation material and external ventilated cladding. The same applies to the roof prefab elements, where also the upper and lower plate are already connected and cannot be inserted separately. As a consequence, the in-situ joints were inserted in one step, where the entire roof element is lowered onto the wall tenons, along the World Z axis.

Figure 14: 5-axis CMS CNC production center at the wood processing factory Schilliger Holz, CH-Küsnacht

4. FABRICATION Due to the 114 different folding angles in the basic folding form of the theater, various slanting cuts are required for the fabrication of the components. The parts were therefore manufactured with a 5-axis CNC NC-PMT/190-TUCU/ISO40 machining center from the manufacturer CMS, which was available at the facilities of the timber plate manufacturer Schilliger Holz AG. The setup is illustrated in figure 14. With an X-axis length of 28.5 meters, the machine allowed for the cutting of the up to 15 meter long raw plates. 4.1.

Cutting of concave corners

Due to many concave corner points in the polygons, for example between the penetrating tenons or at the slot cutouts within the plates, inclined cutting with a shank-type finger cutter was required.

Figure 15: 28 DLFP Plate Contour Polylines of axis segment 1

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Figure 16: Automatically generated 2D matrix of 308 individually shaped plates

Figure 17: 5-axis CNC production center at the wood processing factory Schilliger Holz, CH-Küsnacht

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The necessary 5-axis CNC machining, which is required at approximately 500 different component edges, with thousands of differently inclined tenon geometries, could not be efficiently generated with standard CAM software solutions for regular timber construction tasks. Instead, we use a custom developed DLFPFabrication CAD plug-in for the automated ISO Gcode generation of integrally inserted wood-based panels. The underlying algorithm has already been used in previous projects and has been further improved and adapted for the Théâtre Vidy [7]. One of the necessary adaptations was a special postprocessor for the CMS machine of the industry partner company. Using the CAD plugin, various special details of integral connections can be created automatically. These include, for example, notch cuts in the concave corners, which are necessary for the insertion of the sharp corners on the inserted tenons. 4.2.

Development of a custom interface

Figure 18 shows the CAD plug-in, programed in Microsoft Visual C#, which was implemented in the visual programing environment Grasshopper®, which is part of the Rhino 3D® CAD software. This interface allowed converting the plate contour data out of the 2D plate matrix shown in figure 16,

automatically into ISO G-code that can be sent to the machining centers OSAI Series 10 control system, simply by a hatch selection. The custom-developed plugin required inputs for the general cutting parameters, as well as a list of polyline contour curves, defining the plate shapes. Within this list, the program automatically finds top and bottom contours that belong together, defining an outside contour or inside cutting contour (tenon slot). The differentiation between outside and inside contours was achieved through the different orientation of the curves, inside contours were clockwise, while outside contours were counterclockwise. The application was designed to automatically respect details, such as the previously described notch cuts, and constraints of the construction system, as well as limitations and functions of the specific CNC machine that was used. This plugin was split into five main components: -

drilling of temporary fixation points

-

5-axis cutting shank-type cutters (fig 18a)

-

5-axis cutting with saw blades

-

Visualization of tool paths (fig 18b)

-

Simulation of machine (fig 18c)

Figure 18: Generation of the G code program for CNC machining with a DLFP-Fabrication CAD plugin. After a hatchselection of pairs of plate contour pairs, the machine-specific G-code is output automatically

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angles. It was also impossible to check this code manually, because the CNC files for the fabrication of individual plates were more than 10.000 lines long. The CNC technician at the factory could use this function to check every CNC program for possible errors, before sending it to the machine. A slider in the visual programing environment allows to scroll through the program line by line, from the beginning to the end of the G-code. This standard procedure was required for safety and therefore a crucial component in the collaboration through a custom-built code generator. Figure 19: Simulation of the machine movements in the DLFP-Fabrication CAD plugin: The production of the plate components with concave corner points and differently inclined flanks is achieved by means of 5-axis machining. The tool is rotated about both axes of rotation of the CNC machining center, while at the same time a translation movement takes place

This special “app” that was supplied to the manufacturer, was an alternative to the generation of CNC G-Code files directly by the planning team. The chosen CAD plugin solution however allowed for a much improved flexibility at the manufacturer. While the company was not able to program the GCode for the fabrication of the plates for the theater with their usual CAM software packages, the chosen solution for this project was to provide the head CNC technician at the factory with project specific tools, which allowed him to generate the required G-Code by himself, rather than providing pre-generated G-code files. This allows for the nesting of the final plate geometries onto raw plate work pieces by the company. With this strategy it is also possible to respond to changes in the project, or to re-arrange or re-fabricate individual plates during the production process, or to change the order of production. 4.3.

