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Synopsis

 This techncial note identifies the increasing importance of the use of 

3D modelling in stadium design. Two case studies are used to

identify the methods by which 3D parametric modelling can

streamline structural analysis and design. The case studies also

highlight the broadening range of skills required by engineers to

keep pace with the evolution of computational modelling and

analysis.

In the light of this, the content of university courses is evaluated

and consideration is given as to how courses may be improved to

provide a balance between traditional structural theory and

complementary computational methods.

3D modelling of stadia

Stadia are structures in which function governs the geometrical

form of the building. Successful stadium design maximises the

user’s experience by correctly defining the superstructure so that

spectators have a clear, unrestricted view of the playing surface.

 They must also be able to enter and, more importantly, leave with

speed and ease and there must be ample opportunity to use the

stadium’s facilities. Accommodating these requirements restricts

the available space for structure and services.

Increasingly, key parameters, such as sight-line quality, are

becoming standardised by sporting governing bodies. This allows

architects and engineers to create computational code which can,

for example, automatically define the shape of a stadium’s seatingbowl or create basic column grid layouts. This automated creation

of bowl structure and grid lines forms the skeleton of the full 3D

parametric model of the stadium.

Stadium structures have complex geometries and often go

through many design iterations, meaning the benefit of producing

parametric models is significant. 3D models allow the client to see

their finished investment months before construction begins.

 Architects can refine aesthetics and interface with engineers to

resolve clashes between structural, mechanical and electrical

components. The full 3D information can be used to provide

accurate cost estimates and help determine construction

programmes, improving efficiency in a competitive market. Fig 1

shows how parametric models can become a pivotal tool in the

design process.

Data extraction

3D computer models have many further advantages for structural

engineers, as shown in Fig 1. Digital information allows

optimisation of the number and type of different parts and allowsefficient CAD/CAM prefabrication of components for site, or scale

models for testing. However, perhaps the most useful property of 

the 3D data is the ability to extract pertinent parts of the structure

into finite element packages for analysis and design.

 The existence of a full stadium model makes it tempting for the

engineer to create a ‘total’ analytical model of the complete

structure. This temptation should be avoided as the resulting

overload of data makes it harder to complete simple checks and

the behaviour of individual elements can be clouded by the vast

quantities of data produced. In turn, this can lead to the

superficial checking of computer models and, ultimately, an

increased risk of error.

Instead of the ‘total model’ approach, the following case

studies show how computational methods can be used to break the structure down into simpler, smaller models. In doing this the

engineer must carefully consider the aims of the individual studies

and ensure that the 3D parametric model contains the relevant

data to complete this efficiently.

Stability modelling

Lateral stability in reinforced concrete stadia is usually provided

through the use of stability cores. Staircases, lift shafts and plant

Technical note

Use of 3D software in stadia designSam Styles and Chris Longergan of Arup discuss the need for engineers to

understand and be able to adapt 3D computer programmes used in design*

1 Flow of digital information in a project1

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risers are naturally incorporated into stadium design due to the

significant vertical transportation of spectators and services during

operation. It is therefore efficient to use these elements to provide

stability. To determine whether sufficient lateral restraint is supplied

from the stability cores, a finite element model of the structure is

generated and analysed as detailed below.

Stability model strategy

Gehry Technologies’ Digital Project parametric software was used

to model the stadium’s geometry. The core geometry is extracted

and used as the basis of a finite element analysis using Oasys

GSA, with each core modelled as a regular mesh of 2D elements

of uniform thickness. Diaphragm action within floor slabs is

modelled by rigidly constraining the cores together at each level. Appropriate lateral loads are then applied to the centre of mass of 

each floor and a linear analysis completed to determine deflection

and indicative internal forces for each core.

Extraction of geometrical Information

 To build the finite element model the 3D geometry must be distilled

into a series of one- and two-dimensional components. For cores

and shear walls the required data is the 2D plane along the centre

line of each wall. To efficiently extract this data the cores are first

defined as this central plane, as shown in Fig 2. Subsequently, the

plane is given thickness and doors and openings added to create

the full 3D feature for documentation. Modelling in this way allows

the engineer’s 2D information to drive the full 3D model.

 The process of identifying key data and how specific elementsshould be modelled is developing as the use of 3D parametrics

increases. This requires good communication and cooperation

between engineer and modeller and it is essential that engineers

have an appreciation of the methodology of the 3D modelling

process.

Meshing

 The method of creating finite element meshes from the imported

geometry will depend upon the analysis software being used. The

process used to create this particular model is a ‘semi-automatic’

meshing procedure. When the geometry is imported into GSA 

each section of core wall is initially formed as one, large element. It

is then possible to use the element editing tools within GSA to

manually refine large or ill-conditioned elements. ‘Semi-automatic’meshing gives more freedom to control element definition than fully

automatic procedures, whilst efficiently using the available

geometric data to avoid time consuming manual mesh creation.

 Analysis and results

Having completed the extraction and meshing, restraints,

constraints and loads are applied to the model and the analysis is

completed. The deflected shapes shown in Fig 3 are an example

of the output that it is possible to produce. Internal and reaction

forces can also be outputted and used to determine the size of the

cores, their walls, foundation solutions and initial estimates of 

reinforcement. Further studies of individual cores may also be

completed by evolving the meshes used to create this initial model

during detailed design stages.

Thermal modelling

In a large stadium the expansion and contraction of structural

elements due to both temperature change and shrinkage can be acritical design requirement. To determine the range of thermal

movements the effect of worst-case heating and cooling

temperature changes on the structure are modelled. These

temperature ranges include equivalent thermal loads for concrete

shrinkage, and an allowance for a range of thermal environments.

