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The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
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Novum Structures www.novumstructures.com
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
Soeren Stephan Feng Pan Yongqjan Huang
Novum Structures USA, China, France, Germany, India, Singapore , Turkey, UAE, United Kingdom
Novum Structures www.novumstructures.com
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
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The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
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The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
1. Introduction
2. Pavilion Structure
3. Grid Shell Geometry
4. Freeform Grid Shell Node Connector 4.1. Node Connection Bending Stiffness and Capacity Tests 4.2. Numerical Calculation of Node Connection Bending Capacity 4.3. Analytical Calculation of Node Connection Stiffness 4.4. Finite Element Analysis of Node Connection
5. Structural Analysis 5.1. Global Stability Analysis
6. Fabrication and Installation
Picture: Foster + Partner
Novum Structures www.novumstructures.com
1. Introduction
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Design Architect: Foster + Partner, London, UK • Design Engineer: Halvorson & Partners, Chicago, USA • Architect & Engineer of Record: ECADI East China Architectural Design & Research Institute Co.Ltd. • General Contractor: CSCEC China Construction Industrial Equipment Installation Co. Ltd. • Contractor Freeform Structures: Novum Structures China Co. Ltd. in cooperation with
Novum Structures LLC (USA) & GmbH (Germany)
Pictures: Foster + Partner
Novum Structures www.novumstructures.com
1. Introduction
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Pavilion shape is resembling 3 sand dunes as natural formations typical for UAE deserts like the Rub Al Khali (aka “the Empty Quarter”) with distinct dune features – gradually curved windward sides, sharp ridges and almost flat leeward sides
• Height of the southern dune is 20 m, height of northern dunes is about 18 m • Pavilion has almost circular footprint with a diameter of about 65 m • After the EXPO 2010 the pavilion will be disassembled & moved to Saadiyat Island, Abu Dhabi, UAE
Picture: Foster + Partner
Novum Structures www.novumstructures.com
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
1. Introduction
2. Pavilion Structure
3. Grid Shell Geometry
4. Freeform Grid Shell Node Connector 4.1. Node Connection Bending Stiffness and Capacity Tests 4.2. Numerical Calculation of Node Connection Bending Capacity 4.3. Analytical Calculation of Node Connection Stiffness 4.4. Finite Element Analysis of Node Connection
5. Structural Analysis 5.1. Global Stability Analysis
6. Fabrication and Installation
Picture: Foster + Partner
Novum Structures www.novumstructures.com
2. Pavilion Structure
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Southern halves of dune shapes (“windward sides”) are single layer freeform grid shell structures • Northern halves of dune shape (“leeward sides”) are inclined, straight -beams (horizontally braced) • Dune shapes are subdivided and supported by a central spine structure with portal frames every 6 m • Northern dune shape is additionally supported by 2 -beams in inflection zone of grid shell • Crescent shaped canopies with “tension ring belt” edge beams & entrance wall structures are
enclosing the northern and southern buidling entrances • Dune ridges are made of curved, large diameter pipes • Pavilion structure is supported on reinforced concrete
stripe foundation
Novum Structures www.novumstructures.com
2. Pavilion Structure
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Conceptual grid shell design by Halvorson & Partners was calling for SHS profiles 200x200x6 mm • To avoid extremely large node connectors , profiles were changed to RHS 240x80x8 (steel Q345) • Grid shell members are interconnected with concealed bolted Novum FF node connectors in order
to enable the diassembly, shipment and reuse of the complete pavilion structure after the EXPO • Cladding is supported by posts, bolted to the top surface of the node connector
Novum Structures www.novumstructures.com
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
1. Introduction
2. Pavilion Structure
3. Grid Shell Geometry
4. Freeform Grid Shell Node Connector 4.1. Node Connection Bending Stiffness and Capacity Tests 4.2. Numerical Calculation of Node Connection Bending Capacity 4.3. Analytical Calculation of Node Connection Stiffness 4.4. Finite Element Analysis of Node Connection
5. Structural Analysis 5.1. Global Stability Analysis
6. Fabrication and Installation
Picture: Foster + Partner
Novum Structures www.novumstructures.com
3. Grid Shell Geometry
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• 2 basic methods to develop a grid on continuous surfaces:
Surface Grid Development
Planar Projection Method Surface Partitioning Method
