- 731
THE ROLE OF STRUCTURAL MODELS IN THE DESIGN OF
BRITISH BRIDGES-1800 - 1870
A Thesis submitted to the University of London
for the award of the degree
of
Doctor of Philosophy
by
DENIS PATRICK SMITH
Department of History of Science and Technology
IMPERIAL COLLEGE OF SCIENCE AND TECHNOLOGY
NOVEMBER 1 9 7 6 CONTENTS
Chapter 1: INTRODUCTION 1. Bridge Design before the Railway Era. 1. Structural Models and Railway Bridge Design. 5. Theory and Practice. 7. The Source of Capital. 10. Structural Model Types. 11. The Decline of Structural Model Testing. 13.
Chapter 2: ARCH BRIDGES 19. Proposed rebuilding of London Bridge - 1801. 21. Atwood's Treatise on Arches - 1804. 31. Laminated Timber Arches. 33. W.H. Barlow's Paper on Arches 1846. 34. Model Experiments on Metal Arch Ribs. 37. Biographical Notes. 48.
Chapter 3: SUSPENSION BRIDGES 50. Proposed Suspension Bridge at Runcorn. 51. Proposed Suspension Bridge at Montrose. 57. Menai Suspension Bridge - Chain Geometry Model. 58. Wood as a Material for Suspension Chains. 59. James Dredge and the Taper Chain Controversy: 61. The Dredge and Clive Correspondence. 70. The Ballee Mal Bridge, Calcutta. Suspension Bridges and Railways: 77. P.W. Barlow's Experiments - 1857. 80. G.B. Airy's Experiments - 1867. 88. Wind Loads on Suspension Bridges. 92. Biographical Notes. 102.
Chapter 4: BEAM AND GIRDER BRIDGES 103. Wrought Iron Tubular Girders: 104. The Conway and Britannia Bridges: Experiments in London and Manchester 1845-1847. 111. Apparatus and Experimental Techniques: Fairbairn's.Preliminary Tests at Millwal1.115.
Hodgkinson's Experiments in Manchester. 116. Experiments on the Large Tube at Millwal1.118. The Role of Experiment in the Design of the Britannia Bridge. 120. Lattice Girders: Doyne and Blood's Model Warren Girder - 1851. 131. Airy's Bowstring Girder Model - 1868. 136. Web Buckling in Plate Girders. 141. Continuity in Beams and Girders: 143. The Torksey Bridge 144. Brunel's Continuity Model 148. Edwin Clark's Britannia Bridge Continuity Model. 150. W.H. Barlow's Continuity Experiments - 1858. 150. Stoney's Analytical Textbook. 151. Polarised Light and Model Structures: 152. Brewster's Model Beam Experiments - 1816. 154.
Chapter 5: INSTRUMENTATION 173. Measurement of Applied Load. 174. Measurement of Force. 174. Measurement of Deflection. 176. Measurement of Strain: 179. Joseph Colthurst - 1841. 180. W.H. Barlow's EXperiments - 1855. 182.
Chapter 6: SIMILARITY 187. Scaling Laws in the first half of the Nineteenth Century. 187. Beam Design and the Mechanic's Pocket-books: 188. Robert Brunton's 'Compendium of Mechanics'. 189. William Grier's Pocket-books. 191. The Engineer's and Contractor's Pocket-book - 1847. 194. The Technical Journals. 195. Similarity and the Britannia Bridge Experiments: 201. William Fairbairn. 202. Eaton Hodgkinson. 203. Edwin Clark. 205. Appendix: Select Bibliography. 211.
Chapter 7: CONCLUDING REMARKS. 212. ii
FIGURES
Introduction
1.1 Model bridge type - Test objective matrix. 1.2 Incidence of Structural model testing 1800 - 1870.
Arch Bridges
2.1 Analysis of 1801 Select Committee Evidence. 2.2 Atwood's Semi-circular model arch. 2.3 Atwood's Semi-circular model arch (Semi-arch rig). 2.4 Atwood's segmental model arch. 2.5 W.H. Barlow's arch models. 2.6 W.H. Barlow's arch models. 2.7 Chappe's Trent bridge model. 2.8 Chapp6's Trent bridge model - deflection measurement. 2.9 Chappe's Standish bridge model. 2.10 Chappe's Standish bridge model - load configurations. 2.11 W.H. Barlow - St. Pancras station roof model.
Suspension Bridges
3.1 Telford's pocket-book: Runcorn bridge 1814. 3.2 Telford's pocket-book - load increments on model. 3.3 Telford's link-polygonal apparatus. 3.4 Drewry - wooden link's for suspension chains. 3.5 Typical Dredge tape-chain bridge. 3.6 Clive's suspension bridge. 3.7 Clive's model suspension bridges. 3.8 W.H. Barlow - suspended wooden box girder 1857. 3.9 W.H. Barlow - suspended angle girder 1857. 3.10 W.H. Barlow - first plank girder 1857. 3.11 W.H. Barlow - second plank girder-1857. 3.12 Airy's experimental model - 1867. 3.13 Airy's experimental model - thick spline. 3.14 Airy's experimental model - thin spline.
iii
Beam and Girder Bridges
4.1 Tubular girder experiments for the Conway and Britannia Bridges: Chronology Chart. 4.2 Millwall apparatus: Preliminary experiments. 4.3 Millwall apparatus: Preliminary experiments. 4.4 Edwin Clark's diary: Experiment expenses. 4.5 Hodgkinson's Manchester apparatus. 4.6 Hodgkinson's Manchester apparatus. 4.7 Edwin Clark's diary: tube failure sketch. 4.8 Millwall apparatus: Large tube. 4.9 Edwin Clark's diary: Model calculations. 4.10 Doyne and Blood: Model Warren girder. 4.11 Doyne and Blood: Results. 4.12 Airy's model bowstring girder: 1868. 4.13 Airy's model bowstring girder: loading. 4.14 Airy's 'Monochord'. 4.15 Airy's specimen results. 4.16 Torksey Bridge: continuity model. 4.17 Brunel's continuity model. 4.18 Brunel's continuity model: Results. 4.19 Britannia Bridge continuity model (Edwin Clark). 4.20 W.H. Barlow continuous beam experiments. 4.21 W.H. Barlow continuous beam experiments - Results. 4.22 David Brewster's experiments 1816. 4.23 Kerr's and Carus-Wilson's glass beam experiments - 1891.
Instrumentation
5.1 Millwall Tubular girder experiments: Deflection measurement. 5.2 Joseph Colthurst: 1841 neutral axis experiments. 5.3 W.H. Barlow: neutral axis experiments 1855. 5.4 W.H. Barlow: neutral axis experiments 1855. 5.5 W.H. Barlow: neutral axis experiments. 5.6 W.H. Barlow: model beams.
iv
Similarity
6.1 Similarity calculations. 6.2 Similarity calculations. 6.3 Hodgkinson: Abstract of results. 6.4 Hodgkinson: Manchester experiments results. 6.5 Scale factor and limiting superimposed load relationships (Edwin Clark) - Specimen calculations. 6.6 Scale factor and limiting superimposed load curves. ACKNOWLEDGEMENTS
I am indebted to Professor A. Rupert Hall and the Department of History and Science and Technology at Imperial College for the stimulating environment which has sustained this work over six years, and in particular, to Dr. N.A.F. Smith for his constructive critical influence during the final stages of writing.
I also gratefully acknowledge the enormous debt that I owe
Lynda, Matthew, and Jenny who suffered much disruption of family life and without whose understanding and tolerance this work could not have been completed.
The staff of many libraries have been most helpful but I am particularly grateful to Mr. H. Richardson and the staff of the library of the Institution of Civil Engineers. My thanks are also due to Mr. J.G. James for the loan of Edwin Clark's personal copy of
Fairbairn's book on the Britannia and Conway Bridges, and to Mrs.
Audrey Hilson for typing this thesis.
vi SUMMARY
This thesis deals with one aspect of structural analysis and
design in nineteenth-centry Britain; namely the testing of experimental
models. The study reveals this to have been almost exclusively devoted
to elucidating problems of bridge design, and that model experimentation
activity was closely related to the demands of railway transport. These
unprecedented demands necessarily led to structural innovation in terms
of new materials and increasingly complex structural forms. This in
turn rendered accepted design techniques totally inadequate, and the
development of alternatives unavoidable. The response of the British
engineer to this challenge was characterised by his use of models.
Reasons for this are discussed together with those which explain why structural models were not used in Britain during the last three decades
of the century.
The subject is discussed by considering the problems arising from the design of the spanning elements in the three major bridge
forms; namely arch, suspension, and girder structures. In addition
chapters are devoted to the instrumentation of experiments and of similarity concepts in relating the performance of model and full-size structure.
Structural model testing was important in British bridge design between 1800 and 1870. Why was this characteristic of Britain?
Of the contributory factors the most important was certainly that it was
British engineers who first tackled the problems posed by railways and who found themselves without structural precedents. In their analytical dilemma they turned to models for reassurance and help with intractable problems, particularly in connection with large-span metal structures. vi i Another factor was the British engineer's mistrust of theory, or mathematical analysis.
From 1870 onwards there was a marked reduction in the number of bridges built in Britain, and as more of the engineer's analytical problems responded to mathematics and graphics, model testing naturally declined. In fact the technique only regained its place in the structural analysist's repertoire in the early part of this century with the development of electrical techniques of strain measurement making it
possible to investigate stress distribution in models of complex structures.
v i i i Chapter 1
INTRODUCTION INTRODUCTION
During the last two centuries civil engineering has demanded increasingly large capital expenditure and is, moreover, an undertaking in which the consequences of structural failure can be of disastrous proportions in terms of human life. The engineer's responsibility therefore for providing his client with a structure which is both safe and economic is indeed onerous. This is particularly true of bridge design where the pioneering development of railway transport in this country in the first half of the nineteenth century provided an unrivalled stimulus, and indeed necessity, for innovation. It follows that British bridge designers were the first to tackle problems arising from the unprecedented demands of load, span, and vibration produced by the steam locomotive. The response of the British engineer to this challenge was characterised by the use of experimental models to help resolve intractable analytical problems. Hence structural models played an important role in the design of British bridges between 1800 and 1870 and this thesis presents a study of the factors which led to the use of models, their relative importance in Britain, and why they were not used in the last three decades of the nineteenth century.
