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involvement in the fi elds of renovation and conservation.

Physical scale modelling attempts to cross this divide between full-scale behaviour and the laboratory experimentation. Using abstractions of scale and material, physical models try to reproduce, on a reduced scale, the physical phenomenon observed in real structures.

For the purpose of this paper, physical models are categorised as conceptual models, form-fi nding models and experimental scale models. Conceptual models are qualitative models used in the early stages of design to explore structural design ideas; form-fi nding models are designed to generate the shape of the structure using predefi ned load and support boundary conditions; and experimental scale models are those built specifi cally to provide quantitative data on specifi c aspects of structural behaviour. There are, arguably, further categories of physical models, including photoelastic models and pilot-scale models, but these are beyond the scope of this paper. It should be noted that these categories are defi ned in terms of their structural purpose, but in addition all forms of models inform the design process due to their visual impact.

Physical models in the 20th century: overviewConceptual models

The use of conceptual models is less well documented than other types of models; this is not surprising given their nature as a fi rst approximation to the design problem. Nonetheless, there are interesting examples of how conceptual models have been used at the inception of some complex projects.

Eduardo Torroja used a simple card model¹ to develop an initial understanding of the behaviour of the El Frontón Recoletos roof (Figure 1a). The cardboard model was attached to timber end-pieces representing the concrete transverse walls at either end. Simple testing on the model gave Torroja an insight into how well the intersecting barrel vaults behaved as a longitudinal beam spanning between the end-walls. He also eventually developed an experimental scale model for quantitative testing (Figure 1b) as a means of verifying the analytical results obtained during the detailed design.

Heinz Isler is known to have employed ice models to test some of his preliminary concepts, and he even used local Emmental cheese to model concrete shells² (Figure 2a). Both materials – cheese and concrete – undergo elastic behaviour under reasonable

A case for physical models

Introduction Physical data on the behaviour of structures is collected on a number of levels. At the most elementary level, sample and component test results provide the basis of our understanding of material behaviour. Laboratory experimentation – mostly undertaken by academic researchers – has traditionally provided the majority of this data. The results obtained are the backbone of the mathematical idealisations of stress, strain and local failure mechanisms that are used in analysis.

At the full-scale level experiments and load tests, complemented by a wealth of observations, provide data about movements, tears, cracks and instabilities in built projects. This data comes from a limited number of full-scale laboratory experiments, but mostly from the practising engineer’s active monitoring during the construction of complex structures, and also from

Dancho AzagraMEng(Hons), CEng, MIStructE

Tom Hay MIStructE

Synopsis

This paper discusses the relevance of physical models in the contemporary design of building structures. It starts with a brief overview of the use of physical models in the last 100 years, followed by a description of some recent projects where physical scale modelling played an active role in the design development. The examples are used to illustrate various categories of physical models: namely conceptual models; form-fi nding models and experimental scale models, and to analyse the limitations of physical models in contrast to digital tools. Ultimately, physical models are presented as a tool to be used in conjunction with and alongside the computer.

W Figure 1aInternal view of Recoletos roof (image courtesy of Archivo Torroja, CEHOPU-CEDEX)

E Figure 1bExperimental scale model (image courtesy of Archivo Torroja, CEHOPU-CEDEX)

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establish equilibrium forms at various stages of the construction process.

More recently, the use of experimental scale models in linear-elastic structural analysis has been somewhat diminished by the use of computational techniques. But in other areas of structural analysis, notably non-linear material behaviour (including ‘micro concrete’ – i.e. scale reinforced concrete – and timber), dynamics and complex loading, experimental scale modelling has maintained an important role. The Institution of Structural Engineers’ Study Group ‘Model Analysis as a Design Tool’ has in recent years been an active forum for developments in this sphere of structural engineering, including areas beyond the scope of this paper.

Form-fi nding models

Heinz Isler and the Institute of Lightweight structures in Stuttgart led by Frei Otto can be seen as the major proponents of a diff erent tradition of structural modelling in the 20th century, namely form-fi nding models. Using hanging membranes and soap fi lm they developed techniques to accurately predict effi cient structural forms. The root of such form-active techniques can be found in Robert Hooke’s hanging chain model experiment, which defi ned the catenary form7. The pioneering work of Antoni Gaudí is also important in this area. For the development of the church for the Colonia Güell, Gaudí constructed a three-dimensional hanging-chain model in the pursuit of a pure compression form, a design process that took him and his collaborators several years (Figure 3a). The branching parabolic columns and the vaults of La Sagrada Familia (Figure 3b) were developed by Gaudí following the understanding he gained from the Colonia Güell model.