Simulation for customized 5-axis cutting

Another important aspect of this chosen strategy was the possibility to integrate customized functions for the tool path display and a cutting simulation component (figure 19) This simulation tool allows to display the machine motions during the cutting, which is particularly important with the large amount of cuts at different

4.4.

Perpendicular cutting

As explained in section 4.1, concave corners in the plate contour polygons require the cutting with a cylindrical shank-type cutter (with only convex corners, simple cutting with a saw blade would be possible). For the theater project, a cylindrical cutting tool with a diameter of 12mm was chosen. This relatively small diameter required three cuts along the entire plate contour, splitting the total depth of the cut into smaller parts, which reduces tool vibrations. A particularly critical parameter in this context is the tool alignment angle β during the cutting. In many situations, the cutting with an inclined tool introduces a pull on the work piece, which can cause strong vibrations. The first counter measure to this problem was an improved clamping strategy. While the thicker CLT plates which are usually cut at this factory at a 90° angle are not clamped at all, the plates for the theater project where clamped with an average of 10-20 wood screws onto the machine table. The holes for this clamping techniques were also handled by the CAD plugin. A second measure to avoid vibrations was to avoid tool inclinations along the axis of motion of the current toolpath. Considering a lower and upper polyline defining the plate contours, this can simply be done by choosing a tool orientation axis, which is the shortest path between the two rails. However, this is not always possible. Figure 20 shows how the fabrication tool deals with this problem. The tool moves along this contour in a counterclockwise orientation (climb cutting) from the right side of the image to the left. It first encounters a concave corner, where the tool must be inclined.

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Figure 20: Automatic extension of tool paths on convex corners

Figure 21: Double-penetrating tenon joints

On the next segment, the end corner is convex. Therefore, the toolpath must start with the inclined orientation from the previous cut, but it can change its orientation to a (perpendicular) shortest line between the upper and lower cutting polygons. Before this change of orientation, the tool retreats to a safety plane 20mm above the plate, and returns with the perpendicular orientation. At the end of the line, an extension of the tool path is calculated to fully separate the pieces with the required length. The following line segments in the picture follow the same logic. Whenever the tool inclination along the cutting line can be avoided, the cuts are instead extended. Concave corners however are preserved and tangential notches are added. 4.5.

Hybrid cutting technology strategy

The previously explained principle is further improved through a hybrid cutting strategy for line segments with a concave start point and a concave end point, using a saw blade for certain cuts automatically. The figures 15 and 16 show that the plate contours of the Théâtre Vidy contain various concave corners, which require the cutting with a shank-type cutter. However, there are also longer

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straight lines in the cutting paths, where the shank type cutter is unnecessarily slow. Along these line segments, cutting with a saw blade improves the efficiency greatly. This problem was addressed through the integration of a threshold value, which indicates the segment length, where the use of a saw blade improves the overall efficiency. This value was finally set to 500 mm, which proved to be the length under which the continuous cutting with the shank type cutter would be faster. All longer cuts which qualify for a saw blade cut are skipped in the initial cutting procedure with the shank type cutter, which will instead pull off and start a rapid (ISO G0) motion above the end point of the line, where it returns to the next cut. The workflow of the G-Code production was as follows: First, the plate contour polygons from the 2D plate matrix on the world XY plane were nested onto the raw CLT work pieces, trying to reduce the waste material as much as possible, as illustrated in figure 22. In the next step, fixation points for the clamping of the plates were added, each with a safety distance away from the tool cutting paths. In order to transfer these points onto the raw plate on the CNC machine, a drilling program was generated in order to mark the fixation points, by the CAD plugin.

Figure 22: Nesting of 3 roof plates out of segment no 2, onto a 9400 x 2300mm 45mm 5-layer CLT raw piece.

4.6.

