transparent shells - form, topology, structure; schober, hans

Hans Schober

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This book describes the design, detailing and structural engineering of filigree, double-curved and long-span glazed shells of minimal weight and ingenious details. Innovative, clear and understandable geometric prin-ciples 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. 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 para-meters, many details and node connections of con-structed 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 struc-tures. He gathered these during his time with the engineering firm schlaich bergermann und partner.

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

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 transpar-ent 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 Volk-win Marg (gmp), Rafael Vinoly, Hani Rashid (asymp-tote), David Childs (SOM), James Carpenter, I. M. Pei, Cesar Pelli, Massimiliano Fuksas, and Shigeru Ban.

9 783433 031216

ISBN 978-3-433-03121-6

TRANSPARENT SHELLSFORM TOPOLOGY STRUCTURE

6

Foreword

This book describes a specific, but beautiful, build-ing design: the glass grid shell for large-span, double-curved glazed roofs with minimal structural weight and ingenious details.Skilfully and diligently the description encompasses the whole range, from grid shells with flat quadrilat-eral 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 ap-plied 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.

Jörg SchlaichBerlin, May 2015

Preface

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 architec-ture” 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 in-novative 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 develop-ments and to lead a fulfilling professional life.

7

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 propor-tion of the book. There are now computer tools available that gener-ate grids with the desired properties on unmeshed, completely freeform surfaces, thus producing homo-geneous structures. Whilst this would be impossible without this software, I do believe that simple, under-standable 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 “justi-fied” 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.”

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 al-ways accompanied in shells by shape optimization. Hiroki Tamai and Daniel Gebreiter illustrate various methods, some still under development, that demon-strate, among other things, the importance of coop-eration 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].

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 regard-ing geometry, structure and node formation. As publi-cations exist for most of the projects, the relevant refer-ence has been included for each in place of a detailed project description.

The book concludes with the chapter on Holistic De-sign, which is understood to be a complex interaction between geometry, topology and structural calcula-tions in order to achieve specified optimization tar-gets 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 en-couraged to design aesthetic, efficient, and lightweight shell structures and thus to contribute to the “Bauku-ltur” (building culture).

Hans SchoberStuttgart, May 2015

4

Foreword 6Preface 6Acknowledgements 8About the Author 9With the collaboration of 10

1 Introduction to shells 131.1 Designing shells 14

2 History 192.1 Historical examples 20

3 Design principle of grid shells 313.1 Development of the design principle 323.2 Construction of the grid shells in Neckarsulm 40 and in Hamburg

4 Graphic design principles for grid shells with flat quadrilateral meshes 494.1 Graphic design principles for translational surfaces 514.2 The barrel vault as simplest translational surface 534.2.1 Optimum section curve 554.2.2 Bracing of barrel vaults 564.2.3 The barrel-vault according to the Zollinger construction method 634.3 Surface of revolution 644.3.1 Array of surfaces of revolution 674.3.2 One-dimensional scaling and rotation 704.4 Domes as translational surfaces 724.4.1 Optimum rise of domes 734.4.2 Examples on dome-like translational surfaces 744.4.3 Arrayed translational surfaces 794.5 Hyperbolic paraboloid with flat quadrilateral meshes 804.5.1 On the load bearing behaviour of hypar-shells with straight edges 824.5.2 The hypar as translational surface with flat quads 844.5.3 The hypar as ruled surface with flat quadrangles 874.5.4 Equation of the hypar at given 4 straight edges 914.5.5 Cut-outs from the hypar surface along the generating lines 944.5.6 Array of hypar surfaces 1014.5.7 Rain water drainage of ‘flat’ surfaces 1124.6 ‘Skew’ translation 1134.7 Graphic design principle for scale-trans surfaces 1224.7.1 Scaling of spatial curves 122

5

4.7.2 Scale-trans surfaces 1244.8 Lamella surfaces with flat quadrangular meshes 1324.8.1 The regular lamella surface 1354.8.2 Cut-outs from lamella surfaces 1364.9 Scaling of double-curved surfaces with flat quadrangular meshes 1374.10 Application for spatial sheet metal constructions 1404.11 Application for formwork in concrete construction 142

5 Free formed grid shells 1475.1 Grid shells with flat quadrangular meshes based on free-forms 1495.2 Grid shells with warped quadrangular meshes 150 5.3 Combination of flat quadrangular and triangular meshes 154

6 Form-finding and optimisation of grid shells 1616.1 Form-finding on the inverted hanging model 1636.2 Form-finding with membrane elements 1656.3 Form-finding based on dynamic relaxation and the force density method 1686.4 Holistic ‘form-finding’ using shape optimisation 175

7 On the structural design of grid shells 1857.1 Structural analysis of glazing 1867.2 Analysis of the structure 186

8 Built examples 1898.1 List of glazed shells 1908.2 Node connections 2088.2.1 Introduction 2088.2.2 Bolted nodes 2148.2.3 Welded nodes 229

9 Holistic design – developments and outlook 239

Bibliography 250 Bibliography on projects 251 List of projects 252 Picture credits 254 Imprint 256

134

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 ex-ample, the generated lamella plane is homogeneous, as shown in Fig. 4.92. Different angles were selected between the lines through apex.