N Figure 2aIsler shell, Norwich (image courtesy of Prof. John Chilton)

E Figure 2bExample of form-fi nding model (image courtesy of Prof. John Chilton)

N Figure 3aFrei Otto’s reconstruction of Gaudi's funicular model of Colonia Güell

N Figure 3bBranching columns and hyperbolic-paraboloid vaults: La Sagrada Familia

compressive loads whilst having very low tensile capacity; this enabled Isler to spot areas where cracking was likely to occur. Later on, in order to obtain the precise geometry of the shells, he employed form-fi nding models using self-setting polyester resin on hanging membranes (Figure 2b). He also conducted load testing on scale models.

Experimental scale models

Experimental scale models owe much to Froude’s demonstration of the utility of the dimensionless constant in scaling phenomenon and Buckingham’s general rules of dimensionless analysis (Pi theorem)³. These developments opened up the possibility of obtaining quantitative results from the accurate measurement of scale models and extrapolating, using rules of similarity, to the full-scale construction. They played a crucial role during the early years of the 20th century in the development of concrete shells, through the work of Franz Dischinger and Ulrich Finsterwalder and afterwards through the work of renowned engineers such as Anton Tedesko, Eduardo Torroja and Pier Luigi Nervi4. In each case, experimental scale models were used to analyse both complex three-dimensional

forms and non-linear behavioural problems such as buckling.

In the 1970s and 1980s experimental scale modelling continued to be used for a number of dynamic and static applications including complex forms, notably the Mannheim Timber Gridshell5 and Tsim Sha Tsui Cultural Centre6 in Hong Kong. In both these projects, physical models were used in combination with computational analysis to

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Examples of recent use of structural models Conceptual models – Folkestone Academy

A set of 1:200 models (Figure 4 a-d) was used for the concept design development of the roof over the atria spaces of the Folkestone Academy in Kent. The architectural objective was to transform the interstitial spaces between the rectangular teaching wings and the cylindrical buildings into functional areas. At the time of making the models, neither the fi nal function nor the environmental conditions for the various atria were defi ned, and therefore diff erent structural typologies were modelled as a ‘brain-storming’ exercise by the design team. On the one hand, the confi guration of the cylindrical buildings around the atria seemed to off er the opportunity for daring roof solutions, while on the other, a single roof over the whole school was seen as a way to create a unifying eff ect connecting all the school buildings. Shells, grillages, arches, masts, and pulled-down membranes were among the options investigated. The basic structural behaviour of these options could be explored by gently pushing the roof and by altering the support positions.

The models were helpful to investigate complex transitions between areas of roof, and to verify the advantages of a unifi ed roof. The chosen design, following a fl at diamond grid (Figure 5a) closely resembles one of the concept models. It is interesting to note that the expressive potential of the grillage structure – something that can be easily perceived in the model – was used in the actual roof to visually connect the various atria spaces (Figure 5b).

Form-fi nding models – Weald and

Downland Museum gridshell construction

sequence model

Form-fi nding models use the physical properties of the models themselves to generate the form of the structure. In the majority of cases, a set of boundary conditions – typically the support conditions and load distribution – are used to create a unique form, representing the structural optimum for the boundary conditions chosen. The hanging-chain models used by Gaudí, the soap fi lm studies of Otto, and Isler's hanging membranes are all examples of this. However, form-fi nding models can also incorporate material properties as in the case of The Weald and Downland Museum's Gridshell construction model (Figure 6). In this instance, the technique was used to model a construction process, which generated a specifi c load-path and form for the structure, rather than to obtain an optimal form.

