Page 1

Hans Schober

ISBN 978-3-433-03121-6

9 783433 031216

Form Topology STrucTure

Numerous examples built all over the world in close partnership with renowned architects from 1989 to 2014 offer orientation and assistance in the design of such double-curved shells. Essential design parameters, many details and node connections of constructed projects are presented and evaluated. This book draws on the author‘s contemplations and experiences, and includes his descriptions of recent developments in the field of transparent shell structures. He gathered these during his time with the engineering firm schlaich bergermann und partner.

neering at the University of Stuttgart, before joining schlaich bergermann und partner in 1982. In 1992 he became a partner at the Stuttgart headquarters, then taking over the position of managing director of the New York branch in 2005. In 2009 he then returned to Stuttgart as partner until 2013. Since then he has worked as a consultant. As a student of Jörg Schlaich he devoted his time to pedestrian and railway bridges; focusing particularly on the design of filigree transparent shells and stressed cable net facades. On various projects he worked in collaboration with a number of internationally renowned architects including, amongst others, F. O. Gehry, Meinhard von Gerkan und Volkwin Marg (gmp), Rafael Vinoly, Hani Rashid (asymptote), David Childs (SOM), James Carpenter, I. M. Pei, Cesar Pelli, Massimiliano Fuksas, and Shigeru Ban.

TransparenT shells

Innovative, clear and understandable geometric principles for the design of double-curved shell structures are explained in a practical manner. The principles are simple to apply with the use of functions now available in most CAD programs. The author demonstrates how floating and homogeneous structures can be created on these „free“ forms, particularly grid shells of planar rectangles. These are especially suitable for glazing with flat panes and offer structural, economical and architectural advantages. Examples are provided to illustrate in simple ways the latest methods of form finding calculation and holistic optimisation through the complex interaction of structure, form and topology.

Dr.-Ing. Hans Schober graduated in Structural Engi-

Hans Schober

This book describes the design, detailing and structural engineering of filigree, double-curved and long-span glazed shells of minimal weight and ingenious details.




This book describes a specific, but beautiful, building design: the glass grid shell for large-span, doublecurved glazed roofs with minimal structural weight and ingenious details. Skilfully and diligently the description encompasses the whole range, from grid shells with flat quadrilateral meshes to freeform domes and the optimization of their shape, structure and construction, supported by many examples taken from the author’s practical experience. This book is aimed mainly at structural engineers. It introduces them to a new and attractive yet challenging field with which they can approach not only architects but also clients. It therefore opens up a whole range of opportunities to structural engineers, thanks not least to the many examples featured, including one of the first applications of this design principle which was applied in the roof of Munich’s Olympic stadium in 1972. So I, who was fortunate to share an office with the author for many years and facilitate this development, can only welcome this multifaceted book with open arms and recommend it eagerly, in the certain hope that it will stimulate creative engineers to build other appealing structures using lightweight, elegant glass grid shells.

In the 1980s, technological development inspired the construction of single and double-curved glass buildings. The development of powerful computers and CAD programs, combined with CNC machines meant that geometrically complicated structures also became competitive. This led partly to a type of architecture that was unshackled, to “blob architecture” or organic, free-form architecture. Designing completely free forms requires special skills which very few designers possess, since only in the rarest cases are opulent and undisciplined “blobs” good architecture. Building design can only be called great architecture when an appealing appearance goes hand in hand with a clear functional design that is fit for its purpose. The building’s visual appearance should be seen as an integrative part of the technical development. During this period, the offices of schlaich bergermann und partner in Stuttgart developed grid shells: an innovative supporting structure that used prestressed cables to convert the supporting framework into a single-layer shell structure that is suitable for single and double-curved shapes. This book is by no means exhaustive but in it I have set down my thoughts and experience regarding the development of these transparent shells; experience gathered since that time to the present in the offices of schlaich bergermann und partner sbp. I owe a dept of gratitude to my teacher and longtime “boss” Jörg Schlaich for providing a creative, open environment in the office which made it possible for me to participate in interesting and innovative developments and to lead a fulfilling professional life.