Bridge Design before the Railway Era
During the eighteenth century the majority of bridges were of arched form and built of stone or brick. Such structures comprised the essential load-bearing arch above which a rubble fill transmitted the road loading to the arch itself. This fill was contained between solid spandrel walls carried up to form a parapet. These bridges, of modest span, were enormously heavy compared with the traffic loading arising from the road transport of the period. The greatest threat to such structures with a high dead/live ratio was lack of stability in the 1 foundations. Bridges were commonly designed (without analysis) by
masons on an establishment of precedent basis which was perfectly
adequate in the climate of slow evolutionary development. The
empirical approach is typified in the sequence of collapse, modify,
and rebuild applied to William Edwards'bridge at Pont-y-Prydd, where the
collapse phase could perhaps be regarded as an unanticipated full-scale
test. In the earlier part of the century most bridge designs would
have been produced by the masons themselves, without charge to the
client, on the anticipated profit ensuing from the construction of the
work. But from the middle of the eighteenth century there emerged the
independent, fee-earning, civil engineer rather as we know him today. 1 John Smeaton, for example, set up in practice and was consulted by
clients for whom he would produce a design and a set of drawings 'for 2 the direction of workmen'. It is worth noting that although Smeaton 3 made use of models in the design of a cofferdam and of wind and 4 water mills he did not use them in his bridge designs, nor was there
any need as he only designed masonry arch bridges for road traffic.
The introduction of cast iron in the last quarter of the
eighteenth century as a structural material for bridges is often
described as revolutionary, but whilst the Iron Bridge of 1779 was
certainly an innovation it did not lead to a new analytical technique
nor to the use of a model experiment to predict its behaviour. Neither
did Telford consider it necessary to resort to the use of models in the
design of his early cast iron arched bridges. The reason for this is
undoubtedly that the elastic properties of cast iron in such compression
systems were not significant, and although the open-spandrel form led
to a lighter structure the imposed road loads were still modest when
. compared with the self-weight of the bridge. So novelty of form and a
new material were not, in themselves, sufficient motive to induce bridge
2 designers to turn to experimental models in the eighteenth century. It was to be different when railway loads and spans had to be considered.
Nevertheless, in 1800, Telford's London Bridge design comprising a cast
iron arch of 600 feet span - nearly three times greater than that of the 5 largest iron bridge then in existence - did lead at least to a
discussion of the merits of a model test (see chapter 2). There was
no precedent for an iron arch of such magnitude and hence no accumulated
experience on which to draw, and it is interesting to note that although there was no engineering tradition of structural model testing
in this (or any other) country the adjudicators of the design considered
the notion of an experimental model worth considering. It was a
classical situation providing a motive for model testing. In addition
to the lack of previous practical experience, the inadequacy of
contemporary theoretical analysis was expressed by Professor John
Playfair when giving evidence to the Select Committee;
it is not from theoretical men that the most valuable information in such a case as the present is to be expected. When a mechanical combination becomes in a certain degree complicated, it baffles the efforts of the geometer, and refuses to submit even to his most improved methods of investigation. This holds particularly of bridges, when the principles of mechanics, aided by all the resources of the higher geometry, have not yet gone farther than to determine the equilibrium of a set of smooth wedges, acting on one another by pressure only, and in such circumstances, except in a philosophical experiment, can hardly ever be realised. It is therefore from men bred in the school of daily practice and experience, and who, to a knowledge of general principles, have added, from the habits of their profession, a certain FEELING of the justness or insufficiency of any mechanical contrivance, that the soundest opinion on a matter of this kind is to be obtained. 6 7 Another witness to the Committee, Dr. Milner, commented on the misleading role of mathematics in such cases;
3 It is not, generally speaking, owing to any error of computation that erroneous practical inferences are apt to be made by the theorists; the errors almost always arise from the assumptions made either at the setting out of the problem; or, which comes to the same thing, from implied principles being taken for granted in the course of it when the numerical part of the computation is examined, all is found perfectly just; and this is the part of the examination to which every body is equal ... and thus finding what they do understand to be accurate, they are apt to give credit to the rest, and so the conclusion is supposed solid. 8
This is a cautionary, and perceptive, analysis of a situation, which still applies in some cases today, and correctly focussed critical attention on the validity of any initial assumptions. Later it was to become an important objective of model testing to check such assumptions.
Milner was conscious that the traditional methods of experience and precedent were being severely challenged and said;
Persons who direct the execution of great works, are often extremely ignorant of the GENERAL laws by which the powers of nature act ... they do not know how, in new structures, to make judicious allowances for the differences of circumstances between the new and the old ones, which they or others had before executed. Nor does this defect arise from any want of acuteness in the understanding, but merely from not being sufficiently skilled in the abstruser parts of the mathematics and natural philosophy. 9
Although Playfair's comment that theory could not provide the answers to the analytical problems of the cast iron arch was valid at the beginning of the nineteenth century, Milner's statement about the lack of understanding of mathematically-based structural mechanics touches on an issue'which was to become important in the design of British bridges in the middle years of the century. There was to emerge a gulf between theory and practice and a mistrust of mathematics by the essentially practical body of British Engineers. It accounted for the British engineer's confidence in, and preference for, experimental data.
Although the idea of model testing was considered in 1801 the discussion did not lead to its use in connection with arched road
4 bridges where the traditional design methods were adequate. With
the introduction of wrought iron as the structural material for road
suspension bridges Telford, and other engineers, did make use of
models (see chapter 3). But the accepted methods of analysis and
design, the received principles, were only really challenged in the late
1830's and 40's when a new generation of engineers had to face the
problems posed by railway transport.
Structural Models and Railway Bridge Design
A study of structural model testing in nineteenth century
Britain reveals it to have been almost, exclusively devoted to solving
bridge design problems. Rare references to models being used in the 10 design of large span metal roofs may be found, but this is in any case
a similar structural problem. However, another field of application was
the study of retaining wall stability where the motive was the uncertainty
and complexity of contemporary earth pressure theory. The subject was
principally studied by military engineers who had long been interested 11 in the design of revetments for fortification. Although retaining walls
when used as wing walls to bridges could be regarded as coming within the
scope of this thesis it is too large a subject to be dealt with here.
For the same reason column design will have to be excluded. However,
the behaviour of compression members in lattice girders and the buckling
of thin-walled structures are considered since both issues figured in
the study of the spanning elements of bridge structures and it is solely with these that this thesis is concerned.
The reason that model bridge experiments outnumber all others • ■••■••■■11.■•••••••■■ stems from their extensive use in connection with the entirely new scale of problems posed by railway requirements:
5 Until this present era of the "railway and the steamship and the thoughts that shake mankind", the studies of the engineer, like those of the lawyer, were confined to acquiring details of precedent, while the knowledge of the scientific principles of his profession was neglected as of comparatively little importance ,.. But with the railway arose a new epoch in the history of engineering: works were required to be constructed of unprecedented magnitude and solidity, and for the execution of which a higher amount of mechanical science and a wider range of experience were required. 12
This extract is typical of many which appeared in the contemporary
technical press. Undoubtedly the difficulties confronting the railway
bridge designer in Britain were enormous, and it should be remembered
that it was the British engineer who was first exposed to such questions.
The steam locomotive posed problems of speed, vibration, load, and span
of an order of magnitude different from those which bridge designers
had faced previously. Compared with the traditional masonry road
bridge the railway bridge designer had to produce structures with a • considerably higher live/dead load ratio and it was this that prevented
the adoption of the suspension bridge for railway traffic. Designers
pursued two distinct, yet related, lines of development in solving their
problems; increasingly complex structural forms were introduced, such as
lattice and tubular girders, and there was increased exploitation of
metal construction. Both innovations demanded a drastic revision of
design methods. The traditional design method utilised accumulated
experience and it was this that was lacking when everything changed.
In 1859 a writer could say; 'The rule of thumb is fast losing its old
despotic sway in engineering; and few things, perhaps, have contributed
more to its downfall than the introduction and successful use in many
of our great works of wrought-iron' .13 Thus new problems forced recourse
to a new method and experiment was the only sound approach. The British
' engineer, in his analytical dilemma, naturally turned to models to
evaluate combinations of new materials and novel structural form and it
was with railway bridges that he met his greatest challenge. 6 Theory and Practice
Given then that the British engineer's use of experimental models was principally motivated by the unprecendented challenge of railway bridge problems, what other factors account for model testing as characteristically British? The next important issue in the hierarchy of contributory factors involves what might be called the intellectual
climate in structural engineering in nineteenth century Britain. This
may best be discussed by contrasting the situations in Britain and
France. The engineers of both countries were separated by more than a. language and the Channel - there were differences of temperement and social background. Although in eighteenth-century France engineering was
a practical activity it had, in addition, an intellectual dimension
which was missing in Britain. In addition, the strategic situation of
France gave rise to a State demand for bridge and road designers whilst
in Britain our defence demanded maritime supremacy. In Britain
engineering was in the hands of artisans; millwrights, carpenters,
stonemasons, and ironfounders and although science in Britain was an
intellectual activity this was not true of engineering. Symptomatic of
these differences on each side of the Channel is the sequence of germinal
events in education and professional organisation. In France engineering
schools appeared first; the Ecole des ponts et Chaussees in 1747 and the ./ Ecole polytechnique in 1795. Only in 1848 was the Societe des
inanieures civils de France founded to represent the interests of
practical engineers. This early attention to academic matters is
reflected in the scale and quality of French contributions to
mathematically-based structural mechanics. In Britain on the other
hand practising engineers formed professional bodies long ahead of the
emergence of educational opportunities at university level. As early
as 1771 the Society of Civil Engineers was formed, and although
ostensibly it was a dining club members did discuss their engineering
7 problems although they did not publish technical papers. The Society
did not seek to regulate entry into the profession in terms of education
and training, these functions having to await the formation of the
Institution of Civil Engineers nearly half a century later;
On the 2d. January 1818, a number of persons practically connected with the profession of a civil engineer, met and agreed upon the plan of an institution, and have since that time been employed in forming laws and regulations for its government ... it was resolved at a meeting held on the 3d. February 1820, to invite Thomas Telford, esq., civil engineer, to become President of the Society. Mr. Telford having accepted this office, the institution may be considered as established. 14
Naturally enough the early meetings of the Institution were almost exclusively devoted to papers descriptive of important civil engineering works - it was with the practice of civil engineering that the members were largely concerned. This was to change gradually as the century
progressed and an increasing number of analytical papers are to be found in the Proceedings of the Institution. Although analytical techniques were well established in France in the first half of the nineteenth century, it was only in the second half of the century that mathematical analysis of structures began to bear fruit in Britain. This was one of the consequences of increased educational opportunities for British engineers. When the Institution was formed very few university places were available to anyone in Britain and although some useful engineering education could be gleaned from existing courses in natural philosophy these did not have a great impact on engineering. But the situation was soon to change, albeit slowly. In 1837 King's College London already had 15 a 'Class of Civil Engineering and Mining' and in 1840 the University of
Glasgow instituted the first chair of Engineering at a British university.