The purpose of the model was to examine how the three-dimensional structural

W Figure 4a-dFolkestone Academy conceptual models N Figure 4d

N Figure 4c

N Figure 4b

N Figure 4a

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"A single roof over the whole school was seen as a way to create a unifying effect"

form could be generated by lowering the structure into position from a horizontal grid, prior to the stabilisation of the overall form with diagonal bracing. This approach was diff erent from previous gridshell projects, where the strategy had been to jack up the entire structure into position. It was felt that using the natural weight of the structure to create the form would distribute the loads better than the lifting approach8. The model was constructed by Frank Jensen at the University of Bath, for which he was awarded The Structural Engineer’s Model and Full Scale Testing Award.

Following the exploration of a few test models, the fi nal 1:43 model was constructed using a wire mesh grid9. This material was found to be easily deformable and had a low in-plane shear stiff ness, which could model the scissor action of the members rotating relative to one another as the two-dimensional grid was moved into the fi nal three-dimensional form. Dimensional analysis using Buckingham’s Pi theorem indicated that the self-weight was too low, so additional weight was added by distributing nails across the surface.

The model was one of a range of analytical and form-fi nding techniques used on the project including physical modelling, numerical modelling and a prototype¹0. Although it was not possible to measure the behaviour of the model precisely, the qualitative behaviour of the form proved to be highly informative in this process. The model was useful in demonstrating the general principle of construction, and highlighted areas where discontinuities in geometry and edge conditions resulted in a form that was diffi cult to achieve by the construction process. Most importantly, the contractor was able to use the model to test out his propping sequence, prior to undertaking each incremental step of the erection process.

Experimental scale models – a tower in the

Gulf region

Experimental scale models are used for testing complex structural behaviour, verifying analytical results, or obtaining design data regarding complex loading conditions. This tends to be carried out in the latter stages of the design process, once the architectural development of the building is well advanced. However, this is not always the case, and the following example is a good illustration of the use of experimental scale models during the early stages of design development.

The project is a high-rise tower more than 400m tall in the Gulf region. The top third of the tower was designed to be an unoccupied feature (with no fl oors and access limited

to maintenance) formed by a tapered pinnacle with spire at the top. The possibility of making the building porous in the unoccupied top area was discussed early in the design as a potential way to attenuate the dynamic eff ects (in particular cross-wind excitation) expected for a building of this height.

HFFB (High-Frequency Force Balance) boundary-layer wind tunnel tests were conducted very early on to assess the wind eff ects on the structure¹¹. As is common with these type of tests, a 1:500 model of the building made of lightweight foam was used together with a stiff carbon fi bre central spine connected to the base where the

N Figure 5aFolkestone Academy roof during construction (image courtesy of Buro Happold ©Robert Greshoff )

S Figure 5bCompleted atrium space (image courtesy of Buro Happold ©Robert Greshoff )

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materials cannot be modelled with extremely plastic materials; but beyond this, there is considerable room for manoeuvre.

As conceptual models are only used to test the qualitative behaviour of the structure, checking sensitivity to geometric or support changes and quantifying the relationship between the real and the modelled material is normally not important. Nonetheless, for a complex structure made of diff erent materials, or for a mix of various structural systems, the ratio of stiff ness of the modelling materials needs to be similar to those of the real materials - otherwise some elements may inadvertently attract most of the load, grossly misrepresenting the actual behaviour. However, it should be stressed that the purpose of conceptual models is not to quantify scalable properties.

Sensitivity studies similar to those provided by the conceptual models can be carried out using simple computer models

dynamic shear forces and moments were measured. Rather than testing a perfectly defi ned geometry, three diff erent porosity confi gurations for the top third of the tower were studied (Figure 7a-c).

The fi ndings from the wind tunnel testing showed that a 25% distributed porosity would attenuate considerably the dynamics eff ects of the wind loading, allowing for the design of a much more economic structure. This was acknowledged by the design team as a considerable benefi t and became a major driver for the architectural development of the top of the tower.

Limitation of the use of physical models and assessment of alternative digital tools In order to assess the benefi t of physical models, it is important to consider the limitations of their use, and to contrast them with the possibilities provided by computational advances.