Variation in plate thicknesses

The 5-layered CLT plates that were used for this project were not sanded down to a precise thickness after the lamination procedure. Therefore, as generally with timber plates, there was a variation in thickness of 45mm – 48mm. Here it was ensured that the thickness would not be less than 45mm, and a complementary strategy was chosen to ensure that the penetrating tenon joints fit precisely into their neighboring plates. This was achieved through an additional “planning” program for each plate, where rectangular pockets were milled along all tenons and double-tenons. The depth of these pockets was set to exactly 45mm

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

above the CNC tables zero plane. This would make sure that the plate thickness of the final plates is exactly 45mm in these critical areas, where the tenon size should be equivalent to the slot size in the roof counterparts, once the parts are jointed. Generally, the plates where produced with a thickness slightly above 45mm. In combination with this pocket-milling strategy, gaps between penetrating tenons and slots in the final structure where reduced as much as possible.

required for the construction of the roof elements in three consecutive steps, for the insertion of the center plates (A), intermediate plates (B), and outer plates (C). This procedure requires four supports in the form of vertically, in the YZ plane positioned planar “M-shaped” plates, with the approximate negative shape of the intermediate roof plates (B). Figure 23 shows this setup, which was designed to be re-used for the eleven roof elements of the theater.

5. PREFABRICATION ASSEMBLY 5.1.

Supports for the insertion pre-positioning

A key advantage of the integrally attached, doublelayered folded plate construction system is that it allows for the construction of wide spanning shell structures without the need for a full-size mold or elaborate support structure, as it is necessary in concrete shells or other types of timber shell structures. Instead, the integral connectors act as assembly guides, defining a unique insertion direction for each of the plates. This does not only allow for a much reduced construction cost, time and manual labor, but it also allows for the construction of large amounts of individually shaped plates. In the Théâtre Vidy, this allows for a double-curvature in the roof structures, which provides a shell behavior rather than the cylindrical, singly curved vaults that were used in previous prototypes of antiprismatic folded surface structures. However, in the full-scale prefabrication assembly, a certain, minimal support structure was

Figure 23: Crane/Vacuum lift assisted insertion of the intermediate plate elements (B) of a roof segment. The photo shows the assembly step 1 from the schematic figure 4, which requires two re-usable linear supports

Figure 24: Re-usable supports for the prefabrication-roof assembly

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In order to define the right angles for the intermediate plates, which is individual for each roof segment, the short connecting posts between the M-shaped plates and the ground supports were fabricated with different lengths for each roof segment. The exchange of these posts allowed for the rest of the supports to be re-used. In figure 4, Step 2 it was already shown that the intermediate segments must be connected first. Therefore, these elements must be placed on the support structure, in a position that allows for the insertion of the remaining plates. A precise placement is required especially for the center elements, as those connect to the intermediate elements on both sides simultaneously. For the final, “locking” plates in each roof segment, the system was designed to have the insertion direction from above for all top layer plates, which simplifies the assembly. Generally, the plates were moved and inserted with the use of portal cranes mounted at the roof of the factory and equipped with vacuum grippers (Figure 23). This allowed for a simple and precise handling of the large and heavy pieces. Therefore, the insertion and placement of the parts in the full-scale prototypes proofed to be unproblematic. In a final step, the thermal insulation material isofloc was injected into the hollow spaces of the prefab segments. In order to monitor the effectiveness of the vapor barrier and infiltration with water, an electronic monitoring system was installed in between the layers, on the lower ends of all roof segments on both sides. 5.2.

Figure 25: Chamfered double penetrating tenon joints

Table 5: Calculation DTTJ tab length, perpendicular and along oblique insertion vector

Loffset,perp ltab,perp θ loffset,ins1 ltab,ins1

Insertion-optimized chamfered joints

After the assembly of the first building axis, which was used as a test element, but also used in the final building, the procedure was optimized with chamfered penetrating tenon joints, where the tips of the tenons are 15mm less wide on two thirds of their protrusion length. Similarly, the sides of the double-penetrating tenons decrease in their width by 15mm on each side, on two thirds of the intermediate space between the two layers of timber plates (see figure 25). This chamfering allowed for a quicker positioning and insertion of the plates. The implementation of these chamfer details at a late stage of the project was easy to implement, due to the algorithmic generation of the plate