Jörg Schlaich Berlin, May 2015


The graphic design principles for grid shells, which are simple, clear and easy to understand and can readily be applied using the currently available modules of customary CAD programs, take up a significant proportion of the book. There are now computer tools available that generate grids with the desired properties on unmeshed, completely freeform surfaces, thus producing homogeneous structures. Whilst this would be impossible without this software, I do believe that simple, understandable principles, whose basic mathematical and geometric concepts can be reconstructed and which therefore do not constitute a black box, still have their place. The mathematically based shapes are “justified” and disciplined, and mathematical relationships have their own inherent aesthetics. Rational design principles are timeless. That which is understandable is usually perceived as good or right – this applies to both the geometry and the distribution of forces. With reference to the famous statement about good theory, Jörg Schlaich said it in a nutshell: “There is nothing more practical than a transparent theory.”

So as not to exceed limits, I have used only the grid shells designed by schlaich bergermann und partner (sbp) as executed examples, and have listed them in Chapter 8 together with essential information regarding geometry, structure and node formation. As publications exist for most of the projects, the relevant reference has been included for each in place of a detailed project description. The book concludes with the chapter on Holistic Design, which is understood to be a complex interaction between geometry, topology and structural calculations in order to achieve specified optimization targets such as force-flow-oriented geometry and rod structure, weight minimization, homogeneous material utilization. etc.. This creates a delicate and effective structure with technical discipline and order that is of good quality and has excellent aesthetics; something which can only be achieved with close cooperation between architects and engineers at an early stage of design. The idea of the book is to set down the knowledge relating to transparent shell structures that has been acquired at schlaich bergermann und partner, and to make it available to interested colleagues. The author’s goal will have been achieved in full if, as a result, even just a few architects and structural engineers are encouraged to design aesthetic, efficient, and lightweight shell structures and thus to contribute to the “Baukultur” (building culture).

In Chapter 5, I confine myself to brief notes on the use of complex programs for generating (geometric) grids on free forms. The simple graphic design principles of Chapter 4 can be helpful here in determining the topology. Chapter 6 covers structural optimization which is always accompanied in shells by shape optimization. Hiroki Tamai and Daniel Gebreiter illustrate various methods, some still under development, that demonstrate, among other things, the importance of cooperation between architects and engineers during the design phase. Readers who wish to study the topic of form-finding and optimization in greater detail are also recommended to consult the book [22/1].

Hans Schober Stuttgart, May 2015


Foreword6 Preface6 Acknowledgements8 About the Author 9 With the collaboration of 10 1 1.1

Introduction to shells  Designing shells 

13 14

2 History 2.1 Historical examples 

19 20

3 3.1 3.2

31 32 40

Design principle of grid shells Development of the design principle Construction of the grid shells in Neckarsulm  and in Hamburg

4 Graphic design principles for grid shells with flat quadrilateral meshes 49 4.1 Graphic design principles for translational surfaces 51 4.2 The barrel vault as simplest translational surface 53 4.2.1 Optimum section curve 55 4.2.2 Bracing of barrel vaults 56 4.2.3 The barrel-vault according to the Zollinger construction method 63 4.3 Surface of revolution 64 4.3.1 Array of surfaces of revolution 67 4.3.2 One-dimensional scaling and rotation 70 4.4 Domes as translational surfaces 72 4.4.1 Optimum rise of domes 73 4.4.2 Examples on dome-like translational surfaces 74 4.4.3 Arrayed translational surfaces 79 4.5 Hyperbolic paraboloid with flat quadrilateral meshes 80 4.5.1 On the load bearing behaviour of hypar-shells with straight edges 82 4.5.2 The hypar as translational surface with flat quads 84 4.5.3 The hypar as ruled surface with flat quadrangles 87 4.5.4 Equation of the hypar at given 4 straight edges 91 4.5.5 Cut-outs from the hypar surface along the generating lines 94 4.5.6 Array of hypar surfaces 101 4.5.7 Rain water drainage of ‘flat’ surfaces 112 4.6 ‘Skew’ translation 113 4.7 Graphic design principle for scale-trans surfaces 122 4.7.1 Scaling of spatial curves 122