Stability cores apply restraint to floor slabs, leading to the

generation of thermal stresses. In turn the floors apply shear forces

which create bending moments within the core. To provide a safe

design, the following outputs are required from the thermal model:

– displacements and stresses in the slabs,

– forces and bending moments transmitted to the stability cores.

Thermal model strategy

2D finite-elements are used to model the slabs, allowing principaltensile and compressive forces to be identified. At scheme design

it is sufficient to check the shear forces and bending moments

within the cores as a whole, without specific knowledge of stress

distributions. The cores are therefore modelled as 1D beam

elements with appropriate section properties, rather than more

computer-intensive 2D elements.

In reality, framing action of the columns provides some restraint

against thermal movement. This effect is small and is neglected in

the thermal model, ensuring that the forces transmitted to the

cores are conservative. Neglecting the effect of columns also

allows for a simpler visualisation of how the stresses flow through

the floor slabs, which is essential for simple checks of the model’s

validity.

Extraction of geometrical information

 The thermal model requires geometric information regarding the

floor slab outline and centres of gravity and footprints of cores. The

floor slabs can be obtained directly from the Digital Project

geometry using the semi-automatic meshing procedure outlined

2 Stability core modelling process

3 Example of deflected shape output2

3

Horizontal Loads applied at centreof mass of each floor slab

West Stand stability model

800x deformation magnification

1 Core footprint

defined

2 Footprint ‘swept’

into central plane

3 Surface

thickened for 

documenta-

tion or 

extracted for 

analysis

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4 Comparison of reinforcement requirements

with and without partial movement joint

earlier, while core footprints can be exported from Digital Project

and converted into beam section properties for analysis.

 Analysis & results

GSA applies thermal loading to the 2D element floor slabs through

user defined temperature ranges. The relevant displacements and

forces within the slabs and cores are then assessed. Output plots

of displacements, stresses and required reinforcement can then be

configured. An extension of the thermal study compares different

models with various movement joint arrangements. In Fig 4 it is

shown how a central partial movement joint (allowing movement in

the circumferential direction only) greatly reduces the stresses in

the floor slabs and the moments transmitted to the cores. This has

been adopted in the stadium design.

Evaluation of the changing skills of structural engineers

In the light of the work highlighted within this technical note it is

worth considering how skills requirements of structural engineers

are evolving and how university courses can prepare young

engineers for the ongoing transition within the industry.

Whilst the benefits of 3D parametric modelling are already being

seen in practice, there is potential for further development of the

bespoke software that automatically generates column layouts and

complex geometrical shapes such as the stadium bowl. It is to be

expected that future stadium (and perhaps eventually all) projects

will be designed using this technology and undergraduate

engineers should therefore be familiar with the principles of 3D

modelling packages. As seen previously, choosing the correct modelling techniques

to create 3D geometry greatly influences the efficiency of data

extraction for ‘traditional’ engineering analysis. Without the

engineer understanding the modelling process it is difficult for

effective modelling strategies to be derived. A ‘Computer

Modelling’ module covering the options available in structural

analysis packages would be a useful asset for young engineers.

It should be noted that whilst training in 3D CAD is important for

prospective engineers, it is not a substitute for hand sketching.

Sketching enables engineers to think and understand in 3D and

this ability greatly enhances their ability to express ideas, resolve

clashes and understand how space may best be used. 3D models

are an effective visual tool which can enhance these fundamental

skills.In addition to learning CAD packages, a further useful asset for

engineers is a knowledge of computer programming. ArupSport

use languages such as Microsoft Visual Basic to write bespoke

programs and macros which enhance the functionality of their

commercial packages. Instead of treating it as a black box,

engineers should be able to adapt and improve the functionality of 

their software. It is also important that engineers learn the theory

behind finite element programs. Knowledge of the basics of finite

element modelling is an extremely useful tool for troubleshooting

and providing the engineer with confidence. It should however be

acknowledged that learning specific programs is not necessarily

relevant to under-graduate engineers. Companies choose which

packages they use for commercial reasons and so knowledge of 

methodology gives the young engineer the flexibility to work with

the many available packages.

Whilst computers are undoubtedly revolutionising the art of 

structural design, it is of paramount importance that students

understand the basics of structural theory. It is tempting to learn

how to use computers and then assume that the machine is alwayscorrect. Studying structural theory allows the engineer to intuitively

understand how structures behave and gives the engineer the

chance to critically assess their computational output through

simple ‘back of envelope’ checks. Although computer aided design

packages do exist, it is still the responsibility of the engineer to

complete the necessary designs and specify the sizes of sections,

reinforcement, and materials. Computers are merely tools used to

provide engineers with the evidence they need to complete a

reasoned, accurate and safe design.

Conclusions

 This techncial note highlights the increasing importance of 3D

parametric design in structural engineering, in particular how 3D

information can be extracted and adapted to complete analysis anddesign in stadium structures. Notably the work exhibited here

demonstrates how engineers must adapt and add to their skills to

embrace methods of electronic data management, programming

and computational analysis. To achieve this it is recommended that

the fundamentals of structural engineering taught in universities are

embellished with the addition of skills which may not be traditionally

associated with the subject.

* From a presententation to the Young Members Centenary Conference organised by the

Lancashire & Cheshire Branch at Salford University in April 2008.

Chris Lonergan graduated in 2007 with a B.A M.Eng(Hons) from Cambridge University,

having specialised in civil, structural and environmental engineering. Chris joined Arup

North West as a Graduate Structural Engineer in 2007 and has since been involved in the

design of several projects, most notably as part of the engineering team within ArupSport.

Sam Styles graduated from Imperial College, London in 2007 with a M.Eng(Hons) in civilengineering. Since 2007 Sam has been working as a Graduate Structural Engineer in Arup’s

North West office focussing on the 3D modelling and analysis of stadium superstructures.

4

Location of partial

movement joint