MACLEOD statically determinate frame structures graphical methods were in use. For statically indeterminate structures new methods came in: for example Richard Southwell’s relaxation

106 Centenary Issue 21 July 2008 The Institution of Structural Engineers

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MacLeod:Layout 1 10/7/08 13:01 Page 106

The Institution of Structural Engineers Centenary Issue 21 July 2008 107

Opposite: Finite element model (Photos: the Halcrow Group and the Environment Agency) / Fig 1. The Galilei Problem Fig 2. Front page for the 1st Edition of Navier’s Leçons

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DefinitionsFor the purposes of this paper I use the following definitions:Structural mechanics – the mathematical logic and proceduresused both for structural analysis and for technical design.Structural mechanics is therefore the basis for the main calcu-lations used in structural design.Structural analysis – the use of structural mechanics to predictthe behaviour of structures under load.Technical design – the use of design rules, which are mainlybased on structural mechanics and set out in code of practiceprovisions, to assess the adequacy of structural members andcomponents.

The dawn of structural mechanicsTo understand the historical context of structural mechanicsone needs to go back three centuries before the Institution ofStructural Engineers was founded. In 1638 Galileo published anattempt to predict the strength of a cantilever beam. To illustratehis ideas1 he used the charming picture in Fig 1 of a cantileverbeam set in to an overgrown and unstable looking wall.Unfortunately the integrity of his theory was of a similar stan-dard to that of his wall. But this was the first lightening of thesky to herald the coming dawn of structural mechanics. Theprediction of the strength of a beam became known as ‘TheGalilei Problem’. During the next 200 years the great appliedmathematicians of Europe worked on the theory of bending

The ascent ofstructural mechanics

Iain A. MacLeodPhD, BSc(Eng), CEng,FIStructE, FICE

Keywords: History, Structuralmechanics, Innovations, Computers, Structural analysis

© Iain A. MacLeod

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and related topics. By the early 1800s many pieces of the structural mechanicsjigsaw of ideas had been developed. There was a unique opportunity for someoneto collect the prize for putting them together.

I wonder if the students at L’École des Ponts et Chaussées in Paris in the 1820sknew that the ideas that their Professor, Louis Navier, was propounding repre-sented a nascent revolution in engineering practice? The published version ofthese lectures as the Leçons2 not only described a range of techniques for struc-tural analysis, including the theory of bending as is extensively used today, butalso proposed techniques for technical design to provide a comprehensiveapproach to the use of calculations in the design of structures. The publication ofthe Leçons, Fig 2, represents the full dawn of structural mechanics.

Prior to Navier, the design of structural systems was based on rules of thumb,ad hoc testing, trained intuition and craft knowledge (passed on from master topupil). Because engineers did not have tools to predict behaviour, the incidenceof failure of bridges for example, was very high. The risk involved in structuraldesign reduced significantly when Navier’s methods started to be used.

Navier’s methods were not of course immediately adopted by the engineeringprofession. While many people are keen to promote change there is always a corewho resist the change, the core often being in the majority. I expect that Navier’sformulaic methods were initially viewed as too radical and that their use woulddestroy the basic ‘feel’ that engineers had for structural behaviour. The first Englishtext which presented Navier’s methods was by Moseley3 in 1843. This book wasused around 1850 to apply structural mechanics to the design of RobertStephenson’s Britannia Bridge but it appears that this had by no means becomenormal practice at that time. Charlton4 was of the opinion that the influence ofMoseley and others ‘does not seem to have been sufficient to achieve an endur-ing unity between theory and practice such as that which was typified in theBritannia Bridge’. The enduring unity was slow to develop.

The early years of the InstitutionBy 1908 structural mechanics had become widely used in structural design: the‘enduring unity’ was becoming a reality. It had been used not only for conven-tional structural engineering but also in the design of machinery and ships andwas soon to find major use in aircraft engineering.