4.7.2 Scale-trans surfaces 4.8 Lamella surfaces with flat quadrangular meshes 4.8.1 The regular lamella surface 4.8.2 Cut-outs from lamella surfaces 4.9 Scaling of double-curved surfaces with flat quadrangular meshes 4.10 Application for spatial sheet metal constructions 4.11 Application for formwork in concrete construction 5 Free formed grid shells 5.1 Grid shells with flat quadrangular meshes based on free-forms 5.2 Grid shells with warped quadrangular meshes 5.3 Combination of flat quadrangular and triangular meshes

124 132 135 136 137 140 142 147 149 150 154

6 6.1 6.2 6.3 6.4

Form-finding and optimisation of grid shells Form-finding on the inverted hanging model  Form-finding with membrane elements Form-finding based on dynamic relaxation and the force density method Holistic ‘form-finding’ using shape optimisation 

161 163 165 168 175

7 7.1 7.2

On the structural design of grid shells Structural analysis of glazing Analysis of the structure

185 186 186

8 Built examples 8.1 List of glazed shells  8.2 Node connections 8.2.1 Introduction 8.2.2 Bolted nodes 8.2.3 Welded nodes

189 190 208 208 214 229



Holistic design – developments and outlook

Bibliography  Bibliography on projects List of projects Picture credits Imprint


250 251 252 254 256


y line through apex on a straight elliptical cone

Fig. 4.92  Lamella surface with flat quads, designed with 32 lines through apex on a straight elliptical cone.

To obtain regular surfaces we recommend placing the lines through apex in a regular order. If the lines through apex are positioned in a straight elliptical cone for example, the generated lamella plane is homogeneous, as shown in Fig. 4.92. Different angles were selected between the lines through apex.

If the design is based on an oblique elliptical cone, the result shows a skew surface in the elevation.


4.8.1 The regular lamella surface If the lines through apex are placed on a straight circular cone, and have the same angle to each other, the result is the rotation-symmetric lamella surface with flat diamonds, as shown in Fig. 4.93. A diamond is a flat quadrangle where all 4 sides are of equal length. All bars have the same length s. The key data of the lamella surface [20] are the length of the lines through apex s, their quantity n, and the length of the half-axes a and c:



(42) Consequentially for a = c

Finding: A lamella surface with flat quadrangular meshes can easily be designed by using n lines through apex (vectors) of arbitrary lengths and inclinations, which intersect in one point, then combining these vectors. If the lines through apex are positioned on a straight circular cone at the same angle, the result is a regular lamella surface. Control parameters of the shape: – the inclination of lines through apex α controls the shape (stretched/shrunk) – the bar length s and the quantity of lines through apex n controls the size of the surface – the quantity of lines through apex n controls the roughness of the surface.

∝ = 32.47°

The contour curve is defined by (43) The coordinates of the points P0 (0,0,0), P1 ... Pi ... Pn of the first loop result in 


zi = i ⋅ s ⋅ sin(∝)

All other loops are obtained by rotation and mirroring.

Fig. 4.93 (right)  Lamella surface with flat diamonds, designed with 32 lines through apex on a straight circular cone with ∝ = 32.47°

135 4 Graphic design principles for grid shells with flat quadrilateral meshes

4.8.2 Cut-outs from lamella surfaces Different forms with flat quadrangles can be obtained through cut-outs and cut-offs from the lamella surface.

Fig. 4.94 shows examples of cut-outs from the regular lamella surface. With the exception of the spandrels at the edge the surface consists of flat diamond-shapes. Vertical sections lead to oval, whilst horizontal sections lead to circular curves in the ground plan.

Fig. 4.94  Cut-outs of a regular lamella surface, all meshes are flat and equilateral.


4.9 Scaling of doublecurved surfaces with flat quadrangular meshes If a flat quadrangular surface scaled in one direction (1-D), two directions (2-D) or three directions (3-D) by the factor λ (in this image λ = 2), the result is again a flat quadrangular element. Fig. 4.95 shows 1-D scaling in x and z direction, 2-D scaling in x and z direction, and 3-D scaling. The effect of 1-D and 2-D scaling is that the scaled plane element is no longer parallel to the initial element, and its edges have different lengths and mesh angles, but the element remains flat. The effect of 3-D scaling is that the scaled element is flat and parallel to the initial element and has a (lambda square) fold surface area. All edges are scaled with (lambda) and all mesh angles remain unchanged.