In the following year a Professor of Engineering was appointed at
University College in London. The British civil engineering profession viewed aspects of these developments with characteristic caution;
8 The professor, however talented he may be, has no very great inducement to accelerate the progress of his pupil; for he is to have his stipulated salary, in nowhise depending upon the success of his teaching. But the engineer has a direct interest in communicating professional knowledge to his pupils as speedily, as fully, and as perfectly as he possibly can; because the sooner he can do this, the sooner he is enabled to employ them in a way profitable to himself; as well as doubly profitable to them. 16
But there was a decline, to some extent, in this characteristic mistrust
of theory by the practitioner as a result of these educational
developments and by 1846 Sir John Rennie, President of the Institution
of Civil Engineers could say;
Although practice, upon the whole, is most important, nevertheless, we should not omit the study of the theory, of principles upon which that practice is, or ought to be, founded, and without the due study and comprehension of which, we may frequently be led into great errors in practice. Our junior members should, therefore, previous to commencing their professional career, be well versed in arithmetic, algebra, mathematics, mechanics, and the principles of natural philosophy in general, and the mode of applying them to practice. 17
Although this educational development with the consequent publication 18 of engineering textbooks and the emergence of journals desseminating 19 technical ideas helped to achieve a wider acceptance of mathematical analysis, there remained an element of this deep-rooted mistrust of
theory which was so characteristic of the British engineer. In 1869
Fleeming Jenkin, Professor of Engineering in the University of
Edinburgh, read a paper on Technical Education in which he made a plea for engineers to' be trained in the established multi-disciplinary universities rather than in specialist schools of engineering. He felt
that such schools would carry preparatory training too far and said;
'A glaring example of this is to be found in the Polytechnic School in
Paris, where every Government engineer receives a training such as would fit him to be a wrangler at Cambridge, and very generally unfits 20 him to be an engineer'. In addition he considered that;
9 The system of pupilage for an engineer must be maintained, and pupilage should begin at the age of eighteen or nineteen. The student has, therefore, no time to acquire the higher mathematics, or to follow any large number of courses on special engineering subjects. If our young engineers could enter the offices and workshops as pupils possessing a competent knowledge of geometry, the elements of algebra, trigonometry, physics, chemistry, mechanics, and drawing, they would be able during their pupilage to make a really good use of their time, instead of, as at present, too often employing these years in learning, in a very rude way, projection, mensuration, tracing, and such other elementary branches as they should have mastered before entering the office. 21
Much more evidence of this attitude is presented in the subsequent
chapters when discussing the engineer's motives for using model
experiments.
The Source of Capital
Another aspect of nineteenth-century British civil engineering which affected structural model testing was the source of finance. Edwin
Clark pointed out that;
It is a national characteristic, in which we may be said to stand almost alone, that our greatest public works are conceived and developed by private enterprise: the peculiar sagacity of a commercial people appears, indeed, most conspicuous in their immediate appreciation of the important principle, that whatever is conducive to the general weal is also to the promoters a certain source of benefit; and, conversely, that the richest harvests of individual enterprise will be always reaped in the broad and fertile field of public philanthropy the introduction of railroads.., enlisted at once the whole commercial community in their construction; and without, as among our Continental neighbours, the assistance of Government patronage, nay, even in the face of Government opposition, the land was speedily covered with a network of elaborate intricacy. 22
This may, at first sight, appear to be unimportant in the story of experimental model testing. But it should be remembered that during the years of the railway mania there was no established Government agency, or University engineering department, able to undertake research on the structural problems posed by the railways. It follows, therefore, that
10 the Engineer to a Railway Company was in an exposed, and somewhat
lonely, position. Faced with intractable analytical problems the
engineer did, as we have seen, turn to models for help. But he was
forced to rely on the Company's resources and would have to persuade
the Railway Directors that an experiment, or a series of experiments,
would be worth the expenditure. Moreover time was not on the side of
the engineer as the Iron Commissioners pointed out in 1849;
the innumerable opportunities of building new bridges which the railways have given occasion to, and a constant endeavour to reduce the expense of building them, a variety of new constructions have been proposed and essayed ... the effects of which have not yet had time fully to develop themselves, on account of the extent and number of new railways, and the rapidity with which they were constructed, in many cases scarcely giving breathing time to the engineers, by which to observe and profit by the experience of each successive new construction. 23
Naturally enough the Directors were concerned to meet stringent
deadlines and to ensure a dividend to the shareholders as soon as
possible. This led to excessive pressure on the engineer and a tendency
to be satisfied with a structure which was proved experimentally to be sufficiently safe rather than to seek the best structure in a given situation. So although private enterprise provided unrivalled opportunities for British civil engineers it also tended to discourage the full investigation of the structural design problems.
Structural Model Types
It is worthwhile at this point to discuss exactly what is meant by a structural model of a bridge. Architects used what they called models to convey form, proportion, texture, and colour to their clients.
This was nearly always more effective than a drawing and as such the value of the architect's model had been recognised at least as early as the Renaissance. Nineteenth-century civil engineers used a similar 24 technique in geology and mapping asas well as for models of structures and machines. Sir John Rennie succinctly summarised the motives for 11 for using this type of model;
Although drawing ... is most valuable, modelling in many cases is essential nothing, except the work itself, gives such a perfect idea or representation as a model; it also enables the engineer to detect many imperfections which otherwise would escape his notice; wherever, therefore, models can be conveniently adopted or employed, it is advisable to do so. 26
Although this visual modelling is still used extensively in architecture
and engineering it is not our concern here. The essential difference
between the merely graphic model and those which are the subject of
this thesis is that the latter were experimental in character, that is,
they were conceived, constructed, and tested to provide data for the
engineer. The objectives of model testing in the nineteenth century
can tell as much about the models themselves (see figure 1.1). When
defining structural models a classification of experimental objectives,
and the ensuing techniques, is helpful. Experiment objectives really 27 fall into four categories, namely;
(1) Exploratory
(2) Confirmatory
(3) Data-providing
and (4) Analytical
It should be remembered however that nineteenth-century experimenters
did not by any means define their objectives so clearly or conveniently,
and in many cases not at all. Exploratory experiments were made before
mathematical analysis, were imprecise in character, and did not provide
quantifiable data but were undertaken in a qualitative manner in order
to clarify a problem. Many small-scale voussoir arch models were. used
in this way (see chapter 2) as indeed were the early experiments on
wrought iron tubes for the Britannia Bridge design (chapter 3).
Confirmatory experiments on the other hand were made after mathemitical
analysis and were particularly useful in checking the validity of the initial simplifying assumptions. The innovatory use of metal in railway 12 bridges made this the more necessary. Atwood's arch thrust model was
in this category as were the model Warren girder experiments of Doyne
and Blood (chapter 3) and the continuity experiments of I.K. Brunel,
C.H. Wild, and Edwin Clark (chapter 3). Experiments of the Data-
providing type do not figure largely in this thesis as they are often
not strictly model experiments. A classic example of this category
were the column, or strut, tests designed to evaluate constraints in
design formulae which were empirically constructed to make allowances
for imperfections of shape, in materials and end conditions. Many
hydraulic formulae are of the same type and the nineteenth century saw
much effort directed to their elucidation as well. However this form of
experimental research forms no part of this thesis not even in the field
of structures. Analytical model experiments were used where an
established mathematical technique was regarded as being too laborious.
A typical example of this was in the case of Telford's Menai suspension
bridge chain geometry model (chapter 2) where the chain configuration was measured on a model in preference to an established technique based on calculation. Analytical models were of particular use in connection with statically indeterminate structures and typical examples were
Barlow and Airy's suspended girder models (chapter 2) and the ingenious musical bowstring girder model of 1868 - the last structural model experiment noted in nineteenth-century Britain. This brings us to the reasons for the abatement of structural model testing in the last three decades of the century.
The Decline of Structural Model Testing
How can we account for the decline, and indeed cessation, of 28 structural model testing in Britain after 1868. Probably there are several contributory factors which need to be taken into account. One, fairly obviously as the decline in bridge building itself in the last
13 • quarter of the century. This is manifestly true of the large-span suspension bridge which had signally failed to establish itself in the
British bridge-builder's repertoire. The reasons for this reflect the failure to adapt the suspension bridge for railway traffic and the fact that the road system did not yet demand the spanning of large estuaries. After the railway boom years there was a drastic reduction in bridge construction, and many of those that were built were repetitive in character, and this led to a stagnation of analytical activity. But this does not entirely explain the loss of interest in structural model testing after 1868 - there was after all a growth of interest in model experiments in other fields at this time. The study of the regime of river estuaries and the relationship of hull shape and ship performance for example were studied by means of hydraulic models 29 30 of estuaries and model ship towing-tank experiments during the same period. This development was due to the essentially empirical nature of fluid mechanics which made data-providing model experiments unavoidable.