Methods for solving indeterminate structures had been developed but thescope of what could be done was limited by severe difficulties in doing the calcu-lations. Without electronic computers, the analysis of even a small indeterminateframe required massive human computational effort. Neville Shute, who prior tobecoming a very successful author was a very successful aeronautical engineer,described in his autobiography Slide Rule 5 how he was responsible in the 1920sfor the calculations for the analysis of the airship R100. It would take his team 4weeks to achieve a solution for just one structural frame with seven unknowns.

Sometimes after a week of slogging through the calculations they would find anerror and have to go back to the beginning. Only for safety critical structures couldsuch effort be justified. The result was that structural forms tended to be severelyconstrained by the ability to analyse them.

For statically determinate frame structures graphical methods were in use. Forstatically indeterminate structures new methods came in: for example RichardSouthwell’s relaxation process6 was used for continuum systems and the HardyCross method of moment distribution7 (also a type of relaxation process) was usedfor unbraced moment connected frames. A large number of techniques for obtain-ing solutions to structural problems were in use in the first half of the 20thcentury – for example the flexibility method, the conjugate beam, the threemoment equations and the moment area method. Very little, if any, use is nowmade of such techniques.

National codes of practice, which deal mainly with technical design, weredeveloped in the 20th Century (BS 449 for steel buildings was introduced in 1932and CP 114 for concrete buildings in 1948). That structural mechanics has becomecodified is evidence of an ‘enduring unity’ between theory and practice, althoughas Table 1 indicates, the existence of codes of practice is still viewed by some withmisgivings.

Milestones

PlasticityNavier’s method of assessing strength using limiting elastic stresses became thestandard approach for over a century. This approach, though conservative, doesnot provide an estimate of strength of a structural member except in the case ofbrittle materials. To estimate the strength of a steel beam for example it is neces-sary to take plastic behaviour into account. According to Heyman8 it wasRobertson and Cook9 in 1913 who first showed how to estimate the strength ofa beam taking account of plasticity. Work on the plastic design of frames wascarried out at Cambridge University10 leading to a reappraisal of how the strengthof such structures should be estimated. This formed a major contribution to theintroduction in the 1970s of the ‘limit state’ approach to structural design (e.g.BS 5950 for steel and CP 8110 for concrete). Adoption of the limit state conceptis an important milestone in the use of structural mechanics.

Soil mechanicsKarl Terzhagi’s book on soil mechanics11 has a similar status to Navier’s Leçonsas a single author text representing the dawn of the application of mechanics ingeotechnical engineering. From the 1950s onwards, soil mechanics developed asa taught subject in civil/structural engineering courses becoming a standardsubject by the 1970s.

Table 1: Effect of innovations

Innovation Advantages Reservations

Introduction ofstructural

mechanics,(Navier 1826)

Structures can now bedesigned much moresafely. Risk of failuresignificantly reduced.

New structural forms canbe more easily introduced.

Engineers tend toconcentrate on systemsto which the mechanics

can be applied.Innovation is stifled.

Intuition less exercised.

Introduction ofnational

structuralcodes ofpractice

Experience fromsuccessful designs is

made available. Risk offailure is significantly

reduced.

Engineers tend toconcentrate on

structures to which thecodes apply. Innovation

is stifled.

Use ofcomputers to

do thestructuralmechanicscalculations

Calculations can be donemore quickly and moreaccurately. The scope of

structural analysisbecomes much wider.

Potential for moreinnovative structures is

opened up.

Users of software canfeed in data and use theresults with little or no

control over theprocess. Potential for

concomitant failures isintroduced.

Table 2: Software and hardware developments for structuralanalysis

FeatureContext

Early (1960s) Modern (2008)

Cost of computersand hencecomputer

time

Expensive for complexmodels.

Entry level PCs are now cheap andare more powerful than the supercomputers of 25 years ago. Costof computer time is no longer an

issue.

Scope of softwareRelatively limited scope oftypes of model; non-linearmodels only for specialist

use.

Wide range of elements and non-linear features available as

standard.

Input to packagesVia data and command files.