These findings now enable us to transform all kinds of double-curved surfaces with flat quadrangles by arbitrary one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) scaling into a multitude of double-curved surfaces with flat quadrangles. The scale-trans-surface in Fig. 4.81 can for example be transformed by scaling into the surfaces illustrated in Fig. 4.96.

Fig. 4.95  1-D, 2-D, and 3-D scaling of a flat plane element, the scaled element is also flat.

137 4 Graphic design principles for grid shells with flat quadrilateral meshes

Fig. 4.96  Generation of a multitude of double-curved surfaces with flat quadrangles by 1-D (red), 2-D (green), and 3-D scaling (light blue) of one and the same form (black).


In another example we scale the regular lamella surface with flat diamonds (see section 4.8.1) in 1-D, 2-D and 3-D. Only 3-D scaling results in flat diamonds. All other scaling procedures transform the diamonds into flat quadrangles (Fig. 4.97).




Finding: One-dimensional (1-D), two-dimensional (2-D) and three-dimensional (3-D) scaling of a spatial surface with flat quadrangles retains flat quadrangular elements. 3-D scaling also retains the mesh angles, whilst 1-D and 2-D scaling do not.




Initial surface z x








Initial surface y x

ground plan

Fig. 4.97  Differently scaled lamella surfaces: 1Dx/1Dy/1Dz = one-dimensional scaling in x-/y-/z-direction 2Dxy/2Dxz/2Dyz = two-dimensional scaling in xy-/xz-/yz-direction 3Dxyz = three-dimensional scaling

139 4 Graphic design principles for grid shells with flat quadrilateral meshes

4.10 Application for spatial sheet metal constructions b) Example of a spatially curved gutter (Fig. 4.99) When we move the edge curve and the scaled curve in vertical direction (translation), as illustrated in Fig. 4.99, we obtain a spatial gutter consisting of flat partitions, which can then be easily assembled.

The geometric procedures explained in chapter 4 are also very suitable for creating spatially curved sheet metal constructions, since in many cases these can be discretised piecewise into flat partitions. Examples for these applications are sheet metal girders, and gutters of free-formed roofs. a) Scaling of discrete spatial curves Centric scaling of a spatial curve creates a new spatial curve with parallel transverse edges. Both curves thus enclose flat quadrangles bordered by longitudinal edges, which follow the central lines (Fig. 4.98). The spatially curved and warped sheet metal strip can therefore be gained from a flat sheet, which is bent only at the longitudinal edges.

c) Example of a sheet metal girder (Fig. 4.100) The girders of the barrel-shaped North-South roof at Berlin Main Station run askew to the glass roof. The longitudinal bars, and therefore also the upper chords of the girder follow the direction of the barrel vault. For this reason the upper chord twists a bit in reference to the girder axis (Fig. 4.100, bottom). As a result, the developed view is slightly S-shaped. It can, however, be easily manufactured without twisting it, just by bending the flat sheet along the skew longitudinal edges.

Fig. 4.98  3-D-scaling of a spatial curve creates flat quadrangles.

Fig. 4.99  Vertical translation of the scaled curve generates a three-dimensional U-shape consisting of flat quadrangles.


unfolded flange

Sections perpendicular to the girder axis

left support


right support

Fig. 4.100  The chords of the twisted girder can be assembled of flat quadrangular sheet metal elements.

141 4 Graphic design principles for grid shells with flat quadrilateral meshes

Project Overview Page

Year of Constr.