By contrast, during this period structural design problems were such that although the Forth railway bridge was designed and built, of novel form and unprecedented scale, there is- no record of Fowler and Baker making model experiments in the course of its design. One reason for the lack of structural model experiments was the increased use of mathematical analysis in the latter part of the century for the reasons discussed previously. It would be simplistic to suggest that the engineer's use of models was inversely proportional to his grasp of mathematical analysis, and yet there is more than an element of truth in this. This is borne out by the changing nature of the papers read to the Institution of Civil Engineers. Another factor of importance was the increasingly widespread use of graphical analysis in engineer's offices. This was an important factor in the decline of model testing in the later '60's. Many of the structural engineer's problems,
14 particularly those concerning statically determinate structures, could now be solved either by simple mathematics or increasingly by graphical techniques. Graphical methods were an attractive alternative to mathematics and well within the capabilities of drawing office staff.
Thrust lines in arches, forces in the members of pin-jointed frames, frame deflection, bending moment diagrams, shear force (subsequently), and the deflected shape of beams were all problems which were amenable 31 to graphical solutions by the 1860's Graphics, rather like models, generated confidence particularly as in many graphical techniques there was a visual check on mistakes. Benjamin Baker, writing in 1870, in the preface to his book - On the Strength of Beams, Columns, & Arches • captured the mood of the period when he said;
In the treatment of the several questions brought under consideration, the author has endeavoured, in all instances, to assimilate the process of investigation to the ordinary routine of the drawing office: in other words, he has preferred compasses to equations, and scales to logarithms, whenever the selection was optional. 32
As more of the day-to-day problems of design could be solved by mathematics and graphics the need to use models naturally declined (see figure 1.2). The re-awakening of interest in structural model testing had to await the development of the resistance wire strain gauge techniques early in this century. This opened up enormous possibilities for stress distribution studies and freed engineers from the nineteenth- century's overriding preoccupation with ultimate load considerations.
Nevertheless, structural model testing played an important role in the design of British bridges between 1800 and 1870 and involved some of the greatest (and some of the least) civil engineers of the period.
What follows is an assessment of their work.
15 OBJECTI V E S a H "'"'s:: t-< 0 ~ •.-4 .j..l t-< CI) =a ~ C) E-o <... CI) Cl CI) il) ~ b H H t-< Z >0 r-4 ~ >::l Z CI) 0 ...:l 'H ~ s Z ~ H ~ ~ c:: Cl "'" 0 t-< a "0 c:: ~ ~ >::l"'" C) "'" C) '-' ~ CI) ~ "'">::l ~ P
MODEL
BEAM solid web ~ ~~ ~ BEAM open web ~ ~ LATTICE GIRDER Parallel boom ~ LATTICE GIRDER bowstring ~ TUBULAR GIRDER ~ ~ ~ ~ ~ PLo\TE GIRDER ~ ~ SUSPENSION BRIDGE ~ ~ ~ ~ ~ MASONRY ARCH ~ ~ ~ ~ TUlliER ARCH ~ METAL ARCH ~ ~
Model type - Obj ective Matrix 1.1
OL9
0981.
0 coN OSE3L
8 00
z 01781, 'E:4•4
0 0E91. L URA UCT TR S
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NCE E ID 01.81. INC
0081. ON SI SPEN SU
THE INCIDENCE OF STRUCTURAL MODEL TESTING
1800 - 1870 Chapter 1:
Introduction
REFERENCES and NOTES
1. See the author's paper; 'The Professional Correspondence of John Smeaton', the Transactions of the Newcomen Society, read 11 February 1976.
2. I.C.E. library, Machine Letters, volume 1, p.87; John Smeaton to Messrs. Osbert and Jas. Denton, 28 August 1782.
3. Royal Society Library, London, Smeaton's Designs, Volume 4, folio 172. This is one of the earliest of Smeaton's Reports.
4. Phil. Trans., volume 51, 1759: 'An Experimental Inquiry concerning the Natural Powers of Water and Wind to turn Mills, and other machines, depending on a Circular Motion'.
5. The largest span was that of Wilson and Burdon's bridge over the river Wear at Sunderland of 240 feet.
6. Parl. Pap., 1801, Reports (2), volume 3, p.289.
7. Isaac Milner (1750-1820), Vice-Chancellor of Cambridge University.
8. Parl. Pap., op. cit.
9. Ibid. p.299
10. See for example: Trans. R.I.B.A., volume 1, 15 February 1836 pp.44-6; 'Metal Roof at Hungerford Market', by Charles Fowler: p.45: 'The application of a central abutment being considered novel, it gave rise to much discussion as to its efficiency; accordingly a series of experiments were made at Messrs. Bramah's (who executed the work) upon models; the result of which was, that this form bore nearly double the weight of a strait bar of the same section'. and; The Mechanic's Magazine, volume 36, 2 Apri1.1842, p.266: 'Metropolitan Music Hall - Hansom's New System of Building'.
11. See for example: Course of Instruction originally composed for the use of the Royal Engineer Department, by C.W. Pasley, London, John Murray, 1817, volume 3, p.493 et seq. which records Pasley's extensive experiments on wooden models of retaining walls, 3 feet long and 26 inches high, in a variety of configurations of batter, counterforts, and loading.
12. The Civil Engineer and Architect's Journal, volume 10, November 1847, p.352.
16 13. The Civil Engineer and Architect's Journal, February 1849, p.65.
14. Edinburgh Phil. Journal, volume 111, 1820, p.202.
15. See The Civil Engineer and Nrchitect's Journal, volume 1, 1837-8, p.231.
16. The Surveyor, Engineer, and Architect, September 1840, p.175.
17. Proc. I.C.E., volume v, 20 January 1846, p.116.
18. A number of excellent textbooks were published during this period, notably professor Rankine's two classic works: A Manual of Applied Mechanics (1858) and A Manual of Civil Engineering (1861), both ran to many editions. It was Rankine who first rigorously defined the terms stress and strain and in these papers they are used in their modern sense.
19. The Mechanic's Magazine was first published in 1823. Other principal technical journals and their starting dates are: The Civil Engineer and Architect's Journal (1837), The Surveyor, Engineer, and Architect (1840), The Builder (1842), The Engineer (1856), and Engineering (1866).
20. Paper read by Professor Fleeming Jenkin to the Royal Scottish Society of Arts in Edinburgh, 11 January 1869 and published in Papers Literary,Scientific, &c., by the late Fleeming Jenkin, 2 volumes, London 1887, volume 2, p.174.
21. Ibid. p.175
22. The Britannia and Conway Tubular Bridges, Edwin Clark, 2 volumes, London 1850, volume 1, p.l.
23. Parl. Pap., 1849 (1123) XX1X, Report ... Iron Commissioners, p.xvi and p.xvii.
24. Proc.I.C.E., volume 1, 22 June 1841, pp. 163-8: 'On the Construction and the Use of Geological Models in Connexion with Civil Engineering', by Thomas Sopwith, F.G.S., M.Inst.C.E.
25. Proc.I.C.E., volume 2, 31 May 1842, p.155: 'On the construction of Model Maps, as a better mode than Sectionplanography for delineating the Drainage and Agricultural Improvements of a Country, or projected lines of Railways, Canals, &c.', by John Bailey Denton, Assoc.Inst.C.E.
26. Proc.I.C.E., volume v, 20 January 1846, p.114.
27. Based on the categories given by Pippard and Baker in; The Analysis of Engineering Structures, London, Arnold, 3rd edit. 1957, pp.515-516.
28. The last structural model recorded in the Proc.I.C.E. in the nineteenth century is Airy's bowstring girder model (see chapter 3).
17 • 29. See British Association Report 1887, pp, 555-562: 'On Certain Laws relating to the Regime of Rivers and Estuaries, and on the possibility of Experiments on a small scale', by Professor Osborne Reynolds.
30. See The Papers of William Froude (1810 - 1879), The Institution of Naval Architects, London, 1955.
31. In the latter part of the century the British Association for the Advancement of Science took a particular interest in the application of graphics to engineering problems and many interesting papers are to be found in their Reports. See for example the 1874 Report (Belfast meeting), p.229: A New Construction for finding the Vertical Shearing Stress and the point of greatest Bending-Moment in a beam loaded in any Way', by John Neville, C.E. In the 1899 Report (Newcastle-on-Tyne meeting), pp.322-7: they published the 'First Report of the Committee ... appointed to Report on the Development of Graphic MethodS in Mechanical Science', which contains an excellent bibliography.
32. On the Strength of Beams, Columns and Arches, Benjamin Baker, London, Spon, 1870, Preface.
18 Chapter 2
ARCH BRIDGES ARCH BRIDGES
The masonry voussoir arch is one of the oldest horizontal
spanning elements in structure and, although built traditionally by
empirical methods, received a considerable amount of analytical
attention in the eighteenth century. In fact, by the end of the century
the analysis and design of masonry arches presented no real problems.
The work of French analysists in particular, had produced a valid
design method making the following implicit, or explicit, assumptions:
(1) That masonry had no tensile strength.
That masonry had infinite compressive strength, and
That friction would prevent sliding.
It follows from (i) that the 'line of thrust' must be contained within
the masonry, from (ii) that the compressive stresses are negligible, and from (iii) that the only possible collapse mode was that of rotation about hinges at the intrados or extrados, producing a mechanism of collapse. Assumptions (i) and (ii) essentially said that the elastic
properties of the masonry could be ignored and it follows that complex • scaling laws relating stress in model and bridge are not necessary.
Therefore, if a small-scale masonry structure (or 'model') is stable, then if all dimensions are scaled up by a simple geometric scale-factor the large structure would also be stable. It was possible therefore to extrapolate directly from a small successful structure to one of larger size. The secret proportionality rules of the medieval masons, although stated in terms of the musical modulation ideas of Augustine and codified concepts of beauty (the 'golden section', 'ad quadratum', 'ad triangulum' etc.) would, nevertheless, have provided valid design rules. The design method worked on the basis of establishment of precedent and extrapolation - a beautiful bridge must presumably have been a stable one..And hence it is possible to say that gothic and renaissance 19 structures were designed without necessarily imputing analysis to
their builders.
The work of the eighteenth century analysts cannot be dealt with here but it is worth noting that although their techniques were largely graphical, models were used to demonstrate precise collapse modes under varying loads, minimum abutment requirements, and even to 1 determine the forces on arch centering during construction. John
Smeaton certainly understood the validity of scaling from an existing structure. On his drawing for Blackfriars Bridge he showed the arch
profile of Westminster Bridge together with two bar-scales and the caption:
Plan and elevation for a bridge over the river Thames of the same length, breadth and height under the middle arch as Westminster Bridge, drawn in the year 1754, according to the scale A, but may be adapted to the river at Black Fryers by measuring from the scale B. 2
It follows, therefore, that structural models of masonry voussoir arches did not play an important part in the design of arch bridges in the nineteenth century.