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.

y

x

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

1354 Graphic design principles for grid shells with flat quadrilateral meshes

4.8.1 The regular lamella surfaceIf the lines through apex are placed on a straight circu-lar 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 ∝ = 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

(44)

zi = i ⋅ s ⋅ sin(∝)

All other loops are obtained by rotation and mirroring.

Finding:A lamella surface with flat quadrangular meshes can easily be designed by using n lines through apex (vectors) of arbitrary lengths and inclina-tions, which intersect in one point, then combin-ing 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 con-

trols 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.

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

136

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

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

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.


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 scal-ing 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.

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

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.

4.9 Scaling of double-curved surfaces with flat quadrangular meshes

138

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 sur-face 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).

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

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

ground plan

elevation

1Dy 1Dz 1Dx

z

x

2Dxy 2Dxz 3Dxyz Initial surface

1Dy 1Dz 1Dx 2Dxy 2Dxz 3Dxyz Initial surface

y

x

140

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.

4.10 Application for spatial sheet metal constructionsThe 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 gird-ers, and gutters of free-formed roofs.

a) Scaling of discrete spatial curvesCentric scaling of a spatial curve creates a new spa-tial 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.

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.

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 de-veloped view is slightly S-shaped. It can, however, be easily manufactured without twisting it, just by bend-ing the flat sheet along the skew longitudinal edges.


Sections perpendicular to the girder axis

unfolded flange

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

left support Centre right support

202

ProjectOverview Page

Year of Constr.

Architect Company Structure/Span Glazing Mesh sizeMember length

Diag. cablesNode type

Grid bars

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

(see [45])

1994 Studiebureau Arrow,Brussels, Belgium

Helmut Fischer, Talheim, Germany

Triangular gridmax. Span l = 20 m Rise f = 4.5 mf/l = 0.23

Insulating glazingLaminated glass 2 x 6 mmAir gap 12mmLaminated glass 2 x 4 mm

Triangular mesh1.50 –1.60 m

Node type 4bolted

40 × 60 mmSolid profiles

29)House for HippopotamusBerlin Zoo, Berlin, Germany, Roof over basin

(see [7], [46])

1997 J. Gribl,Munich, Germany


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

Insulating glazingFully tempered glass 6 mmAir gap 12 mmLaminated glass 2 × 4 mm

Quadrangular mesh1.20 × 1.20 m

Diagonal cables 2 × 8 mmNode type 2built: Diagonal cables 1 × 14 mmNode type 4

60 × 40 mmSolid profilesbuilt:40 × 40 mmSolid profiles

30) DZ Bank, Pariser Platz 3,Berlin, Germany, Atrium roof

(see [7], [47], [48])

1998 F. O. Gehry,Santa Monica, USA

Josef Gartner, Gandel-fingen, Germany

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


Triangular mesh1.55 × 1.50 m to1.55 × 1.95 m

Node type 12bolted

40 × 60 mmSolid profilesStainless steel

31) Uniqa Tower Vienna,Austria, Atrium roof

(see [49])

2004 Neumann + Partner, Vienna, Austria

Mero, Würzburg, Germany

Scale-trans surface with flat quadrangular meshesSpan 24.6 mRise f = 4.5 mf/l = 0.18Cable truss distance 13 mCable truss Typ 3

Insulating glazing Quadrangular mesh 1.30 × 1.60 m

Diagonal cables 2 × 8 mmNode type 15welded


32) Messe Mailand,Italy, Roof over access route

(see [50], [51], [52])

2004 M. FuksasRome, Italy


Triangular and quadrangular grid

Single glazingLaminated glass 2 × 8 mmInsulating glazingFully tempered glass 8 mm, Air gap 16 mm, Heat-strengthened glass 2 × 6 mm

Quadrangular mesh1.80 × 1.80 mTriangular mesh1.90–2.80 m

Node type 11bolted

60 × 160 mm to 60 × 200 mm60 × 80mm to 60 × 350 mm T-sections

2038 Precedents


Year of Constr.