Limited provisions to automatically generate data.

Via graphical user interfaces.Extensive data generation facilities

normally available.



Fig 3. Surge barrier at Hull a) View of barrier b) Finite element model (Photos: the Halcrow Group and the Environment Agency)

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The dawn of the computer era Electronic digital computers started to be available in the UK in the late 1940s.Structural analysis had been held back for over a century by the need for fast solu-tion of simultaneous equations and was therefore an ideal application for comput-ers. In 1951 R. K. Livesley wrote a computer program for structural analysis12

helped by a John Bennett of Cambridge University who had written a program tosolve a frame with two unknowns. I suspect that this was predated by work inthe aircraft industry. Aircraft design is more safety critical than conventional struc-tural engineering and resources to develop advanced structural analysis wasmore forthcoming from that direction. In any case, around this time was thedawn of the computer implementation of structural mechanics, the significanceof which is on a similar level to the publication of Navier’s book in 1826.

Traditional structural analysis was applied to skeletal frameworks, of which thedivision into separate line elements to represent members of the frame wasobvious. But such structures only form a small proportion of the total. Continuumstructures (i.e. non-skeletal) had been modelled using differential equations whichwere solved for various loading and boundary conditions by identifying a suitablesolution function often involving a series solution. These are sometimes describedas analytical solutions. They work well for simple shapes and standard conditions.For example, Navier included the solution to some plate bending problems in hisLeçons and Timoshenko with Woinowsky-Krieger13 provided a range of analyticalsolutions.

But real problems tend to inconveniently diverge from situations that can besolved by such methods. A more universal approach that could cater for complexgeometry, material properties, loading and a range of support conditions neededto found.

Finite elementsIn 1954 John Argyris14 published the first plane stress element stiffness matrix inAircraft Engineering. This was the dawn of the finite element method which wassimultaneously developed by the aircraft industry in USA15. It was introduced tocivil engineering applications by Ray Clough at the University of Berkeley inCalifornia and to the UK civil/structural engineering community in the1960s byOleg Zienciewicz16. Professor Zienciewicz was the recipient of the IStructE’s GoldMedal in 1991 for his contribution to the development of the Finite ElementMethod.

While traditional analysis of frames treated the members as discrete elements,the assumed behaviour of each element did satisfy the governing differentialequations (e.g. for bending) and whether one or 100 elements were used, thesame answer would be obtained. The fundamental idea behind the finite elementmethod (FEM) is that the elements into which the system is divided are charac-terised by mathematical functions which only satisfy the governing equationsapproximately, but by using a sufficient number of elements in the mesh, theoverall behaviour will give adequate accuracy. Such an approach is entirelydependent on computer power to provide solutions.

The FEM was initially applied to structural engineering systems – frames,plates, shells, mass structures, etc. For example Fig 3 shows the shell and beamelement model for the analysis of the surge barrier at Hull. The FEM is now usedfor a wide range of models including heat flow, fluid flow and electronic devices.

Impact of computers on structural analysisTable 2 shows how hardware and software have developed from the 1960s tothe present day. It shows that it is now much more feasible to set up, and cheaperto solve, complex analysis models than in the early days of computing. Traditionalstructural analysis can be defined as using elastic models of skeletal structureswhereas advanced structural analysis may involve: non-linear and time depend-ent material properties, non-linear geometry effects, time dependent loading,contact phenomena and complex finite elements e.g. curved shell elements.Computer solutions for traditional structural analysis models are used as standardin practice but use of advanced structural analysis is not pervasive.

Two main factors affect this situation. Firstly most structures are designed tocodes of practice obviating the need for advanced analysis. Secondly engineersare inhibited from using advanced structural analysis due to problems with thecurrent philosophy of doing calculations. This can be expressed by a hand calcu-lation principle as:

Doing the calculations by hand is an essential activity for developing under-standing of the process being used and the behaviour of the system being consid-ered.

