Gridshell Structural Research

Department of Architecture Faculty of Architecture

The University of Hong Kong

LEXIE_LI XUECHANG

RIBBED TIMBER SHELL ROOFING

Xuechang

Architect Geier and Geier

Structural Engineer Wenzel, Frese and Barthel

Completion

1987

Cost 20 million DM Structural system Suspended Lattice Shell Area Timbershell Roof, 2500m²

Brine Baths at Bad Dürrheim, Germany

Students: Xuechang LI Site

The location of the site is Solemar, Hubertstraße 8, 78073 Bad Dürrheim, Germany.

It is an old spa and lies on a plateau at a height of about 700 metres. The place is bedded in the mountain landscape of spruce and fir-trees of the Southern Black Forest.

The newly built mineral bath was supposed to receive a roof that, through its form and its support, would express the close connection with the surrounding landscape.

Introduction

In that period of time(1980s), the public baths have under gone a dramatic change. There has been not only a pro liferation of the types of bath one can enjoy warm-water, cold-water, artificial-wave, kiddies‘ and whirlpool bath; such supplementary facilities as saunas, solaria, therapu room, cafes and resting and relaxing areas now alsoa bound. This has given rise to new spatial concepts that accentuate individual areas without separating them one from the other——fluid spaces as it were. [1]

The public brine baths in Bad Dürrheim is a building erected as an extension of the town‘s spa facilities. The

decision to use wood for the roof was an early one, for timber’s natural resistance to highly alkaline and corro sive atmospheres makes it an ideal material for roofing swimming pools and salt water baths. Apart from that with this material the architects wanted to relate the building to the wooded region around it.

The project sees the use of glulam ribs assembled to form gridshells draped over five glulam columns (trees) between 9.1 m and 11.5 m tall spaced 20 m apart. With a surface area of 2500 m2, the roof covers a floor area of 1500 m2.

Fig.

Fig.

Project

Architectural Concept

The shell consisting of a skeleton of GluLam beams covered crosswise by planks - rests on five tree-like supports and has a total surface of 2500 sqm. The treesupports with heights between 11.5 m and 7 m are grouped around a central place. Between them “hangs“ the doubly curved diaphragm- like shell, using the treesupports as high-points and parts of the edge beams as low-points. From the ringshaped closing upper edge of each tree-support ”meridian ribs“ run to the other trees and to the edge beams. They are intersected vertically by horizontally positioned ringribs which are held together by finger jointing so that they can withstand both tension and compression forces. The overall length of the ringribs is 2900 metres. [2]

Functions

The whole of the ground level, including the floor and such individual units as the brine grotto, stair-towers, shower cubicles, etc. are of in-situ concrete. The whole of the mul tifarious panorama is covered by a vast roof with a total area of 2500 m2. Like a net the roofshell dips and rises from one tree-like column to the next and then down to the building’s arched boundaries. The saddle-like sur faces between the columns split up the interior into sepa rate areas. The columns open up tree-like towards the top with “branches” that carry annular beams. From these the shell is suspended and above them rise cupolas of glass. The highest of the “trees” is 11.50 m, stands on an island in the large swimming-pool and carries a ring of beams 8 m in diameter. It is the centre of a space 36 m in diameter. Next to the swimming-pool stands the second highest tree 10 m high and supporting a ring 7 m across. It thus forms

Fig. 5: Plan/top view of the primary structure

Fig. 6: Inside view

7: Outside view

Fig. 4: Section through the primary struc

RIBBED TIMBER SHELL ROOFING

Typical Joint

Typical Support

each

being held together by fin ger-jointing, each rib can withstand both tension and compression forces. The meri dians, measuring 200 mm × 205 mm in section, connect columns and edge boun daries of the structure. The annular rings are spaced at 800mm centres. These two systems are connected together using true pins. The tension rings and perime ter arches were designed as box section in such way that the ribs can be pinned bet ween the box panels (Figure 8). [4]

Fig.

The roof

from five tension rings,

tree-like

9.1 and

10)

The

arches

bearings(Figure

mainly

The deadweight of

is supported by the façade.[5]

Fig. 9:

of the Connection of arch and shell

Fig. 10: Photo of Support (right)

Because of the large number of curved and twisted ribs and boundary arches a special works programme and production method were necessary. At intervals of some 80 cm the three coordinates and the two angles of twist of the cross-section had to be calcu lated for each individual rib and boundary beam.