Grid bars

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

(see [45])

1994 Studiebureau Arrow,Brussels, Belgium


Triangular gridmax. Span l = 20 m Rise f = 4.5 mf/l = 0.23

Insulating glazingLaminated glass 2 x 6 mmAir gap 12mmLaminated glass 2 x 4 mm

Triangular mesh1.50 –1.60 m

Node type 4bolted


29)House for HippopotamusBerlin Zoo, Berlin, Germany, Roof over basin

(see [7], [46])

1997 J. Gribl,Munich, Germany


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


Quadrangular mesh1.20 × 1.20 m

Diagonal cables 2 × 8 mmNode type 2built: Diagonal cables 1 × 14 mmNode type 4

60 × 40 mmSolid profilesbuilt:40 × 40 mmSolid profiles

30) DZ Bank, Pariser Platz 3,Berlin, Germany, Atrium roof

(see [7], [47], [48])

1998 F. O. Gehry,Santa Monica, USA

Josef Gartner, Gandel-fingen, Germany

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


Triangular mesh1.55 × 1.50 m to1.55 × 1.95 m

Node type 12bolted

40 × 60 mmSolid profilesStainless steel

31) Uniqa Tower Vienna,Austria, Atrium roof

(see [49])

2004 Neumann + Partner, Vienna, Austria


Scale-trans surface with flat quadrangular meshesSpan 24.6 mRise f = 4.5 mf/l = 0.18Cable truss distance 13 mCable truss Typ 3

Insulating glazing Quadrangular mesh 1.30 × 1.60 m



32) Messe Mailand,Italy, Roof over access route

(see [50], [51], [52])

2004 M. FuksasRome, Italy


Triangular and quadrangular grid

Single glazingLaminated glass 2 × 8 mmInsulating glazingFully tempered glass 8 mm, Air gap 16 mm, Heat-strengthened glass 2 × 6 mm

Quadrangular mesh1.80 × 1.80 mTriangular mesh1.90–2.80 m

Node type 11bolted

60 × 160 mm to 60 × 200 mm60 × 80mm to 60 × 350 mm T-sections

204


Year of Constr.



Grid bars

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

(see [44])

2007 Chapman Taylor,London, UK

SH Structures LTD, North Yorkshire, UK

Dome, scale-trans surface irregular ground planSpan l = 40/60 mf/l = 0.19

Single glazing Quadrangular mesh1.50 × 1.00 m to1.50 × 1.75 m


60 × 80 mmSolid profilesexecuted: Hollow sections 80 × 120 mm, Without diagonal cables

34)Odeon Munich, Germany, Atrium roof

2007 Ackermann and Partner, Munich, Germany

Müller Offenburg GmbH, Offenburg, Germany

Triangular gridSpan l = 24/32 mRise f = 2.8 mf/l = 0.11Tie cables d = 30 mm a = 4 m

Single glazing2 × 8mm laminated glass, heat-strengthened

Triangular mesh1.90 – 2.10 m

Node type 18welded

50 × 70 mm to 50 × 90 mmSolid profiles

35)Paunsdorf Center, Leipzig, Germany Mall roof

2012 Roschmann GroupGersthofen, Germany

Barrel vault with transition areaTranslational surfaceSpan of barrel vault 13 mRise of barrel vault f = 2 mf/l = 0.15

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

Node type 16welded

Hollow sections Quadrangular mesh50 × 90 mm,diagonals 40 × 80 mm

36) Madrid Townhall,Spain, Inner courtyard roof

(see [56])

2009 ArquimaticaMadrid, Spain

Lanik,Cibeles - Dragados,Madrid, Spain

Triangular gridSpan 14/21/36/45 mRise f = 4.4– 6.2 mf/l = 0.17– 0.21

Insulating glazing Triangular mesh1.80 – 2.10 m

Node type 10bolted

80 × 80 mm to 80 × 120 mm Hollow sections

37)Yas Viceroy Hotel, Abu Dhabi, United Arab Emirates, building envelope

(see [53], [54])

2009 Asymptote architectureNew York, USA

Waagner-Biro, Vienna, Austria

Quadrangular mesh with mega trianglesTotal length 220 mTotal width 45 mTotal height 35 m

Single glazingLaminated glass 8 + 10 mm

Quadrangular mesh3.20 × 2.90 m to1.60 × 1.20 m

Node type 19welded

Grid100 × 250 mmHollow sectionsMega triangles200 × 500 mm

2058 Precedents


Year of Constr.