Conceptual models

Conceptual models are used early in the design process to explore structural behaviour and to evaluate diff erent options using what could be described as an intuitive process of making and testing. They are devised in such a way that they can be easily modifi ed and are reactive to gentle pushing and pulling. They are typically built from a combination of common materials such as card, string, stretchable fabric, plastic tubes, timber sticks and in some cases metal pieces¹². Although no quantitative structural or geometrical information is expected, the materials used in the models do attempt to approximate the behaviour of the four main construction materials. It is therefore important that the behaviour of the ‘scaled-down’ material is, at least in its fundamental aspects, related to that of the real material. Common sense applies here: isotropic material cannot be modelled with highly non-isotropic materials, and elastic

N Figure 6Downland Gridshell model (image courtesy of Buro Happold)

S Figure 6Downland Gridshell

S Figure 7Wind test models (1:500) showing diff erent porosity confi gurations

N Figure 7a solid

N Figure 7c 50% open

N Figure 7b 25% open

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running on standard analysis software. For example, on the tower in the Gulf project, the eff ect of the size, number, position and stiff ness of outriggers was quickly explored using a very simple model where the core, outriggers and outrigger columns were all modelled as simple sticks with specifi c values of Young's modulus and second moment of inertia. However, as many of the forms in contemporary architecture derive from sculptural shapes – and not from a catalogue of existing solutions – simplifi ed computer models are often not possible. It is the experience of the authors that computer models involving complex geometries and unclear structural systems tend to be too time consuming for the concept stage and can provide results that are diffi cult to interpret; it can be diffi cult to decouple the various ‘structural modes’ involved, in a way that can be used to propose structural improvements.

The authors note that despite the fact that we are now into the fi fth decade of the personal computer, structural engineering software remains largely within the domain of structural analysis and is little used as an intuitive design tool in the way that physical conceptual models can be. This appears surprising, considering the degree of sophistication computer games have attained over the same period. To some extent a new generation of programs such as Kangaroo (developed to be used within Rhino) or Project Vasari (developed by Autodesk as a tool for concept exploration) are now attempting to overcome this shortcoming of structural software. These programs give ‘real-time’ dynamic responses of the structures to forces, using techniques directly borrowed from computer gaming (Figure 8a). Such software developments will certainly have a place, particularly in education, but it remains to be seen how far-reaching their impact will be.

Form-fi nding models

Form-fi nding models have traditionally been used to deal with form-dependent structures: pure tension or compression systems where there is a ‘coupling’ of geometry and loads. Iterative computer calculations used to search for an equilibrium form (such as those carried out by software packages employed in the design of tensile structures) can be used instead, with the advantage of providing instantaneous information about the geometry (Figure 8b), avoiding laborious measurement techniques. Nowadays, it is diffi cult to think of many situations where a physical model would present an advantage over a digital form-fi nding process, except in the case of models that are materially dependent and have more complex boundary conditions, as in the case of the Weald and Downland Museum Gridshell construction sequence model.

Experimental scale models

Experimental scale models are specifi cally built to extract quantitative structural information in terms of reactions, displacements, accelerations, pressures or stresses. These models are ‘deductive’, in that they require the application of a pre-established set of verifi cation techniques in a methodical way. Adequate calibration of the instrumentation, dimensional analysis, and clear laboratory procedures are key to these types of models. Torroja´s model of the Recoletos roof (Fig. 1b) and the wind tunnel models used for the Gulf region tower (Fig. 7a-c) are examples of this.

Experimental scale models tend to be expensive and complicated to build, as geometric accuracy is important, and precise instrumentation necessary. In addition, a number of completely diff erent models of the same structure will typically be required to check various issues such

as strength, stiff ness or dynamic behaviour. For example, HFFB models are employed to obtain base moments and shears; pressure models (equipped with multiple pressure taps) measure wind loading along the height of the building, and complex aero-elastic models study the eff ects of fl uid-structure interaction. As a result, for problems where equivalent computational analysis has been calibrated and verifi ed, the use of experimental scale models has been superseded; in time this may well include all but the most novel problems that currently require wind tunnel testing. However, in areas of research with a high degree of innovation, experimental models are likely to remain a powerful tool.

Conclusion The case studies presented in this paper give a brief overview of some of the possibilities created by physical models in the design of building structures. In each case, the use of the physical model as a tool was complemented by computational techniques and provided an additional dimension to understanding the complex challenges of the problems being considered. Arguably, although there are specifi c areas of innovation in which experimental scale models can be essential for progressing the design, the role of physical models is in general that of an additional tool – but one that signifi cantly extends the horizon of the structural engineer’s thinking.