• Boundary lines get subdivided into portions of similar length, thus creating “orthogonal” auxiliary grid on surface
• Final grid is tied into this auxiliary grid
• Planar grid is projected on continuous sur-face and manually improved where needed (suitable for surfaces with small curvature)
Novum Structures www.novumstructures.com
3. Grid Shell Geometry
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Grids created by those 2 methods have different specific properties:
Surface Grid Development
Planar Projection Method Surface Partitioning Method
Grid along boundaries is unproblematic Resulting grid can appear slighly more irregular, although this strongly depends on the current perspective of the viewer
Resulting grid is usually evenly spaced and balanced Planar grid projection is not considering boundary lines, thus creating problematic grid zones along boundaries
Southern dune grid created with planar projection Southern dune grid created with surface partitioning
Novum Structures www.novumstructures.com
• Final step of grid development is the identification of local coordinate systems for nodes and members based on the given grid panels: 1. normal vector of a member is the average normal vector of the 2 adjacent grid panels 2. normal vector of a node is the average normal vector of all adjacent grid panels
3. Grid Shell Geometry
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
Normal Vector Node
Normal Vector Panel
Normal Vector Member
Normal Vector Node
Normal Vector Member
Normal Vector Panel
Novum Structures www.novumstructures.com
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
1. Introduction
2. Pavilion Structure
3. Grid Shell Geometry
4. Freeform Grid Shell Node Connector 4.1. Node Connection Bending Stiffness and Capacity Tests 4.2. Numerical Calculation of Node Connection Bending Capacity 4.3. Analytical Calculation of Node Connection Stiffness 4.4. Finite Element Analysis of Node Connection
5. Structural Analysis 5.1. Global Stability Analysis
6. Fabrication and Installation
Picture: Foster + Partner
Novum Structures www.novumstructures.com
4. Freeform Grid Shell Node Connector
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Concealed bolted Novum FF node connectors, used for grid shell member connections, consist of: - 2 forged discs 200x85 mm (steel #45) with individually machined faces as required by geometry - each machined face has one threaded hole to receive a M24 or M27 bolt - precision cast steel adapters (steel GS-20Mn5V) with top & bottom hole, welded to member ends - concealed & pretensioned socket head bolts 10.9, fixing the end adapters to the 2 node discs
• The semi-rigid behaviour of these bolted node connections has to be adequately considered in the structural model - typically as a rotational spring stiffness at the end of each grid shell member
Novum Structures www.novumstructures.com
4.1. Node Connection Bending Stiffness and Capacity Tests
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• 4-point bending test (stiffness & capacity)
( )
()
Test
#
Failure
Mode
Ram Load,
at Failure
Bending Moment,
at Failure
1 Bolt 127 kN 76.8 kNm
2 Bolt 128 kN 77.4 kNm
3 Bolt 129 kN 78.0 kNm
(M24 bolts)
Novum Structures www.novumstructures.com
4.2. Numerical Calculation of Node Connection Bending Capacity
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Bending moment capacity of the node connection as a function of the axial connection force was determined using an iterative numerical calculation method assuming planarity of member end section [Space Structures 5, Telford Publ. 2002, p. 759-773]
• Calculations were performed for 3 limit state conditions: elastic, plastic capacity and failure limit
• Test results are conservatively close to the failure limit bending moment
Initial parameters: orig
it
orig
it
orig
itMzmz,Mymy,Nn,0it
Strain parameters: AE
no,
JyE
my,
JzE
mzit
itit
ity
itit
z
itit1ititit1ititit1itMzmzmz,Mymymy,Nnn
> Compression stress in the connection profile / Element force & moments
> Tensile stress in the bolts / Bolt force & moments
> Internal connection force & moments : N<it>, My<it>, Mz<it>
> Deviations from given force & moments: N<it>, My<it>, Mz<it>
All deviations 0 ? it = it + 1 Stress distribution
determined !
N
O
YE
S
(M24 bolts)
Novum Structures www.novumstructures.com
• The node connection stiffness can be determined using the measured load-displacement curves • The measured total mid span deflection is obviously a combination of flexural deformation of
the specimen and rotational deformation of the node connection:
• The flexural mid span deformation of the specimen can be calculated as follows:
• The rotational connection stiffness can be determined using a combination of the above formulas:
• The average total mid span deflection in the tests with M24 bolts was 18.5 mm at 100 kN ram load (equivalent to 60.5 kNm connection bending moment)
• The corresponding node connection stiffness is 16110 kNm/rad.