Nevertheless, British engineers did make use of models in discussing arch bridge designs in masonry, timber, and metal. Although models played a minimal role in the design of masonry bridges, when engineers came to design arches in metal and timber the extent to which masonry design rules were valid was explored by using models - albeit in a confused manner. The subject will be discussed here in strict chronology. The nineteenth century opened with the lengthy discussion of Telford's London Bridge design.
20 The Proposed Rebuilding of London Bridge
In June 1801 a Government Select Committee published its
Report stating that it was 'essential to the Improvement and
Accommodation of the Port of London, that London Bridge should be rebuilt' and that 'an Iron Bridge, having its centre arch not less than
65 feet high in the clear above High Water Mark, will answer the intended Purposes, with the greatest convenience, and at the least 3 expense'. After their report was framed they received two designs quite different from any previously considered;
The first from Mr. Black, proposing a Bridge of Granite, of Three Arches, of an extent much exceeding those of any Stone Bridge which has been attempted in Europe; and the other from Messrs. Telford and Douglass, recommending an Iron Bridge of a Single Arch, of the Height pointed out in the Resolutions of the Committee, and no less than 600 Feet in the Span. 4
The originality of these designs induced the Committee to annexe a supplement to their report with engravings of both bridges. The single arch scheme of Telford and Douglass particularly appealed to them but they considered it so avant garde that it was;
absolutely necessary for their own information, as well as for the Purpose of affording some Grounds upon which the House might hereafter form their judgement as to its Expediency, to request the Opinions of some of the Persons most eminent in Great Britain, for their Theoretic as well as Practical Knowledge of such Subjects. 5
The audacity of the unprecedented 600 foot span can be imagined by considering that the Iron Bridge across the Severn (1779) was of 100 foot span, and that over the Wear at Sunderland (1796) had a span of
236 feet and was the largest cast iron bridge until 1876. Telford's cast iron arch bridge at Buildwas (1796) over the Severn had a span of
130 feet but contained less than half the metal used in the first iron bridge.
21 The Committee drafted a set of twenty-one questions which 6 were put to seventeen witnesses and it is with the analysis of their evidence that this section is concerned. When considering nineteenth century structural model testing this report of 1801 is of interest in two ways; firstly it appeared at the beginning of the period under review, and secondly it contained a unique cross-section of professional opinion from men concerned with structural analysis, design, and construction. Although the bridge was not built and in the event no model tests were made, the Report nevertheless makes possible an interesting comparison of the attitudes of eminent men of the period to questions of bridge design. Of the twenty-one questions only two are relevant to our topic, namely number VIII which asked:
IS IT NECESSARY OR ADVISABLE TO HAVE A MODEL MADE OF THE PROPOSED BRIDGE, OR ANY PART OF IT, OF CAST IRON; IF SO WHAT ARE THE OBJECTS TO WHICH THE EXPERIMENTS SHOULD BE DIRECTED? TO THE EQUILIBRIUM ONLY, OR TO THE COHESION OF THE SEVERAL PARTS, OR TO BOTH UNITED, AS THEY WILL OCCUR IN THE IRONWORK OF THE INTENDED BRIDGE? 7 and number IV which asked:
OF WHAT SIZE OUGHT THE MODEL TO BE MADE, AND IN WHAT RELATIVE PROPORTION WILL EXPERIMENTS ON THE MODEL BEAR TO THE BRIDGE WHEN EXECUTED? 8
These questions are precise and required answers to two essential questions relating to model testing, namely, why make a model - what could be gained from testing it? and secondly, and more important, how is the model performance related to that of the full-scale structure?
In the absence of a tradition of structural model testing in Britain it is surprising to find such questions asked in 1801 and, in particular, that which raised the crucial question of similarity. Only twelve of the seventeen witnesses questioned attempted an answer to these two questions and of them only four had anything to say about similarity.
The evidence of each will now be considered and a tabulated summary is given in figure 2.1.
22 Dr, Nevil Maskelyne, the Astronomer Royal, thought 'it might be useful to have an exact model of the present bridge ... or of some part of it, made in cast iron, for trying experiments on' and that it should be tested for 'cohesion of the parts, and the capacity of it to sustain a shock from a body in motion falling (striking) perpendicularly 9 against the arch'. The latter was really the answer to question six dealing with horizontal load on the bridge. He gave no details of his proposed model but on the question of scale introduced a note of economy;
If the model could be made use of afterwards in some of the roadways about the bridge, it might then be worthwhile to make it of considerable size, with its linear dimensions 1/10th or 1/12th of those of the intended bridge, or the model may be made at pleasure with the dimensions, suppose 1/30th or 1/50th. 10
A 1/10th scale model would have a span of 60 feet but the 1/50th scale model would only be 12 feet long making it difficult to reproduce the details of the bridge in an 'exact' model. The large model would obviously only have been usable after testing if it was not loaded to destruction and it is difficult therefore to see how it could be used to demonstrate the ultimate 'cohesion of the parts'. He was rather • more precise when discussing similarity; considering strength under dead load only he said:
The model will be stronger than the bridge, relative to supporting its own weight, in the same proportion in which the linear dimensions of the bridge are greater than those of the model. For example, if the linear dimensions of the bridge are ten times those of the model, and the bridge may be just broken by its own weight, the model will require ten times its own weight to break it. 11
Maskelyne appeared to ignore the possibility of lateral instability of the ribs in compression and was only concerned with the compressive breaking stress of the material. However, as the model and bridge were both made of cast iron the breaking stress would be the same for both.
23 Admitting this, his statement can be shown to be true:
Let the self-weight of the model = w and that of the bridge 3 Then,if the geometric scale factor was 10 then W = 10 w.
Now the compressive stress in the model is proportional to load/area, w i.e. 1X = w, and the stress in the full-sized bridge is proportional 1 3 W • W 10w to — - = -- = 10 w. The stress in the bridge material 2 - 2 10X10 10 10 was to be such that it was 'just broken by its own weight', therefore,
the model would indeed require 'ten times its own weight to break it' -
that is an additional load of 9 w would just break the model. However, a difficulty would arise in applying such an additional load to simulate accurately the distribution of self-weight, unless the model could be made of a material having ten times the density of cast iron. The weight of iron in the bridge had been estimated at about 6,000 tons and
Maskelyne added a comment on the relative effect of live load on the
bridge;
As to the effect of a weight, suppose a loaded waggon going over the bridge, taking that to be 6 or 8 tons, it will be only 1/1000th of that of the bridge, and its stress on the middle of the bridge will be 1/1000th part of the stress of the whole weight of the bridge there; but it will be easy to make the bridge strong enough to bear 1/000th more than its own weight. 12
He ignored the different effect of distributed and concentrated loads.
Linear-elastic behaviour is assumed and he claimed a low live/dead ratio.
This is allowable in the traditional masonry arch bridge but the ratio would undoubtedly be more critical in the open web spandrel structure
proposed by Telford.
John Playfair, Professor of mathematics in the University of
Edinburgh, took a broader, more philosophical, view in his answer sounding a rather doubtful note on the role of models;
24 Though a great deal of benefit might accrue to the theory of arches in general, from a well constructed model of an iron bridge, adapted to the making of experiments, yet I cannot say that I think such a model indispensable with respect to the present bridge. If it were so contrived indeed as to afford means of measuring the pressure on the abutments, or on other sections of the bridge, it might lead to very important discoveries, and enable us to compare the conclusions of theory with matter of fact. 13
He advocated straightforward experimental verification of the forces
predicted by 'theory' - though he said nothing of his theoretical method
of analysis. He was nevertheless optimistic about the project; 'I see
no reason from theory from thinking that the bridge ... is at all
impracticable, or that there is anything to prevent it, notwithstanding
its boldness and novelty, from becoming, with due care, a substantial 14 and durable edifice'.
The Committee consulted Playfair's Edinburgh colleague, John
Robeson (or Robison) the Professor of Natural Philosophy. He received
the questions only eight days before having to reply and illness
prevented him giving 'a subject so new, so uncommon, and of such
magnitude and intricacy' the considerations it deserved - 'Each 15 particular would require a careful and minute study'. He exceeded
the brief of question eight by suggesting a model material other than
cast iron;
Were I to make a model, it should be of plaister of Paris. I think that such a model would be instructive. One rib is enough, giving it considerable dimensions transversely; I would cast it in one piece, that it may be uniform in its texture. I would set it up between planks ... and I would pour small shot on it, till it begins to crush, and would notice the progress of failure. 16
It is difficult to see how this homogenous, monolithic, model could be said to represent the braced-spandrel rib of the bridge. Its breadth would prevent buckling and it is apparent that Robison was only
25 concerned with material breakdown by crushing, His intention to observe the progress of failure is interesting and would be facilitated by his use of lead shot making possible small increments of load. He would presumably have adopted the intrados curve of Telford assuming it be free from tension; indeed he said, 'A friable model like this will show the manner of failing at the crown which I dread from compression, 17 or from yielding of the abutments'. He proposed another plaster model representing voussoirs, or possibly the individual cast iron elements of the proposed arch, in the manner of Wilson and Burdon's
Wear Bridge at Sunderland:
I would cut another cast into sections, by passing a fine spring saw along certain radial joints. I would set up this model, by putting slips of card paper in the joints, to make up for what the saw takes out. I would try this model in the same manner, and I should expect useful information from the way in which they failed in the different parts. I apprehend that it will appear, that equilibrium is very little concerned, in any other way than what I mentioned at first. 18
This is a puzzling statement. He seems to be considering the stability of a series of voussoirs which would be affected by tension at the joints which might produce sufficient hinges to form a collapse mechanism. This is difficult to reconcile with his statement that
'equilibrium is very little concerned'. He did not mention a scale_ factor or deal with the similarity of model and bridge.