The first step was the erection of the tree columns. These were each brought to the site in two sections and glued together on the spot. Then the bottom parts of the tree

rings and the curved edges were fitted. at the facade columns the height and slope of the edges were exactly measured; tole rance compensation was possible at the supports. No other geodesic checks were necessary during the installation work. It sufficed to fix the meridian ribs at the top and bottom connecting points with a tem porary screw and to support them with a strut. With the positioning of the annular ribs, which by their spread determined the spacing of the meridian ribs, the shape of the roof developed on its own. [6]

layers of roof

RIBBED TIMBER SHELL ROOFING

Geometry

The forms in the actual project were gen erated digitally using the software EASY and followed approximate stress trajecto ries. [7]

In the form-finding, the geometry is gener ated in Rhino with the grasshopper plug-in ‘Kangaroo’. The prototype is the tension net which can be generated by a flat net. The net is supported by 5 ‘trees‘ in timber, along with several steel columns on the

edge.

Parameters

a. the number of the segments of net;

b. the height and location of support points; c. the weight of the load;

d. the strength of the net segment.

Results

The final shape generated by grasshopper is actually not the accurate shape of the real. There is a certain difference between the computer logic and the actual genera tion of shapes. In my form-finding, I used a mesh while the actual process used a series of line.

It was difficult to mimic the generation process at that time, because there was no logic to follow in the arrangement and sparseness of the grid lines, and they could only be traced down based on the existing

19: Curvature Analysis

Gaussian surface curvature K

The Gaussian curvature K is commonly used to describe the shape and magnitude of surface curvature. The Gaus sian curvature of a surface at a point is defined as the product of the two principal normal curvatures. (K=k1+k2)

If the two principal curvature radii centers lie on opposite sides of the surface, then the part of surface is negative. The curvature of the present surface is all negative so the range of K is all negative num bers.

Spatial curvature K

The spatial curvature decreases from the bottom to the top.

Normal curvature k n

The normal curvature kn is a measure of how much the surface is curving rather than how much the curve is curving. Basically, from the bottom to the top, the Kn is gradually decreasing.

Geodesic curvature k g

A geodesic is a locally lengthminimizing curve. The geo desic curvature measures how far the curve is from being a geodesic. The Kg of annual lines decrease from the bottom to the top and the highest values on the bottom.

The Kg of meridian lines remain the same value and the maximum.

Geodesic torsion t g

The torsion of a curve quanti fies the twist of a curve about its tangent vector as the curve evolves.In the geometry of surfaces, the geodesic torsion describes how a surface twists about a curve on the surface. There is no torion happens to the surface, so the geodesic torsion is 0.

RIBBED TIMBER SHELL ROOFING

Summary

The Bad Dürrheim swimming pool would probably be desi gned on the computer today. But in retrospect, one must recognize the model design of that time as the basis of impeccable dimensioning, the implementation was well thought out constructively and structurally and the buil ding was continuously maintained by the operators for decades. The wooden ribbed shell can be considered a suitable building type for a brine bath and gains in unique, formal power compared to many new wellness temples. The durability and ease of care of the material-appropriate construction type are always remarkable.

[8]

[

Bibliography

[

1] Gotz Gutdeutsch, 1996, Building In Wood: Construction And Details, Birkhauser Berlag, Basel Berlin Boston, pp. 45

2] Holzbau-Konstruktionen, 1987.6, Solebad in Bad Dürr heim, DETAIL

[

3] Gotz Gutdeutsch, 1996, Building In Wood: Construction And Details, Birkhauser Berlag, Basel Berlin Boston, pp. 45

[4] Gotz Gutdeutsch, 1996, Building In Wood: Construction And Details, Birkhauser Berlag, Basel Berlin Boston, pp. 47

[5] MSc Thesis by M.H. Toussaint, 2007, A Design Tool for Timber Gridshells: The development of a grid gene ration tool, pp.26. https://homepage.tudelft.nl/p3r3s/ MSc_projects/reportToussaint.pdf

[

6] Gotz Gutdeutsch, 1996, Building In Wood: Construction And Details, Birkhauser Berlag, Basel Berlin Boston, pp. 49

[

7] MSc Thesis by M.H. Toussaint, 2007, A Design Tool for Timber Gridshells: The development of a grid gene ration tool, pp.26. https://homepage.tudelft.nl/p3r3s/ MSc_projects/reportToussaint.pdf

[

8] Wenzel, F. Frese, B. Barthel, R.: The timber ribbed shell roof in Bad Dürrheim. In: Structural Engineering Review 1/1989, pp. 75-81

6 Solemar, Bad Dürrheim (Germany):Glass Roof PR60 https://www.lamilux.com/skylights/references/glassroof-and-facade-construction-references/solemarbad-duerrheim-germany.html