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geometries. Figure 25 and Table 6 show how this chamfered double penetrating tenon joint is generated by the algorithm. Values such as the total double tenon width of 270 mm, the shoulder width (e.g. p3l to p4l) of 35mm and the single tenon width of 180mm. In order to compensate for tolerances, the chamfers do not begin directly after the intersection of two plates.

p(toffset,1 - tplate) / cos(π * φdeg / 180.0) tplate / cos(PI π * φdeg / 180.0) VectorAngle(vinsert, nperp) loffset,perp / cos(θ) ltab,perp / cos(θ)

Table 6: Calculation of DTTJ polygon contour

p6l p5l p4l p3l P2l p1l

p0 - nedge * 135 p6l + vins * (loffset,1 * 0.3); (p0 - nedge * 125) + vins * loffset,1 p4l + nedge * 35 p3l + vins * (ltab * 1.2) p3l + vins * (ltab * 2) + nedge * 20

The values loffset,1 and ltab represent the offset and tab lengths of the specific edge, on which the penetrating tenon joint is generated (see table 5). In the case of figure 22 this is a penetrating tenon joint which is perpendicular to the edge. For oblique tenons, the length is calculated respectively.

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

5.3. Measurement segment 1

of

deflections

on

roof

Before the final production phase, the roof segment of the first building section was produced for testing purposes, along with two shortened versions of the wall segments. All connections, fabrication and assembly steps were carried out as in the final building. After the assembly (figure 26), the additional weights were added to the ground plane to prevent any motions. On the roof, a load of 2x 10kN was introduced, as illustrated in figure 26. Afterwards, a vertical deflection of 12-14mm was measured at the reference points illustrated in the figure. Also, a horizontal deflection at the supports of 24 mm was measured. After the unloading, the vertical deflection was reduced by 6-7mm, while the horizontal deflection remained at 24mm unchanged.

Figure 26: Load testing setup for roof segment number 1

Figure 27: Load testing of roof segment number 1. Schematic view of the loads and measuring points

Figure 28: Transportation of a prefabricated roof element. [Photo: Ilka Kramer]

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6. IN-SITU ASSEMBLY 6.1.

Transportation to the site

The prefabricated wall and roof parts were transported from the assembly in the factory, to the building site on special trucks. This was necessary due to the size of the parts. Table 7 shows the dimensions of these assemblies. While the width of the elements was fixed at 2.6 meters, the length increases towards the center of the building up to 21 meters. The total height of the elements increases towards the front and back of the building, up to a maximum of 3.85 meters. Tab.7 Transportation size of prefabricated roof elements

ID 01 02 03 04 05 06

Length 18.66 19.49 20.1 20.5 20.8 20.9

Width 2.6 2.6 2.6 2.6 2.6 2.6

6.2.

On-site Assembly

Height 3.85 3.66 3.54 3.44 3.38 3.33

The Figures 29 and 30 show the on-site connection details of the prefabricated wall elements. On the ground plane, half-lap jointed, pre-cut slants were mounted on the floor slab. This concrete plate was specifically cast along the folded shape of the walls. Figure 29 also shows the ventilated exterior façade, which was pre-mounted on the wall elements in the factory, before the parts were transported to the site. In between the eleven segments with a width of each 2.6 meters, the prefabricated building components meet on ten vertical connection planes in the XZ plane. Here the elements are connected with wood screws diagonally inserted from the outside. After the connection of the wall elements with the ground supports, and with one another, the roof elements could be inserted using a mobile crane. As previously described, the in-situ connections of walls and roof are subject to the highest bending moments in the structure, hence these connections were designed as penetrating tenon joints, even though the assembly had to be carried out on site. The insertion vector of these joints was vertically along the world Z axis, which allowed for a simple and rapid assembly. As for all connections in the entire structure, joints were produced without gaps.