Dr. Milner did not answer, specifically, the two questions relating to a model test and felt that the best results would follow from adequate consultation between engineers and mathematicians. ,
Dr. Charles Hutton, Professor of mathematics at the Royal
Military Academy at Woolwich, gave several reasons for testing a model.
He thought it 'very advisable to have a model made of the whole of the
26 proposed bridge, in cast iron' for 'greater safety and satisfaction' and 'the experience and knowledge derived from the casting and making 19 it'. His objectives were directed to, 'the equilibrium of the whole, the cohesion and fitting of the several parts, the effects of a vertical load on every part separately, and the effects of a horizontal blow or shock against every part in the side of the arch. Also what 20 weight the model frames require to break or to crush them'. It would seem he wished to test voussoir-type stability and to load the model to destruction. He thought the question of a horizontal blow from a ship would be 'much better answered by means of experiments on a proper 21 model, than by theoretical calculations, A PRIORI'. Nevertheless, he felt that 'such a mass of bonded materials' would be quite secure.
Hutton advised a scale factor of 1/20 giving a model of 30 foot span. He obviously intended a strictly geometric model saying it would require
'only the eight-thousandth part of the weight or metal in the bridge, 22 because the cube of 20 is 8,000'. As the bridge was estimated to require 6,500 tons of iron, the model would contain something like three quarters of a ton. Hutton dealt with similarity in one, rather confused, statement;
As to the relative proportions of experiments made with the model; those relating to the equilibrium will be in the same direct proportion with the masses of the model and bridge, as well as those relating to loads or shocks. But the strength of any particular bar or frame will be only as the square of the scantling, while the stress upon it is in the same proportion as the length. 23
This is not at all clear, and in the absence of other'information it is difficult to see that this added anything to his statement.
George Atwood, mathematician, suggested it would be satisfactory to verify experimentally the equilibrium of the arch and also the strength of the fastenings;
27 but if these experiments should be made on the same model, it might be difficult to distinguish sufficiently the effects arising from the adjustments of equilibrium, and any defect thereof, from those which are produced by the fastenings; for which, and other reasons, it appears to me, that more satisfactory results would be the consequence of making experiments for verifying the principle of equilibrium, and on the strength of the fastenings, independently of each other. 24
Surprisingly he made no comment on similarity, but having had his attention drawn to the subject of model arches by the Select Committee he subsequently made some experiments (see following section).
Hutton's senior colleague at Woolwich, Colonel Twiss, thought it 'advisable to have a model made of the proposed arch in cast-iron, and the great object will be to ascertain the best mode of casting and putting together the several parts; it will also be a proof of its equilibration',to which he loyally added,'though of that I should 25 have no doubt if calculated by Dr. Hutton'. He proposed a model scale of one inch to the foot, i.e. 50 foot span. Twiss obviously had faith in the adequacy of calculation for determining stability and saw the model principally as a means of developing constructional techniques - a valid motive in the case of a structure of such complexity. He added,
'should the model be so constructed that it could easily be widened to ten or twelve feet, it might sell, as a permanent bridge, for nearly 26 what it cost'. He obviously did not intend a model test to destruction.
William Jessop briefly dismissed the subject by saying 'I do not think that any satisfactory results can be deduced from experiments 27 made on a model'. This is somewhat surprising considering he spent his years of training with Smeaton in the office at Austhorpe.
28 John Rennie was rather lukewarm on the subject of small
models, saying;
As the durability of bridges depends not only on the perfection of their construction, but also on the tenacity of the materials of which they are composed, I am of opinion no very satisfactory information can be had from a model, unless on a large scale. In a work of this magnitude and importance, it should be at least 1/20th part of the size at large, and would be better if made much larger. The experiments should be directed both to the equilibrium and cohesion. 28
The Rennie family were not conspicuous users of structural models to
provide data for design purposes.
John Southern, manager of Boulton and Watt's Soho foundry,
felt it would 'not be possible to make a model of cast iron precisely
similar to the bridge, but upon a scale which will be deemed too large
and expensive, because the strength of that metal cannot be judged of
comparatively, if less than an inch square, which would call for a 29 model whose span was 75 to 100 feet'. He was the only one to mention
this material scale effect and to overcome this he proposed 'putting the
metal which belongs to all the ribs into one, or at most two ribs of the 30 model'. Southern is again unique in stating that the arch should be
so constructed !to render it impossible for any weight that can actually
be brought upon the bridge to bring on any degree of TENSION upon the
parallel limbs of the frames, and therefore cohesion is not an object 31 of the model'. To this he added the interesting comment; 'neither
is the equilibration tobeascertained by a model, which at the same time
shall be capable of determining obviously the largest extra load the 32 bridge will sustain, or just be broken by'. This appears to reveal an
understanding of the different behaviour of structural members under
light loading and near the failure point. Most model tests in the
nineteenth century were only concerned with the failure load. He also suggested a special-purpose model depending 'upon the doubts which the 29 Committee entertain on any point, and it should be constructed with the 33 view of determining the question of doubt'. This attitude appears
extremely advanced and Southern is one of the first to realise the
importance of a structural model designed to examine a specific issue.
On the question of scale and similarity he said
The model should not have a Span of less than 30 feet, if made of two ribs, for ascertaining the force that will break up the bridge; and the force in large will be to that in small, as the whole weight of the bridge is to be whole weight of the model; the altitude of the arch frames being proportional to the span, and the bridge and model loaded similarly and proportionately previously to the extra load being applied. 34
Southern was ensuring that the model and bridge had the same strength/ weight ratio. This is the first reference to such a sophisticated model
concept and altogether his contribution to the discussion was one of the
most informative.
Not surprisingly, William Reynolds of Colebrookdale, strongly advised 'a model to be made of cast iron, which it is very likely may throw some light on many points necessary to be known, previous to the 35 construction to so great a work'. He was equally vague on the question of scale; 'as to the size of the model, that must be determined by the 36 engineers'.
The last witness to mention models was John Wilkinson of
Staffordshire who felt it was,
not only advisbale but absolutely necessary, that a model should be made, which would point more clearly than can possibly be done by theory, if any and what alterations would be requisite. - If one upon a scale of 4 of an inch to the foot was put up, which would be a span of 37i feet, it would answer every purpose, and an opinion should then be formed, and a determination made with a degree of certainty, which cannot now be done. 37
30
•
QUESTION VIII QUESTION IX
OTHER MODEL NAME DECISION OBJECTIVES MODEL SIMILARITY COMMENT SIZE MATERIAL COMMENT
Maskelyne For 'exact model' Cohesion of parts - perpendicular 1/10, 1/12, 1/30 Cast iron * 88 shock or 1/50 si
ea8J Playfair For not Pressure on abutments U s indispensable BO of : E Robeson For Progress of failure at the crown Plaster of Paris oA
vi due to crushing d
enc Milner Against consultation • ewni
preferable E e
ai Hutton For very Equilibrium of the whole - Cohesion At least 1/20 Cast iron *
v advisable and fitting of parts - horizontal blow en t Atwood For Equilibrium - strength of
o S fastenings 1
el Twiss For advisable to ascertain best mode of casting - 50 feet long Timber/cast iron? *
ect C proof of equilibration i.e. 1"=P-0"
Jessop Against ommi
Rennie For only if of Equilibrium and cohesion At least 1/20 Cast iron t
t large scale ee
Southern For must be of Ascertaining the force that will • 75 or 100 ft. Cast iron 4. large scale break up the bridge . span
Reynolds For 'May throw some light on many points To bo determined Cast iron - necessary to bo known' by the engineers
Wilkinson For absolutely to determine 'any and what 37i ft. span necessary alterations would be requisite' i.e. i".1'-0"
TELFORD'S LONDON BRIDGE SUMMARY OF ANSWERS GIVEN TO SELECT COMMITTEE This survey of professional opinion regarding model testing is unique in nineteenth-century Britain and is of greater interest as the discussion occured so early in the century. Although there was an overwhelming decision in favour of a model test none of the witnesses admitted having any experience in the technique. This is reflected in the vague nature of the answers and, in particular, the dearth of opinion relating to the similarity question. There was an instinctive feeling that anything that might provide information would be worthwhile - a reasonable attitude in a project so novel. But this important discussion on models did not lead immediately to a widespread use of such experiments. This was because the discussion took place between elderly men at the ends of their careers and it was the next generation of engineers who re-opened the question of model tests on arches in response to the stimulus of railway bridge problems. The decision not to proceed with Telford's London Bridge in 1801-2 was based on the approach road difficulty posed by so high an arch and as the only model experiments to ensue from the investigation were those of Atwood in 1803-4 we can be sure that models played no part in this decision.
Atwood's Treatise on Arches 1801 - 1804
George Atwood published his Treatise on the Construction and 38 Properties of Arches in 1801 as a direct result of having been interested in the topic by the Select Committee. The first part is full of minute calculations relating the weight of a voussoir to its included angle and the self-weight to the abutment pressure - all to 39 five decimal places. In 1804 he published a supplement in which his earlier propositions were 'verified and confirmed, by new and satisfactory experiments, on Models constructed in brass by Mr. Berge of Piccadilly, whose skill and exactness in executing works of this sort are well 40 known to the Public'. It is for the details of these models, rather
31 than his conclusions, that Atwood is of interest. There can be little
doubt that the idea of making a model was suggested by the Select
Committee questions discussed above, and he said;
Although the various properties of Arches described... respecting the weights and dimension of the wedges, and their pressures against the abutments, require no further demonstration than what has been given in the preceeding pages: yet, as it has been remarked, that philosophical truths, although deMonstrable in theory, have often been found to fail when applied to practice, in order to remove every doubt of this sort, concerning the theory of arches a model of an arch was constructed 41
Thus Atwood is following the fashion of demonstrating the validity of a theoretical solution by testing a model. In fact two models were made and these are shown in Figures 2.2 to 2.4. Such detailed drawings of structural models are exceptional at this period. The first model was of a semi-circular arch, 11.46281 inches intradel radius, with the brass voussoirs increasing in size from the crown to the abutments in a manner reminiscent of the absurd conclusion reached by La Hire, where the 'skew back' stones were required to be infinitely large. The arch was supported on a metal base having level-adjustment and the forces at a voussoir interface could be measured by means of the link, cord, pulley, and weight system shown. Atwood did not describe his technique but it is obvious from the drawings that the pulley could be moved up or down the vertical column on the right until the cord was normal to a radial joint. Weights (possibly lead shot) would then be placed in the can and the magnitude of the weight which would maintain the equilibrium of the semi-arch was compared with that predicted by theory. A 'flat arch' model was treated in the same manner but, in addition, the effect of changing the voussoir angle near the crown was investigated. These experiments are of interest in that they were not merely qualitative, demonstrating either stability or collapse mode, but were quantita-tive and adapted to measure forces. The experiments added little, or
32 Reference: A Treatise on the Construction and Properties of Arches,
G. Atwood, London, 1804 9 plate 1V. 2.2 Reference: A Treatise on the Construction and Properties of Arches G. Atwood, London, 1604, plate 1V. 2.3 Fig. 14. t
/ 1
Fig. 15.