28) Flemish Council in Brussels, Belgium, Roof over assembly hall


Studiebureau Arrow, Brussels, Belgium


J. Gribl, Munich, Germany


F. O. Gehry, Santa Monica, USA


Neumann + Partner, Vienna, Austria


M. Fuksas Rome, Italy

(see [45]) 29) House for Hippopotamus Berlin Zoo, Berlin, Germany, Roof over basin (see [7], [46]) 30) DZ Bank, Pariser Platz 3, Berlin, Germany, Atrium roof

(see [7], [47], [48]) 31) Uniqa Tower Vienna, Austria, Atrium roof (see [49])

32) Messe Mailand, Italy, Roof over access route (see [50], [51], [52])





Mesh size Member length

Diag. cables Node type

Grid bars

Helmut Fischer, Talheim, Germany

Triangular grid max. Span l = 20 m Rise f = 4.5 m f/l = 0.23

Insulating glazing Laminated glass 2 x 6 mm Air gap 12mm Laminated glass 2 x 4 mm

Triangular mesh 1.50 – 1.60 m

Node type 4 bolted

40 × 60 mm Solid profiles

Helmut Fischer, Talheim, Germany

Translational surface with flat quadrangular meshes Dome 1: ø = 24 m, f = 4.95 m Dome 2: ø = 30 m, f = 6.65 m f/l = 0.22/0.20 Total length approx. 60 m

Insulating glazing Fully tempered glass 6 mm Air gap 12 mm Laminated glass 2 × 4 mm

Quadrangular mesh 1.20 × 1.20 m

Diagonal cables 2 × 8 mm Node type 2 built: Diagonal cables 1 × 14 mm Node type 4

60 × 40 mm Solid profiles built: 40 × 40 mm Solid profiles

Josef Gartner, Gandelfingen, Germany

Triangular stainless steel grid Span max. l = 20 m Distance between cable trusses 16.5 m Cable truss (sun-shaped) type 2

Insulating glazing Fully tempered glass 12 mm Air gap 14 mm Laminated glass 2 × 4 mm

Triangular mesh 1.55 × 1.50 m to 1.55 × 1.95 m

Node type 12 bolted

40 × 60 mm Solid profiles Stainless steel

Mero, Würzburg, Germany

Scale-trans surface with flat quadrangular meshes Span 24.6 m Rise f = 4.5 m f/l = 0.18 Cable truss distance 13 m Cable truss Typ 3

Insulating glazing

Quadrangular mesh 1.30 × 1.60 m

Diagonal cables 2 × 8 mm Node type 15 welded

40 × 60 mm Solid profiles

Mero, Würzburg, Germany

Triangular and quadrangular grid

Single glazing Laminated glass 2 × 8 mm Insulating glazing Fully tempered glass 8 mm, Air gap 16 mm, Heat-strengthened glass 2 × 6 mm

Quadrangular mesh 1.80 × 1.80 m Triangular mesh 1.90–2.80 m

Node type 11 bolted

60 × 160 mm to 60 × 200 mm 60 × 80 mm to 60 × 350 mm T-sections

203 8 Precedents

Project Overview Page

Year of Constr.


33) Cabot Circus Bristol, UK, Roof over pedestrian zone


Chapman Taylor, London, UK

34) Odeon Munich, Germany, Atrium roof


Ackermann and Partner, Munich, Germany

35) Paunsdorf Center, Leipzig, Germany Mall roof


36) Madrid Townhall, Spain, Inner courtyard roof


Arquimatica Madrid, Spain


Asymptote architecture New York, USA

(see [44])

(see [56])

37) Yas Viceroy Hotel, Abu Dhabi, United Arab Emirates, building envelope (see [53], [54])





Mesh size Member length

Diag. cables Node type

Grid bars

SH Structures LTD, North Yorkshire, UK

Dome, scale-trans surface irregular ground plan Span l = 40/60 m f/l = 0.19

Single glazing

Quadrangular mesh 1.50 × 1.00 m to 1.50 × 1.75 m

Diagonal cables 2 × 10 mm Node type 15 welded

60 × 80 mm Solid profiles executed: Hollow sections 80 × 120 mm, Without diagonal cables

Müller Offenburg GmbH, Offenburg, Germany

Triangular grid Span l = 24/32 m Rise f = 2.8 m f/l = 0.11 Tie cables d = 30 mm a=4m