Grid bars

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

(see [44])

2007 Chapman Taylor,London, UK

SH Structures LTD, North Yorkshire, UK

Dome, scale-trans surface irregular ground planSpan l = 40/60 mf/l = 0.19



60 × 80 mmSolid profilesexecuted: Hollow sections 80 × 120 mm, Without diagonal cables

34)Odeon Munich, Germany, Atrium roof

2007 Ackermann and Partner, Munich, Germany

Müller Offenburg GmbH, Offenburg, Germany

Triangular gridSpan l = 24/32 mRise f = 2.8 mf/l = 0.11Tie cables d = 30 mm a = 4 m

Single glazing2 × 8mm laminated glass, heat-strengthened

Triangular mesh1.90 – 2.10 m

Node type 18welded

50 × 70 mm to 50 × 90 mmSolid profiles

35)Paunsdorf Center, Leipzig, Germany Mall roof

2012 Roschmann GroupGersthofen, Germany

Barrel vault with transition areaTranslational surfaceSpan of barrel vault 13 mRise of barrel vault f = 2 mf/l = 0.15

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

Node type 16welded

Hollow sections Quadrangular mesh50 × 90 mm,diagonals 40 × 80 mm

36) Madrid Townhall,Spain, Inner courtyard roof

(see [56])

2009 ArquimaticaMadrid, Spain

Lanik,Cibeles - Dragados,Madrid, Spain

Triangular gridSpan 14/21/36/45 mRise f = 4.4– 6.2 mf/l = 0.17– 0.21


Node type 10bolted

80 × 80 mm to 80 × 120 mm Hollow sections

37)Yas Viceroy Hotel, Abu Dhabi, United Arab Emirates, building envelope

(see [53], [54])

2009 Asymptote architectureNew York, USA

Waagner-Biro, Vienna, Austria

Quadrangular mesh with mega trianglesTotal length 220 mTotal width 45 mTotal height 35 m

Single glazingLaminated glass 8 + 10 mm


Node type 19welded

Grid100 × 250 mmHollow sectionsMega triangles200 × 500 mm

206


Year of Constr.



Grid bars

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

2012 Grüntuch Ernst Architekten,Berlin, Germany

Roschmann Group,Gersthofen, Germany

Triangular gridSpan 20/7.7/16 mRise f = 3.55/1.4/2.75 mf/l = 0.17/0.18/0.17


Node type 4bolted

70 x 50 mm to100 x 50 mmSolid profiles

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

2014 Sauerbruch Hutton, Berlin, Germany

Bellapart,LesPreses,Spain

Shallow dome with cable truss, scale-trans surface irregular ground planSpan l = 18/40 mLength 37mf /l = 0.065


Node type 16welded

80 × 140 mmHollow sections

Sculpture as a scale-trans surface

40) Bank of AmericaHeadquarter,Charlotte, USA

2005 James Carpenter,New York, USA

Tripyramid Structures, Westford, USA

Scale-trans surfaceLoad-bearing glassTension members in glass jointmax span 6 m

Single glazing12 mm fully tempered glass 6 mm dichroic float glass


Node type 22Aluminiumbolted

High-strength barsin glass jointø = 4.4 mm

2078 Precedents


Year of Constr.



Grid bars

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

2012 Grüntuch Ernst Architekten,Berlin, Germany

Roschmann Group,Gersthofen, Germany

Triangular gridSpan 20/7.7/16 mRise f = 3.55/1.4/2.75 mf/l = 0.17/0.18/0.17


Node type 4bolted

70 x 50 mm to100 x 50 mmSolid profiles

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

2014 Sauerbruch Hutton, Berlin, Germany

Bellapart,LesPreses,Spain

Shallow dome with cable truss, scale-trans surface irregular ground planSpan l = 18/40 mLength 37mf /l = 0.065


Node type 16welded

80 × 140 mmHollow sections

Sculpture as a scale-trans surface

40) Bank of AmericaHeadquarter,Charlotte, USA

2005 James Carpenter,New York, USA

Tripyramid Structures, Westford, USA

Scale-trans surfaceLoad-bearing glassTension members in glass jointmax span 6 m

Single glazing12 mm fully tempered glass 6 mm dichroic float glass


Node type 22Aluminiumbolted

High-strength barsin glass jointø = 4.4 mm

226

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

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 × 60 mm. The star-shaped node was cut out of thick sheet metal, and then machined on a CNC mill-ing 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

2278 Precedents

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, ar-ranged in two layers to prevent the tubes from in-tersecting. The meshes were cross-braced by high-strength 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 con-nection, and can thus react on variable mesh angles. The prefabricated tube-runs were connected by a cen-tre 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)

228

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

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 × 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 load-bearing capacity. The complicated manufacturing pro-cess is however a downside of this construction.

2298 Precedents

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 ge-ometry 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.

Solid rectangular section 40 x 60 mmFig. 8.22 Node at Bosch Areal Stuttgart (No. 10 in Table 8.1)

230

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

cable clamp cap

milled nodealternative with T-sections

2318 Precedents

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.

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

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

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

232

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

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 el-evated, a ball-shaped solid node can save the manu-facturer 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.

2338 Precedents

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 prefab-ricated in large units.

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

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