Reference: A Treatise on the Construction and Properties of Arches, G. Atwood, London, 1804, plate V. nothing, to bridge design practice. Although inspired by the discussion of Telford's design for London Bridge, and indeed Atwood acknowledged his debt to 'Mr. Telford and several other engineers, who had had the 42 goodness to favour the author with their advice and assistance', it is clear that the models did not simulate the continuity of the proposed 600 foot cast iron arch.
Laminated Timber Arches
Models of this uncommon structural form first appeared in the late 1820's. John Green, a Newcastle architect, became interested in laminated arches of timber at this time and he built a one-twelfth scale model of a 120 foot span arch which he tested and found satisfactory. No contemporary details have been found of this early model but it must have been the one mentioned later by his son and discussed below. In 1835 John Green was appointed architect to the
Newcastle and North Shields Railway, a post requiring him to design several bridges and two large viaducts. The viaducts at Ouseburn and
Willington were each 1000 feet long and 100 feet high. During the construction of these viaducts the British Association for the
Advancement of Science held its summer meeting, in August 1838, at 43 Newcastle. John Green's son, Benjamin, read a paper at this meeting and this is the only source for the little information available about the model test. At the meeting Benjamin exhibited 'models on a large scale of the peculiar "lamination" of timber' and said;
With a model upon this principle for a bridge across the Tyne 120 ft. span, experiments were made in the presence of part of the Managing Directors of the railway, and some scientific persons, which proved highly satisfactory; for a weight of 250 stone was placed upon it, without the slightest deflexion of the arch being perceptible. This, multiplied by 144, according to the scale of the model gives 34,900 stone, or upwards of 218 tons, as the weight the arch of 120 ft. would bear without being affected. A great surplus strength was therefore manifest, to
33 cover all contingencies, and make allowances for the increased span and extra dimensions. 44
The factor of 144 would appear to be the square of the geometric scale 2 factor, that is 12 = 144 but as no further model details have come to light it is difficult to come to any conclusions about the role of this model in the design process. No design calculations however are mentioned in this or other cases of laminated timber arches built between 1835 and 1855 so it is possible that design was indeed based on the 1/12th. scale model of John and Benjamin Green.
W.H. Barlow's Paper on Arches 1846
Following the publication of Professor Moseley's book on 45 engineering analysis in 1843 there was a re-awakening of interest in the analysis of masonry arches. A good example of this was W.H. Barlow's lengthy paper to the Institution of Civil Engineers in February 1846 46 in which he referred to Moseley's 'able and elegant exposition on this subject' but expressed the doubt typical of the engineer's outlook;
though the investigations of Moseley leave little to be done in elucidating the conditions of stability in arches mathematically, yet the deductions have not received that attention from engineers which their importance deserves; chiefly from the absence of any decided practical exhibition of their correctness and utility, and also from the investigation being surrounded by too much mathematical difficulty, to admit of ready application. 47
Barlow's paper was divided into two sections; in the first he used models to demonstrate line-of-thrust principles and the second was devoted to the graphical construction of the curve of equal horizontal thrust. He demonstrated line-of-thrust principles by means of an ingenious model with curved-face voussoirs (see figure 2.5a).
If the original form of the arch be such that the line of resistance passes through the points of contact, no motion will arise among the voussoirs, on removing the centre: but if the arch be a segment of a circle, or any other form which does not coincide with the line of resistance, the
34 a) The Curved face voussoir model
b) The Semicircular Arch model
c) The triangular arch model
Reference: Proc. I.C.E., Voulme V, 3 February 1846, pp. 162-182: Plate 1. voussoirs will take up a new position, the curved surfaces of the voussoirs rolling on each other, to a certain limit, when they come to rest, and if disturbed from this position... they will return to it In this experiment it is obvious, that the pressure must be transmitted through the points of contact; and it affords a practical proof, that this line is the curve of equal horizontal thrust... The experiment admits of further application, by loading the arch so as to vary the form in which the pressure is transmitted ... it will be found, that the limit of stability is when the point of contact of any two voussoirs falls at their outer or inner extremities; thus establishing practically, that the line of resistance, or curve of equal horizontal thrust, must be contained within the thickness at every joint. 48 49 This graphic rolling-voussoir model had great appeal for practical men and was much more convincing than either Moseley's mathematics or indeed Barlow's own link polygon analysis. Various other experiments were made to test the condition that the curve of thrust must lie within the thickness of the masonry at every joint. A semicircular arch with thickness 1/9th. of the intrados radius was made in wood, firstly with four voussoirs (figure 2.5b) the joints being at e and f - the
points where theory predicted that the line of thrust touched the intrados and extrados respectively. This failed, as expected, with the crown falling and the abutments spreading. A similar arch was made in six pieces with joints at ab and dc, which was, of course, stable.
Three triangular arch models with wooden blocks were tested in a similar manner (see figures 2.5c and 2.6a). In addition Barlow made a model to demonstrate 'the analogy between the catenary and the curve of horizontal 50 thrust'. On a vertical plane surface an inverted semicircular arch was drawn with eighteen voussoirs of equal size. Through the centre of gravity of each block a vertical line was drawn (see figure 2.6b) then;
From two pins, fixed at p and p', a strong fine silk cord was hung, and eighteen pieces of chain, of equal weight, were attached to it, representing the equal weights of the voussoirs. This species of catenary was then adjusted, so that each of the chains hung opposite the vertical lines, and the
35 a) Triangular arch models
r
• C • /41
b) Cord catenary with chain loading
Reference: Proc. I.C.E., Volume V, 3 February 1846, pp. 162-182, Plate 1. 2.6 apex fell just within the thickness of the arch as shown on the figure. The similarity of the curve thus produced, to that of the curve of equal horizontal thrust, was immediately apparent. 51
This must have been a delicate experiment to adjust. An interesting extension of the experiment was made by removing the pin at p and extending the cord to another pin at P - the portion p c p' being retained in its original position. The line pP now represents the resultant of the vertical and horizontal components of the force at p.
This vertical/horizontal force ratio was found, graphically, to be
2.75:1. Subsequently an arch in brick was made and this ratio was confirmed experimentally. This cord and chain loading experiment was a unique blend of mechanical and graphical techniques and has been used in 52 this century. Brunel, Bidder, Cubitt, and Robert Stephenson all contributed to the discussion of Barlow's paper which occupied the whole of the following meeting. Cubitt considered the paper so conclusive that it scarcely needed comment but added, 'The great merit of the communication, and of the illustrations, was the adaptation to practice; 53 in most treatises on arches, the theory alone was considered'. But it was Stephenson who really summed up the mood of the meeting, expressing his conviction of
the useful character of the paper, which, he was convinced, would remove many difficulties hitherto felt in examining the subject by the process laid down by Professor Mofiley, whose formulae, though highly scientific, and no doubt very beautiful, were much too abstruse for the use of the practical man. Anything which tended to elucidate these formulae, and render the subject more popular, must be received with great interest by the Civil Engineer, whose labours would be materially facilitated by such clear adaptations of theory to practice. 54
Here again an engineer uses small-scale demonstration models in a reassuring role to clarify theoretical principles.
36 Model Experiments on Metal Arch Ribs
Although the Select Committee of 1801 had discussed the design of Telford's 600 foot span cast iron arch, the only model tests made at that time, those of Atwood discussed above, involved arches having smooth brass voussoirs. The metal rib with continuity was
pioneered at Ironbridge and we know little or nothing of its design or whether this was preceded by analysis - more than likely it was not.
Which makes it more surprising with such a novel structure in the late eighteenth century that no model tests were made. However, the bridge was merely designed for road traffic and the problem of the metal arch had to be faced anew with the coming of the railways.
When cast iron was introduced in railway bridges it was
principally in the form of beams having a limiting span of something 55 like 60 feet. For larger spans cast iron arch ribs were used and their continuity and elastic nature made for analytical difficulties.