Single glazing 2 × 8mm laminated glass, heat-strengthened

Triangular mesh 1.90 – 2.10 m

Node type 18 welded

50 × 70 mm to 50 × 90 mm Solid profiles

Roschmann Group Gersthofen, Germany

Barrel vault with transition area Translational surface Span of barrel vault 13 m Rise of barrel vault f = 2 m f/l = 0.15

Insulating glazing

Diamond-shaped flat quadrangle with diagonal rod 1.50 – 2.20 m

Node type 16 welded

Hollow sections Quadrangular mesh 50 × 90 mm, diagonals 40 × 80 mm

Lanik, Cibeles Dragados, Madrid, Spain

Triangular grid Span 14/21/36/45 m Rise f = 4.4– 6.2 m f/l = 0.17 – 0.21

Insulating glazing

Triangular mesh 1.80 – 2.10 m

Node type 10 bolted

80 × 80 mm to 80 × 120 mm Hollow sections

WaagnerBiro, Vienna, Austria

Quadrangular mesh with mega triangles Total length 220 m Total width 45 m Total height 35 m

Single glazing Laminated glass 8 + 10 mm

Quadrangular mesh 3.20 × 2.90 m to 1.60 × 1.20 m

Node type 19 welded

Grid 100 × 250 mm Hollow sections Mega triangles 200 × 500 mm

205 8 Precedents

Project Overview Page

Year of Constr.


38) Shopping Mall Höfe am Brühl, Leipzig, Germany, Mall roof


Grüntuch Ernst Architekten, Berlin, Germany

39) Roof over Plaza Plaza, Ernst & Young, Luxembourg


Sauerbruch Hutton, Berlin, Germany

Sculpture as a scale-trans surface 40) Bank of America Headquarter, Charlotte, USA



James Carpenter, New York, USA




Mesh size Member length

Diag. cables Node type

Grid bars

Roschmann Group, Gersthofen, Germany

Triangular grid Span 20/7.7/16 m Rise f = 3.55/1.4/2.75 m f/l = 0.17/0.18/0.17

Insulating glazing

Triangular mesh 1.80 – 2.10 m

Node type 4 bolted

70 x 50 mm to 100 x 50 mm Solid profiles

Bellapart, Les Preses, Spain

Shallow dome with cable truss, scale-trans surface irregular ground plan Span l = 18/40 m Length 37m f /l = 0.065

Single glazing

Quadrangular mesh 1.80 × 0.80 m to 1.80 × 1.55 m

Node type 16 welded

80 × 140 mm Hollow sections

Tripyramid Structures, Westford, USA

Scale-trans surface Load-bearing glass Tension members in glass joint max span 6 m

Single glazing 12 mm fully tempered glass 6 mm dichroic float glass

Quadrangular mesh 0.65 × 0.70 m to 0.65 × 0.45 m

Node type 22 Aluminium bolted

High-strength bars in glass joint ø = 4.4 mm

207 8 Precedents

m) Grid shell node for the DZ Bank (Pariser Platz 3), Berlin (node type 12) The triangular grid for the inner courtyard roof at Pariser Platz 3 in Berlin consists of solid stainless steel bars, 40 Ă— 60 mm. The star-shaped node was cut out of thick sheet metal, and then machined on a CNC milling machine, corresponding to the free roof shape. It therefore fits the various mesh angles, and different

articulation and rotation angles (Fig. 8.19). Hence, the straight bars with standardised forks at both ends only need trimming to the correct length. The stiffness of the bolt connection is determined by the Steiner fraction of the moment of inertia on the fork and thus requires precise drilling of the bore holes. This node type should only be manufactured by reliable and experienced companies.

Solid stainless steel cross sections 40 x 60 mm

Fig. 8.19  Star-shaped node, bolted, Pariser Platz 3 (DZ Bank), Berlin (No. 30 in Table 8.1)


n) Grid shell node for the Schubert Club Band Shell in St. Paul/Minneapolis (node type 13) The quadrangular grid for the Schubert Club Band Shell in St. Paul/Minneapolis (see also section 4.3) comprises uniaxially bent, stainless steel tubes, arranged in two layers to prevent the tubes from intersecting. The meshes were cross-braced by highstrength stainless steel rods. These are centred

between the tubes, and the fastening to the node can be re-adjusted. Both tubes are rotatable in the connection, and can thus react on variable mesh angles. The prefabricated tube-runs were connected by a centre bolt on site (Fig. 8.20). The laminated glazing is elevated.