Design thrives on a complex mix of tools and this is perhaps best illustrated with historical examples. As can be seen in Table 1, Torroja, Isler and Gaudí all designed using the full range of mathematical and physical modelling tools at their disposal. The authors would argue that this was a major contributing factor in their success as innovators.

N Figure 8aDynamic response of a structure (image courtesy of Daniel Piker)

S Figure 8Computer simulations using Kangaroo

N Figure 8bForm-fi nding of catenary structures (image courtesy of Daniel Piker)

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References

E 1 Addis, B.: (2007) Building: 3000 years of Design Engineering

and Construction, London, Phaidon Press Ltd, p. 484

E 2 Chilton, J.: (2000) The Engineer’s Contribution to

Contemporary Architecture – Heinz Isler, London, Thomas

Telford Ltd, pp. 35-47

E 3 Sabins, J. M.: (1983) Structural Modelling and Experimental

Techniques, London, Prentice Hall Inc.

E 4 Addis, B.: (2007) Building: 3000 years of Design Engineering

and Construction, London, Phaidon Press Ltd, pp. 480-499

E 5 Happold, E., Liddell, W. I.: (1975) ‘Timber lattice roof for the

Mannheim for the Bundesgartenschau’, The Structural

Engineer, 53/3, pp. 99-135

E 6 Happold, E. et al.: (1990) ‘Tsim Sha Tsui Cultural Centre’,

Proc. Inst. Civ. Eng, Part 1, 88/10, pp. 753-813

E 7 Heyman, J.: (1998) Structural Analysis: A Historical Approach,

Cambridge, Cambridge University Press, pp. 79-80

E 8 Kelly, O. et al: (2001) ‘Construction of the Downland

Gridshell’, The Structural Engineer, 79/17, pp. 25-33

E 9 Jensen, F.: (2001) Construction of the The Downland

Gridshell’, The Structural Engineer, 79/6, pp. 16-17

E 10 Harris, R. et al: (2003) ‘Design and Construction of the

Downland Gridshell’, Building Research and Information,

31/6, pp. 427-454

E 11 Cammelli, S., Azagra, D., et al.: (2010) ‘Adventures in

architectural aerodynamics’, Proc. Inst. Civ. Eng. Structures

and Buildings, 163/2, pp. 119–127

E 12 Hilson, B.: (1993) Basic structural behavior. Understanding

structures from models, London, Thomas Telford Ltd

Table 1: Comparison of modelling tools used by Torroja, Isler and Gaudí

Conceptualmodels

Form-fi ndingmodels

AnalysisExperimental models and prototypes

Post-constructionmeasurements

Recoletos shell roof by Eduardo

Torroja (Fig. 1)

Simple card model of the roof with

supporting end walls made of timber

pieces

None

Analytical calculations following methods developed

for thin shells by Dischinger and Finsterwalder

1:25 test model to measure defl ections and compare them

with analytical calculations.

On other Torroja structures, 1:1 prototypes of

components were built and tested

Measurement of the real defl ection of the completed work to compare them with analytical and test

model results. Structural

investigation of the damage caused by a

bomb impact

Shells by Heinz Isler

(Fig. 2)

Experiments with ice, simple hanging

membranes and Emmental cheese

Accurate measurement of self-setting polyester resin

models generated by hanging membranes soaked in liquid resin

Simple calculations to check concrete stresses on typical

locations, more detailed calculation of the stresses at

support points

Typically load testing of 1:50 scale models

to determine the buckling behaviour. In some cases large

models up to 1:10 were constructed

and tested

Lifetime monitoring of the deformation of

the shells. Measurements

during a programmed demolition of one of

the shells

Vaults, and columns of La Sagrada

Familia by Antoni Gaudí (Fig. 3)

Plaster, fabric and wire models

No overall form-fi nding model made

for La Sagrada Familia, but funicular

model built for the Colonia Güell church (a scaled-

down version of La Sagrada Familia)

Analytical study using static

calculations to fi nd equilibrium of resultant forces

Vaults in the crypt of the Colonia Güell

church built as prototype for the larger ones in La Sagrada Familia.

Compressive testing of columns using hydraulic press

Ongoing monitoring of the built structure as works develop on

the central towers

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