Engineers were slow to adopt structural mechanics post 1826. The misgivingsabout the use of mechanics linger on. Indeed they now loom large in relation tocomputer processed structural analysis. Structural engineers feel that in usingcomputers, control of the process is moving away from them. The potential for this

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Fig 4. Savill Building, Windsor Great Park – an example of world-class work which would not be possible without modern structuralanalysis (Photo: Buro Happold)

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to happen is real but that it does happen is not a necessary consequence ofcomputer use. It is a matter of philosophy and attitude. The hand calculation prin-ciple is flawed. In reality, doing hand calculations is one of the less effective activ-ities in relation to process control. The modelling process set out in the Institution’sUse of Computers for Engineering Calculations publication17 provides the key tocontrolling the use of computers. A process control principle can be stated as:

‘When validation, verification and reviewing are key activities, “calculating”can be safely left to the computer’.

Most of the details of the algorithms used for structural analysis do not helpto develop understanding of structural behaviour. Consideration of the validity ofthe basic assumptions made for the models and reflective assessment of resultsare much more important activities for developing understanding than workingwith the calculation algorithms.

It is important that engineers can do hand calculations when necessary. Butfor process control a different set of knowledge is required to that needed to workdirectly with algorithms for structural analysis. However, the correspondinginformation for this is not available in conventional texts on structural analysis. Anew approach to structural analysis is needed18.

Impact of computers on technical designCalculations for code of practice provisions are commonly carried out by hand butthe process control principle also trumps the hand calculation principle in thiscontext. It is common to hear statements such as ‘Engineers quote results withtoo many significant figures. This did not happen in the slide rule era!’ or‘Engineers just take the computer results and pass them on without reflecting onthem’. These are process control issues: engineers need to be educated andtrained to deal with them.

A major current challenge in structural engineering is the implementation ofthe Eurocodes. The fundamental methodology for this should be to implement thecalculations by computer and develop a control strategy approach for using thesoftware.

Effect of major innovations in structural mechanics In Table 1 the effects of innovations in structural mechanics are analysed. Thefundamental dilemma is between reducing risk and promoting innovation. It isinteresting to note that while early use of mechanics tended to stifle innovationby limiting the use of intuition, modern structural analysis has much greaterpotential to facilitate the development of intuitive ideas.

Overall the use of structural mechanics has been spectacularly successful.Members of the Institution produce world class work. The standard of submissionsfor the Institution’s annual Structural Awards is very high – and the incidence ofstructural failures has been very low.

Structures are now being designed and built which would be impossiblewithout the tools of modern structural analysis. Spectacular structural conceptsand shapes for bridges and buildings have been successfully introduced. Forexample, the Savill Building with its timber gridshell roof structure shown in Fig 4won the IStructE’s Supreme Award for Structural Engineering Excellence in 2007.The success of structures of this type depends, in addition to the use of conven-tional analysis modelling, on the use of ‘form finding’ software to enable geomet-rical and applied mathematical techniques to be employed. Likewise there are theso-called ‘leaning buildings’ which have plan forms where the geometry changesin plan orientation with height. The design of these buildings, for example theTurning Torso Building in Malmö. Sweden (Fig 5), designed by IStructE GoldMedalist Santiago Calatrava, requires complex analysis modelling taking account,for example, of the time dependent nature of concrete deformation.

Structural mechanics in the second century of the InstitutionModern computers provide speed and accuracy in doing calculations undreamtof when the Institution was formed in 1908. By comparison even humans withthe greatest ability to do arithmetic cannot remotely rival this performance. Itseems sensible to let computers do the calculations and let structural engineersget on with tasks for which computer performance cannot match that of thehuman brain. But we are held back in this by the hand calculation principle. Thiswill be overcome by adopting the process control principle. Past experiencesuggests that it will take some time for this transformation to be complete.Features of the new approach to calculation processing will include:• The use of hand calculations will significantly decline although engineers willuse hand calculations when appropriate and will continue to be highly numerate– indeed, due to being better able to control the processes, they will be morenumerate.• The use of advanced modelling techniques will develop because engineers willhave the confidence that they are in control of the process. They will not be inhib-ited by lack of knowledge of advanced mathematics but will be able to betterassess when they can use advanced models and will know when extra expertiseis needed.• The role of the structural engineer will be more cerebral. One of the areas inwhich the human brain scores well as compared with the computer is in abilityto process deep levels of associativity in knowledge. This is a necessary attributefor effective process control.