4.3. Analytical Calculation of Node Connection Stiffness
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
Rot
FlexTotalRotK
lM
2
22 4324
alEI
MFlex
22 4324
2 alEI
M
lMK
Total
Rot
- total measured mid span deflection, m - flexural mid span deformation of the specimen, m - bending moment at node connection, Nm - span, distance from support to support - rotational node connection stiffness of (Nm/rad)
Total
Flex
Ml
RotK
- modulus of elasticity of steel, N/m2 - moment of inertia of tube section, m4 - distance of load introduction point from support, m
E
I
a
Novum Structures www.novumstructures.com
4.4. Finite Element Analysis of Node Connection
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• As an additional verification of the numerical and analytical node connection parameter calculations, a finite element analysis of the test specimen was performed
• The observed mid span deflection of the FE model is only 80% of the average measured value, due to little initial settlements of the real specimen
• This ratio was then used to calibrate the FE model of the node connection used in the structural analysis
Novum Structures www.novumstructures.com
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
1. Introduction
2. Pavilion Structure
3. Grid Shell Geometry
4. Freeform Grid Shell Node Connector 4.1. Node Connection Bending Stiffness and Capacity Tests 4.2. Numerical Calculation of Node Connection Bending Capacity 4.3. Analytical Calculation of Node Connection Stiffness 4.4. Finite Element Analysis of Node Connection
5. Structural Analysis 5.1. Global Stability Analysis
6. Fabrication and Installation
Picture: Foster + Partner
Novum Structures www.novumstructures.com
5. Structural Analysis
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• The conceptual structural analysis by Halvorson & Partners had to be adopted by ECADI considering local regulations and all modifications made during the construction phase
• A major update of the structural analysis was required du to the following: - member profiles changed from SHS 200x200x6 to RHS 240x80x8 in order to minimise node size - Halvorson assumed fully rigid node connections – changed to real semi-rigid connection stiffness
• A meaningful structural model of the grid shell portions has to include all other parts of the pavilion structure as well – therefore ECADI and Novum closely coordinated their structural models and performed the analysis simultaneously (ECADI used SAP2000, Novum used Dlubal RStab)
Novum Structures www.novumstructures.com
5.1. Global Stability Analysis
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• The Chinese guideline JGJ 61-2003 “Technical Specification for Lattice Shells” requires that the ratio of the critical global buckling load to the governing service load combination is at least 4.2 (determined in a linear-elastic buckling analysis of the structure considering global imperfections)
• ECADI established in their structural analysis the governing load cases for the different grid shell portions – for the southern dune this combination was DL + WL45˚ + 0.7 LLroof + 0.7 Tincr (see below)
• The global grid shell imperfections were generated by scaling the first buckling mode to a maximum imperfection value of L/300 = 66 mm (L: span)
• The ratio of the critical buckling load to the governing service load combination was finally 4.6 for the southern dune grid shell
Novum Structures www.novumstructures.com
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
1. Introduction
2. Pavilion Structure
3. Grid Shell Geometry
4. Freeform Grid Shell Node Connector 4.1. Node Connection Bending Stiffness and Capacity Tests 4.2. Numerical Calculation of Node Connection Bending Capacity 4.3. Analytical Calculation of Node Connection Stiffness 4.4. Finite Element Analysis of Node Connection
5. Structural Analysis 5.1. Global Stability Analysis
6. Fabrication and Installation
Picture: Foster + Partner
Novum Structures www.novumstructures.com
6. Fabrication and Installation
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
• Freeform grid shell structures in general (except of small ones) cannot be drawn and fabricated using conventional methods due to time, cost, manpower and reliability constraints
• Instead, interconnected parametric component models for all parts of the members and node connections have to be developed – both in CAD and CAM software programs used
• Then instead of conventional drawings only relevant data and very few parametric drawings are needed to design and fabricate all grid shell components
Novum Structures www.novumstructures.com
6. Fabrication and Installation
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
Node component fabrication: • CNC model data
transfer & check • CNC machining
and marking • Quality control • Crating and shipment
Novum Structures www.novumstructures.com
6. Fabrication and Installation
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
Member fabrication: • Parametric drawing data
transfer & check • Length and hole cutting • Adapter welding • Painting • Crating and shipment
Novum Structures www.novumstructures.com
6. Fabrication and Installation
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
Novum Structures www.novumstructures.com
6. Fabrication and Installation
The Freeform Structure of the UAE Pavilion at the Shanghai EXPO 2010
Stabwerke auf Freiformflächen
Novum Structures USA, China, France, Germany, India, Singapore , Turkey, UAE, United Kingdom
soeren.stephan@novumstructures.com
Thank you !
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