7 John Chilton&Gabriel, 2017, TangTimber Gridshells: Architecture, Structure and Craft, Toutledge, New York, pp. 181

8 Therapiezentrum »Solemar« in Bad Dürrheim. https:// www.db-bauzeitung.de/150-jahre-db/therapiezen trum-solemar-in-bad-duerrheim/#slider-intro-2

9 Gotz Gutdeutsch, 1996, Building In Wood: Construction And Details, Birkhauser Berlag, Basel Berlin Boston, pp. 49

10 John Chilton&Gabriel, 2017, TangTimber Gridshells: Architecture, Structure and Craft, Toutledge, New York, pp. 181

11 Holzbau-Konstruktionen, 1987.6, Solebad in Bad Dürr heim, DETAIL

12 Drawing by Author

13 Drawing by Author

14 Therapiezentrum »Solemar« in Bad Dürrheim. https:// www.db-bauzeitung.de/150-jahre-db/therapiezen trum-solemar-in-bad-duerrheim/#slider-intro-2

15 Fritz Wenzel, Bernd Frese und Rainer Barthel: Die Holzrippenschale in Bad Dürrheim. In: Bauen mit Holz 5/1987, pp. 282-287

List of Figures

1 Therapiezentrum »Solemar« in Bad Dürrheim. https:// www.db-bauzeitung.de/150-jahre-db/therapiezen trum-solemar-in-bad-duerrheim/#slider-intro-2

2 Solemar, Bad Dürrheim (Germany):Glass Roof PR60

3 Holzbau-Konstruktionen, 1987.6, Solebad in Bad Dürr heim, DETAIL

4 Gotz Gutdeutsch, 1996, Building In Wood: Construction And Details, Birkhauser Berlag, Basel Berlin Boston, pp. 44

5 Gotz Gutdeutsch, 1996, Building In Wood: Construction And Details, Birkhauser Berlag, Basel Berlin Boston, pp. 46

16 MSc Thesis by M.H. Toussaint, 2007, A Design Tool for Timber Gridshells: The development of a grid gene ration tool, pp.27. https://homepage.tudelft.nl/p3r3s/ MSc_projects/reportToussaint.pdf

17 Drawing by Author

18 Drawing by Author

19 Drawing by Author

20 Therapiezentrum »Solemar« in Bad Dürrheim. https:// www.db-bauzeitung.de/150-jahre-db/therapiezen trum-solemar-in-bad-duerrheim/#slider-intro-2

Fig. 20: Fhoto

Design Topic Developable Surface on Typical Asymptotic Gridshells

Li Xuechang | Liu Yujie

Fig. 1: Project

Gehry

Structural

Batiments

Introduction

The Foundation Louis Vuitton, is a museum for contemporary art, located next to the Jardin d'Acclimatation in the Bois de Boulogne, Paris. Built at a cost of $143 million, the beautiful Beaux Arts exhibition hall houses around 3500 sqm of space, is to 'enable a broad public to enjoy a multitude of artistic creations, deepening LVMH's ongoing commitment to promoting culture.'

The geometry is first an initial sketch by Frank Gahry himself to represent the 19th glass shelfs of the iceberg. Followed by artistic researches into servaral developable

Structural

40m

area of the

glass

sqm

surfaces. The 12 glass sails represent 13500 square meters of glass made up of 3530 curved glass panels, each one unique. Each size of sails also different ranging from 6-20 meters. With Dassault systems‘ CATA softwore, which is specially developed by Gehry technologies, it achieved the high-precision industrail applications.

With the technology of CNC and a fairly recent machine, the glass penel of each sails could be produced without the use of molds. By giving new definition- the angle of rota tion of glass panel into the machine, it can be individually setted and adopted by computational mathematical opti mizations which could help to find the best-fit cylinders.

Students: Liu Yujie Site

The Louis Vuitton Foundation is located on the northern edge of Bois de Boulogne, in the area of the Jardin d' Acclimatation. Bois de Boulogne was a royal hunting estate by bridle paths and the forest was planted with tall common and sessile oaks. Later, Empress Eugenie ,the wife of Napoleon III, inaugurated Jarden d'Acclinmatation, the landscaped heritage was transformed into an English style garden with waterfalls, pavillions and lakes. Today, as society developed, it became more of a place and garden toplay. With the arrival of the Foundation Louis Vuitton, the site was entirely redefined, returing to the spirit of the original landscape asa place of surprises, invention, and emotion. [1]

Fig. 2: Siteplan

Scale 1:500

Foundation of Louvis vuitton- France, Paris

[1] Filler, Martin., The Foundation Louis Vuitton by Frank Gehry: A building for the Twenty- First Centry, 20-25

CONCEPT

Concept

The project of Brine Baths Bad Bad Dürrheim and the Foundation of Louis Vuitton have in common: Using flat architectural elements (glazing panels and wooden ske leton), bending into specific curvature to achieve the form of developable surface. After learning Asymptotic grid shells, our group is thinking: is there an alterna tive way to improve speed, material efficiency, reusabi lity, and construction process by applying Asymptotic?