ConclusionMeasured in terms of the degree to which it is in daily use, structural mechanicsmay be the most useful branch of applied science. By reducing the risk in struc-tural design it provided a significant contribution to the Industrial Revolution. Itsintroduction in 1826 can also be viewed as a precursor to the InformationRevolution. Now that, by using computers, we are deeply into the information erawe need a new philosophy about how we view their use to ensure that the struc-tures designed by our members are not only innovative and leading-edge, butequally reliable and fit for purpose over their working lives. And we need to cele-brate the importance of structural mechanics as a major contributor to our modernway of life.



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1. Galilei, G.: Discorsi e dimostrazioni matermatiche, Leyden, 16382. Navier, L. M. H.: Résumé de Leçons données a l’Ecole de Ponts et

Chaussées sur L’application de la Méchanique a l’Etablissement desConstructions et des Machines,1826

3. Mosely, H.: The mechanical principles of engineering and architecture,Longman, London, 1843

4. Charlton, T. M. A.: History of theory of structures in the nineteenthcentury, Cambridge University Press, ISBN 0 521 234190, 1980

5. Shute, N.: Slide Rule, ISBN 1-84232-291-5, House of Stratus, 19546. Southwell, R. V.: Relaxation methods in engineering science. A trea-

tise on approximate computation, Oxford University Press, 19407. Cross, H.: ‘Analysis of Continuous Frames by Distributing Fixed-End

Moments’, Proc. Amer. Soc. of Civ. Engrs, Paper 1793, 96, pp 919-928, 1936

8. Heyman, J.: Structural Analysis, A Historical Approach, CambridgeUniversity Press, ISBN 0 521 62249 2, 1998

9. Roberston, A. and Cook, G.: ‘Transition from elastic to plastic statein mild steel’, Proc. Roy. Soc. A, 88, 1913

10. Heyman, J., Baker, J. and Horne, M. R.: The Steel Skeleton: Vol 2:Plastic behaviour and design, Cambridge University Press, 1956

11. Terzhagi, K., Theoretical Soil Mechanics, Wiley, 194312. Livesley, R. K.: Matrix methods of structural analysis – a review of the

past 25 years, Unpublished text of a lecture given at the Universityof Strathclyde, 1979

13. Timoshenko, S. P. and Woinowsky-Krieger: Theory of Plates andShells, McGraw-Hill, 1955

14. Argyris, J. H.: ‘Energy Theorems and Structural Analysis’, AircraftEngineering, 26, pp 137-383, 1954

15. Turner, M. J.: Clough, R. W., Martin, H. C. and Topp, L. J.: ‘Stiffnessand Deflection analysis of complex structures’, J. Aero. Sci., 23, pp805-824, 1956

16. Zienciewicz, O. C. and Cheung, Y. K.: The Finite Element Method,Wiley, 1967

17. IStructE: Guidelines for the Use of Computers for EngineeringCalculations, Institution of Structural Engineers, ISBN: 0 901 297 208, 2002

18. MacLeod, I. A.: Modern Structural Analysis – Modelling Process andGuidance, Thomas Telford Ltd, ISBN 0 7277 3279 X, 2005

‘we need a new philosophy

about how we use computers...

And we need to celebrate the

importance of structural

mechanics as a major contributor

to our modern way of life.’

Fig 5. Turning Torso Building, Malmö, Sweden (©HSB Turning Torso, Photographer: Pierre Mens)

References


Documents

MACLEOD statically determinate frame structures graphical methods were in use. For statically indeterminate structures new methods came in: for example Richard Southwell’s relaxation