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Figure 29: On-site assembly of the walls [Photo: Ilka Kramer]

Figure 30: Half-lap joint ground plane details on site, December 2016. [Photo: Ilka Kramer]

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS

Figure 31: Insertion of roof element number 1 on site, December 2016. [Photo: Ilka Kramer]

7. CONCLUSION The Théâtre Vidy project shows how automated production technology, which is already widely used in timber construction, can be used for new solutions in joining technology – and ultimately lead to new structural typologies. The novel integral connections in this structure allowed not only to transfer forces between the components, but they also served as integrated locator and positioning aids. In the prefabrication, a unique correct alignment of the components can be embedded into the shape of the connections. This allows simple,

rapid and precise joining, even with 308 different plate shapes, 456 different joint angles and over 3.000 automatically generated and fabricated tenons and slots. For the Théâtre Vidy Lausanne, the connections are of particular importance. The two-layer design offers great advantages both statically and also with regard to prefabrications. The system allowed for the integration of inexpensive flock-insulation between the layers, which had great advantages over solid thermal insulation on such a complex shaped folded plate roof structure.

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The project demonstrates a successful realization of the previously proposed double-layered folded plate construction system with integral double penetraing tenon joints [6]. This system does not only use the connections to join the plates within the upper layer and within the lower layer, but it also connects the two layers with each other with the double-tenons, which also act as spacers to define the correct distance between the plates. The automatically generated and fabricated integral joining technology was made possible through the development and application of project-specific CAD plugins, which have allowed for a new type of digital workflow, connecting the fabrication technology and its capabilities closer with the architectural planning process. While the algorithms for the generation of the 3d geometry were only used by the planning team, the fabrication algorithms were packaged into a custom made software tool for the CNC technicians at the wood processing factory. While this workflow integrates the constraints and logic of the construction system, it remains transparent and leaves room for modifications until the final production. This computation-enabled flexibility has proven to be crucial in the design, optimization and calibration of the plate geometries. The basic parameters, such as the folding form, plate thickness and offset between the plate layers, remained variables throughout the project, which could be optimized following test results, calculations and observations.

[2]

Huybers, P. See-through structuring: A method of construction for large span plastics roofs, PhD Thesis, TU Delft, 1972.

[3]

H. U. Buri, Y. Weinand (Dir.). Origami Folded Plate Structures. PhD Thesis, EPFL, n° 4714 (2010). [DOI: 10.5075/epfl-thesis-4714]

[4]

C. Robeller and Y. Weinand. Interlocking Folded Plate – Integral Mechanical Attachment for Structural Wood Panels, in International Journal of Space Structures, vol. 30, num. 2, p. 111-122, 2015. [DOI: 10.1260/0266-3511.30.2.111]

[5]

C. Robeller, Y. Weinand (Dir.). Integral Mechanical Attachment for Timber Folded Plate Structures. PhD Thesis, EPFL, n° 6564 (2015), pp 136-137, [DOI: 10.5075/epfl-thesis-6564]

[6]

Robeller, C., and Weinand, Y. 2016. Robotic Fabrication in Architecture, Art and Design 2016. Sydney: Springer International Publishing, Cham, Fabrication- Aware Design of Timber Folded Plate Shells with Double Through Tenon Joints, pp 166–177. [DOI: 10.1007/978-3-319-26378-6_12]

[7]

Robeller, C., and Weinand, Y. 2016. “A 3d cutting method for integral 1DOF multipletab-and-slot joints for timber plates, using 5axis CNC cutting technology.” In Proceedings of the World Conference on Timber Engineering WCTE 2016. Vienna: Curran Associates Inc.

[8]

S. Roche, J. Gamerro and Y. Weinand. Multiple Tab-and-Slot Joint: Improvement of the Rotational Stiffness for the Connection of Thin Structural Wood Panels. World Conference on Timber Engineering, Vienna, Austria, August 22-25, 2016.

[9]

Roche, S., Robeller, C., Humbert, L., and Weinand, Y. 2015. “On the semi-rigidity of dovetail joint for the joinery of LVL panels.” European Journal of Wood and Wood Products 73, 5: 667–675. [DOI: 10.1007/s00107-015-0932-y]

ACKNOWLEDGMENTS The construction of the Théâtre Vidy was supported by the Swiss federal environmental office BAFU and by the NCCR Digital Fabrication, funded by the Swiss National Science Foundation (NCCR Digital Fabrication Agreement #51NF40-141853). Architect and Civil Engineers: Bureau d'Études Weinand, Atelier Cube Architects, Wood processing partner: Blumer-Lehmann Holzbau AG. REFERENCES [1]

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Engel, H. Tragsysteme, Hatje Cantz Verlag, 2004.