To achieve a homogeneous network, we take advantage of the bisecting property between asymptotic and princi pal curves, to support a developable facade on a rotational surface. Our goal is to build a large-scale research pavi lion as an exhibition and gathering space.

Potentials

Asymptotic grids have zero normal curvature in which always curves sideways freely and can be constructed from straight, planar strips perpendicular to the surface.

On the contrary, the Principle curve has zero geodesic cur vature kg showing they never curve sideways. But they can still be fabricated from straight, planer strips tangential to the surface.

In a rotational surface, the geodesic curve is the principal curve. It means the facade can be cut by geodesic curves and bent on the surface with less force.

The fabrication and the construction process will be sim plified and sped up when we hybrid these two structures as the base structure.

Challenges

The challenges mainly include the design of the joint, sta bility of the structure and material. The design of the node must be reasonable to connect the three different angles and different heights of the wood accurately. We tried a variety of node methods to find the right balance bet ween the node and overall model switching. Moreover, the design of the node should also consider materials, such as not too many nails on wood.

Second, since it is an inverted funnel, the design of the foundation also needs to be considered. For example, how to finish the wood or iron strips elegantly and provide a space for entrance and exit.

Finally, since all modeling and production construction needs to be completed in Grasshopper, any errors that occur in the middle of the process must be changed in time to prevent production. The design relies on computer soft ware and cannot be tweaked on site.

Fig. 3: Concept diagram

FINDING

Geometry

First, using Rhino 7, we generated a rota tional surface by defining a curve and its central axis(Fig.3 A). Then put the parame ter into Grasshopper, and use the glug-in Bowerbird, pick a starting point and iden tify the first Asymptotic curve on the sur face, then copy and mirror it until it fills all over the surface(Fig.3 B). Quantity and density need to be considered repeatedly in this process. The size of the mesh should not be smaller than two times the height

of lamellas, and no larger than about four times their height. To fix it into an archi tectural prototype, we trimmed it with a box (Fig.3 C), adjusted it to the appropriate position and scale (Fig.3 D). Last, create an opening and principle curve on the surface.

Parameters

First, the original rotational are the main parameters of this structure which deter mines the curvature of the surface. Mean while, the final form and geometry varied by two values: the density of the Asympto tic curve and principle curve, which could influence the stiffness, and its position, size, and form of the trim box. The upper trimmed box is situated, the denser the grid would be.

Results

For further investigation and research, we decided to use 16 strips with a square box to achieve a 5m*5m architectural proto type through several testing between both digital models and physical models (Fig.4).

Fig. 5: Centerline ModelFig. 4: Workflow

B

DEVELOPABLE SURFACE ON TYPICAL ASYMPTOTIC GRIDSHELL

Fig. 6: Curvature Analysis

Gaussian surface curvature K

The Gaussian surface curvature of hyper boloid is always negatively presented as blue and green.

The overall Gaussian curvature is gradi ent, is has the most negative curvature on the top and gradually turns to zero in the bottom.

Normal curvature k n

Asymptotic Curve: Since Asymptotic curves

the path of vanishing normal cur vature. The normal curvature kn must be zero.

Geodesic Curve: The geodesic curves have the same curvature.

Geodesic curvature k g

Asymptotic Curve: Geodesic curvature has a vanishing value. It is generally high in the upper part and gradually low in the bottom part.

Geodesic Curve: It has zero Geodesic cur vature k g.

Geodesic torsion t g

Asymptotic Curve: have the highest on the top and lowest on the bottom.

Geodesic Curve: The Geodesic curve is the principle curvature, it has a vanishing geo desic torsion — there is no twisting of it.

Typical Joint

Structural Strategy

Typical Support

propose two rein

of

(Fig.7),

use

decided

rela tionships of

lamellas to support the glass

connection

design aims to fix the bent glass on

structure.

foundations for reference.

is casting a fixed square concrete

and the other is pouring con crete into the triangular gap of the steel lamella. It would be shown in the physical model.

In the initial design, we igno red the impact of the wood density on the model. We first tested it with eight strips of wood, which failed (Fig.11 A). The strips were too thin to form. Later, after encrypting twice as many pieces of wood, the final shape (Fig.11 C).