Fig. 8.20  Node for the Schubert Club Band Shell in St. Paul/ Minneapolis (2001) Two-layered pipes, bolted (No. 24 in Table 8.1)

227 8 Precedents

o) Node for the Westfield Shopping Mall, London (node type 14) This node was developed by Seele. The star-shaped node comprises hollow sections 60 Ă— 180 mm. Individual sheet metal parts are welded together according to the 3D grid geometry. Every face of the star-shape is CNC milled, precisely vertical to

the beam axis, so that the perpendicular ends of the beams produce a perfect fit. End plates are used to connect the beams to the node by a butt joint. The end plates are joined and bolted from the inside (Fig. 8.21). This node features minimal dimensions at a high loadbearing capacity. The complicated manufacturing process is however a downside of this construction.

Fig. 8.21  Bolted node for the Westfield Shopping Mall, London


8.2.3 Welded nodes

p) Grid shell node for the Bosch Areal in Stuttgart (node type 15) The use of solid steel bars with welded nodes allows for minimising the cross sections. All bar ends are right angled. The nodes are milled according to the 3D geometry of the dome (Fig. 8.22). The elements are prefabricated in units as large as possible in the workshop, before they are transported to the construction site. The welds can compensate certain tolerances.

Fig. 8.22  Node at Bosch Areal Stuttgart (No. 10 in Table 8.1)

Solid rectangular section 40 x 60 mm

229 8 Precedents

cable clamp cap

alternative with T-sections

milled node

Fig. 8.22 (continuation)  Node at Bosch Areal Stuttgart (No. 10 in Table 8.1)


q) Grid shell node for the EKZ Paunsdorf Center, Leipzig, by Roschmann (node type 16) At the Paunsdorf Center in Leipzig the triangular grid is made of hollow sections 50 × 90 mm and 40 × 80 mm which are welded to a star-shaped node. The node was cut out of a solid block (Fig. 8.23). The structure is glazed with flat quadrangular panes. Since the diago-

nals are not subject to direct load, the height of the cross sections could be kept minimal. Fig. 8.24, shows a milled solid node with four arms and a cross-section of 80 x 148 mm with hollow sections welded to it. This node was employed in the design of the Ernst & Young Plaza in Luxemburg .

solid rectangular sections 40 x 80 mm, 50 x 90 mm

Fig. 8.23  Node for the Paunsdorf Center, Leipzig (No. 35 in Table 8.1),

Fig. 8.24 Node Ernst & Young Plaza, Luxemburg (No. 39 in Table 8.1)

231 8 Precedents

r) Ball node for the Murinsel (Mur Island) in Graz, Austria (node type 17) If the grid bars consist of tubes and the glazing is elevated, a ball-shaped solid node can save the manufacturer the expensive and time-consuming milling process.

In the case of the construction on the Murinsel Graz the trimmed tubes with perpendicular ends were simply welded directly to the ball node (Fig. 8.25). Depending on the bar angles, the spherically shaped nodes tend to get rather big. They are therefore not the best solution in terms of aesthetics.

Fig. 8.25  Node for the Murinsel, spherical shape with pipe connections


s) Grid shell node for the Odeon, Munich (node type 18) The triangular grid for the inner courtyard roof of the Odeon in Munich comprises solid stainless steel bars 50 × 70 to 90mm. The star-shaped node was cut out of thick sheet metal and machined at the ends in a way

that the straight bars can be connected in a butt joint (Fig. 8.26). The welding seam compensates tolerances, as well as rotation and articulation angles. To minimise welding on site the grid should be prefabricated in large units.

Fig. 8.26  Node of the Odeon, Munich, Solid profiles 50 × 70 to 90 mm (No. 34 in Table 8.1)

233 8 Precedents

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Transparent Shells - Form, Topology, Structure; Schober, Hans  

This book describes the design, detailing and structural engineering of filigree, double-curved and long-span glazed shells of minimal weigh...

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