COMPARATIVE MODELLING

Fig. 14: Physical Prototype Front View

As can be seen from the front view, the overall shape is quite different. The digital model is relatively extended and low, but the physical model is relatively straight and tall, much higher than the digital model. The main rea sons may be: the thickness of the wood used, currently 1.5mm thick and 2cm wide. The wide width and thickness do not allow it to bend well. The second point is that since there is no repeated comparison between the two sides in the model making, fishing line winding is also used to facilitate the production, which increases the error.

Fig. 15: Digital Prototype

View

As can be seen from the top, the final circle of the phy sical model is larger than the diameter of the digital model, and the center of the circle is not aligned. This is due to the lack of proper frame fixation. In addition, the digital model wood has a greater amount of dis tortion, which is difficult to achieve in physical models, especially when the distortion is greatest at the top.

Fig. 16: Physical Prototype Front View

Fig. 17: Digital Prototype

View

For iteration two, we tried to fix the mistakes and redu ced the deviation between the digital model and the phy sical model. The design attempted to adopt a more extended shape. This time we paid more attention to the foundation and the opening. We trimmed the bottom strips in the digi tal model to form four corners for the foundation, which increased the con tact area with the ground. Besides, we repeatedly compa red the model with the digital model to reduce errors.

MODELLING

Fig. 19: Physical Prototype Front View

In the process of modeling, it was found that the upper part of the lamellas had a larger twist compared to those on the bottom, causing some lamellas to fracture. The factors that affect twists might be the bending ability of the material and the width of lamellas. So as you can see the final model is far wider than the digital model.

Fig. 20: Digital Prototype

View

When determining the final shape, we fixed the whole shape with the help of three transparent wires, applying an addi tional force to make it fit the original shape most likely. But unfortunately, because the twist ability of the material is not satisfactory, the final result is still very different from the digital model. In particular, the top shape was twice as long in diameter as the digital model. Maybe reducing the width of lamella can solve this problem, but it may sacrifice some stiffness, whether this is feasible remains to be tested.

Fig. 21: Physical Prototype Front View

Fig. 22: Digital Prototype

View

Architectural Concept

The

of the building is derived from the shape of the

the gradually shrinking roof can finally become a

the whole structure has a sense of wrapping.

Function

be used

while the smaller-scale structure is a landscape

vilion where plants can be planted.

Construction

The materials needed to build this struc ture are steel and glass, all of which can be prefabricated at the factory. As long as the size of the pavilion is deter mined, the same width of steel plates can be used to build pavilions of different scales, which is very flexible and variable. Initially, the two directions of the steel plates can be intersected on the ground and then formed at a specific angle when

it is almost finished. Workers can use scaf folding to form the intersected plates to a certain angle.

Process

Firstly, the concrete foundation is poured on the ground, then the most important few steel plates are installed. And the joints where the plates meet are fixed together with specific pins. When all the plates are finished the glass can be installed. The glass is interconnected with prefabricated steel I-beams, and each piece is intercon nected with the other.

The structure of the steel plates supports the glass, and the glass is built to reinforce the steel plates in turn. Finally, the whole structure will be very strong and stable.

Summary

Our study focuses on the rotational surface and explores how to build a structure consisting of multiple rectangu lar plates with the same width and another layer attached. Making the procedure of prefabrication as simple as pos sible and simplifying the diversity of glass panels is our goal. And what is more encouraging is that we finally get the way to do it, and this construction method has a great potential to build a 1:1 model in the field and test the stabi lity of the structure.

The exploration of the asymptotic curve was full of twists and turns. However, this is only the beginning of the research, and there is still much to explore about the structure and its applications. For example, how would the structure behave if different materials were used, iron sheet or cast concrete? For example, how does the struc ture behave if two or more layers are applied? All in all, it‘s worth looking forward to.

Bibliography

[1] E. Schling, D. Hitrec and R. Barthel, 2017: Designing grid structures using asymptotic curve networks. In: Design Modelling Symposium, Paris, In press: Sprin gerVerlag

[2] E. Schling, R. Barthel, 2017: Experimental studies on the construction of doubly curved structures. In: DETAILstructure 01/17, Munich, Institut für Internatio nale Architektur-Dokumentation, pp. 52-56

List of Figures

1 Therapiezentrum »Solemar« in Bad Dürrheim. https:// www.db-bauzeitung.de/150-jahre-db/therapiezentrumsolemarin-bad-duerrheim/#slider-intro-2

2 Drawing by Author

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