In 1859 Thomas Chapp4 56 presented to the Institution of Civil 57 Engineers a paper on his experiments with elliptical cast iron arch models. Chappe was Assistant Engineer on the Midland Railway acting under W.H. Barlow at whose request the experiments were made. Two models were made; one of a bridge over the Trent near Newark, and the other of a bridge at Standish over the Great Western and Gloucester and Stonehouse Railways. The stated objects of the tests were for the purpose of 'ascertaining, practically, the safe load to which elliptical cast iron arches might be subjected, as well as the most economical 58 distribution of the metal'. Neither was achieved in these ill-conducted experiments. The first model was 'one-fourth the real size, of an arch of a bridge proposed to be erected over the River Trent, near Newark'.59
37 Although Chappe mentioned this geometric scale-factor he made no further use of in terms of similarity. He continued;
The (model) had a clear span of 14 feet 6 inches, and a rise of 16 inches: a camber of 1 of an inch being given in putting the two pieces together making a total rise of 16i inches. The sectional area of the arch at the crown was 2.43 inches; that of the curved rib near the springing was 2 inches; 'about midway between the springing and the crown it was 1.75 inch; and of the spandril 1.34 inch. The weight of each arch was 1 cwt. 2 qrs. 22 lbs. The experiment was conducted upon two ribs, placed 2 feet apart from centre to centre, and resting, at the springings on cast-iron abutment pieces. These abutment pieces were connected by two wrought-iron rails, having at one end a wrought-iron bar, 1 inch in diameter, passed through holes drilled in the rails, and at the other end fitted with wrought-iron cotters, by means of which the abutments were keyed- up tight, against the springings of the arch. At a distance of 16 inches from each end of the arches, cast-iron diagonal stays were bolted; longitudinal struts being also introduced to prevent lateral motion. On the top of the arches, cast-iron plates, 1 foot in width, were fixed at invervals of one foot. These plates had grooves on the under sides for receiving the top of each arch, to which they were firmly wedged. Between the joint at the crown, and also at the springings, a sheet of lead was inserted, to insure an accurate contact of the surfaces. 60
No drawings were published with the paper but figure 2.7 is based on this description. Chappe did not give details of the full-scale bridge so it is not possible to say if he maintained the scale-factor in all details of the ribs. The first thing to note is that although he was concerned with arches, in this case the curved rib was integral with the spandrel. In tying together the model abutments he prevented the system acting as a beam with a curved soffit. The rib was of extremely slender proportions and although the grooved loading plates and the bracing would have provided some lateral restraint, buckling, as we shall see, was the cause of failure. The experimental technique was to load the model with cast iron plates and pig iron, distributed as nearly as possible over the entire length of 15 feet 3 inches, and;
38 15'-3" overall cast iron load ~distributed load plates 1 foot 111111 L 111111111111111 ! 1111111111111111111111111111111111 wide at 1 foot 1" dia. intervals wrought iron bar -~~===~2=.~4~3'in~2~::=:==:::::::::::;;;;;==--t=---i 16 n+t"cambe r 2 in
rought iron rails wrought iron clear span 14'-6" cotter cast iron abutments
two cast iron arch ribs cast iron--..r- abutments
section through model
Chappe's River Trent Model ( t full size) - 1859 (based on written description)
Referecne: Proc.I.C.E., Volume XVIII, pp. 349-351.
2.7 The deflection of the arch was taken at intervals, by means of a straight-edge, accurately set to a mark on the outside flange at one end, and passing under a projecting piece of sheet-iron, fastened to the joint at the crown, registered by marks on the outside flange at the other end. The first mark was made before the arch was loaded equal to its own weight, or with 4 cwt. 61
This is not very clear but a probable interpretation is shown in figure 2.8. Chappe measured the progressive deflection with increase in load. With 20 tons distributed the crown deflected 1.625 inches and after thirteen days had increased by 0.07 inches. Eventually the load was taken up to 30i tons, when 'the spandril of one of the half-arches broke in two places; the fractures oething about ith of an inch'. 62
Chappe must have made analytical calculations as he added that with this load'The pressure at the crown was 8.52 tons, and at the smallest section of the arch 11.83 tons, per square inch of sectional area'. 63
He concluded that the fractures were due to faulty castings and appears to have lost interest in the experiment. He hit the model with a 14 lb. hammer on the side of the broken arch and dropped a half-ton 'monkey' on to the pig iron load; 'but no further fracture occured, although the 64 whole structure vibrated considerably under the blow'. The experiment was cohcluded without reaching the ultimate load of this model.
1 The other group of tests were made on a /6th. scale model of the Standish Bridge and were no more satisfactory. Here again, to facilitate the erection of the bridge, the ribs were cast in two pieces with a bolted joint at the crown. Chappe gave more details of this bridge and figure 2.9 shows the principal dimensions of bridge and model.
Using these details it is possible to check the accuracy of the scaling:
39 'projecting piece of sheet iron fastened to the joint at the crown'
'packing placed to receive the load in case of fracture' straight edge accurately located here
crown deflection d 1 straight edge in contact with underside of projecting iron deflection measured here ( d 4 d ) 1 2
Diagrammatic sketch showing Chappe's method of measuring deflection at the crown of his models of. the River Trent and Standish bridges — 1859.
Reference: Proc.I.C.E., Volume XV111, 1859. • 2.8
14'-4" overall
distributed load weight of each rib 111111111111111[111111111 111111111 1111 11111111111 1 3 qrs. 26 lbs.
1 1' —10" 1.25 int 2 0.993 in 1.055 in 13'-10-a" clear span
The Model ( 1/6th. full size)
86'-4"
joint at crown solid spandrel / . ,,,,,,,,,,..„...... „...... ------______11' 12'-6" 45 int
83'-4" clear span 1" 1- 8 • ir 12'-6" 5 cast iroo,C. arch ribs a.111 AIM 111•11 1' —6" in bridge 35' —0" 5" section through bridge
9"
rib section at crown
Standish Bridge ( near Gloucester)
Reference: Proc.I.C.E., Volume XV111, pp. 351-355. Chappe, 1859. a.9 STANDISH BRIDGE
BRIDGE MODEL FACTOR
2 83 '-"4 1000 , Clear Span 83'-4" 13'-10 /3" _ =0 2 13'-10 /3" 166.66
11`-0 " 132'- a Rise ' 11 '-0" 1 '-10" l'-10 = 22 = ''
2 2 4 2 Area of rib at 45 in 1.25 in - 36 = 6 1525. crown , 160 3 Weight of one rib 9 tons 3 qr.26 lb. = 183.28 = 5.68 20110
This shows that his one-sixth scaling of the span, the rise, and the area of the rib at the crown was exact, but other details were such that self- weight scaling was not maintained exactly. However, as he did not consider the relative strength/weight ratios of model and bridge this was not very important. In fact all he did was to load the inexpertly cast ribs with distributed and relatively concentrated loads in four experiments. The general details were the same as for the previous test.
Figure 2.10 shows the load configuration and the results of each test.
It is not necessary to consider each experiment in detail as they are of such poor quality - his detailed description of the first Standish model test (number 2) will suffice:
The load was spread over the entire length, 14 feet 4 inches, of the model, and was gradually increased up to 15 tons, when a small crack appeared on the spandril. This fracture never opened. It was caused by a lateral strain, owing to the arch bending outwards, in consequence of a small flaw and crack at the under side of the curved rib, not far from the springing, where the casting was slightly honey-combed. With this weight, the model had become much bent in plan, owing to the faulty nature of the half-arch in which the fractures had taken place, and which had bulged outwards considerably. The arches had also risen up the skew-backs about i of an inch. This weight of 15 tons, uniformly distributed, would give a horizontal pressure at the crown of 5.68 tons per square inch of section, and at
40 EXPERIMENT LOAD OEFLECTION REMARKS
® .applied 1S tons 5mall crack appeared in spandril. 1I:111J,11~1~~~111I11111I1 17 tons Arch bent in plan. c:: ~ 18 tons 1.48" 1 ton 'tupI lowored onto model - gave way' where casting was defective.
G) load of 6 tons 0.615" One of the arches broke a) railway through end upright in one half-arch and through top rib in the other. lilln~~I~~IIII11I1I111Ii1 8 tons 0.74" Other end broke at very nearly the same points - fractures in end uprights opened about 1/16th. inch. 12 tons After ten days. b) 22" fi load removed on haunches - C:CIl!iil!IIII!!I!I!!II_~ arch gave way, by faulty casting breaking autwards.
In putting the model together, the end upright cf one half-arch had been braken through.
Gave \oIay on the side of the broken spandrils.
3 tons 0.66"
3 t 17cwt Gave way, going bodily li t .ii!liii.!iI c:: sideways at the crown. The castings ••• were exceedingly brittle, having es 4 b been cast in damp maufds.
5 TAN 0 1 5 H 8 RIO G E M 0 0 E L
Reference: Proc.I.C.E., Volume XVIII, pp. 349-351, Chappe, 1859. 2.10 about midway between the springing and the crown of 7.15 tons per square inch. The weight was then increased up to 17 tons, when the defective casting was so much bent outwards, that it was dangerous for the men to approach. A 'tup', one ton in weight, was then lowered, by a crane, on to the centre of the model, and as the arch carried the weight, the 'tup' was removed, and one ton of pig-iron was added, making the load 18 tons. The 'tup' was again lowered, on to the centre, when the arch gave way, at the point in the curved rib where the casting was defective. Supposing the arch to have carried 18 tons, that weight would give a pressure at the crown of 6.80 tons per square inch of section, and at about midway between the springing and the crown of 8.58 tons per square inch. The greatest measured deflection was 1.48 inch. 65
It will be seen that the vague objectives, the quality of the castings and the method of conducting the experiments were so poor as to serve only to confuse the issue. Certainly Chappe was severely criticised by engineers attending the reading of his paper. Even W.H. Barlow, who had 66 initiated the tests, felt 'The results had been rather disappointing'.
Fairbairn, not surprisingly, felt' as a general rule, that wrought-iron was a preferable material for large railway-bridges, and that it was 67 both cheaper and safer'. Rennie considered that 'although the experiments were valuable in themselves, it would be difficult to draw conclusions from them' and added 'The spandrils might have been omitted in the model arches, because the experiments related to the arch and not 68 to the spandrils'. Henry Maudslay went so far as to say 'these experiments ought not to have been brought before the Institution,as 69 they were evidently imperfect and incomplete'. Robert Stephenson dismissed the whole subject by saying that although the object of the experiments appeared to be to determine the strength of cast iron arches he felt that;
no advantage could be gained by employing cast- iron, or even wrought-iron, in that form, for bridge purposes; and he thought the idea of so using either material had been long ago abandoned... the experiments were conducted upon
41 exceedingly bad girders; for nothing could be worse than the mode of forming the arch. 70
These experiments by Chappe in 1859 were the only such tests on model metal arches discussed at the Institution of Civil Engineers in the nineteenth century. They added nothing to the understanding of the subject and were soon overtaken by developments in mathematical and graphical techniques of analysis. Typical of this new emphasis was a lengthy paper read to the Institution in 1870 - 'On the Theory and 71 Details of Construction of Metal and Timber Arches'. It is significant that this entirely analytical paper was written by a French engineer, M. Gaudard, and made no mention of the need for model testing.
Typically, W.H.Barlow rose in the discussion and said 'in respect to a continuous arch, although the form in which M. Gaudard had brought it forward could be easily handled by mathematicians, yet it presented considerable difficulty to the practical man ... formula of such complexity had the effect of deterring many persons from entering on 72 the subject'. Barlow went on to mention the problems he had encountered in designing the roof of St. Pancras Station - a large metal arch, in which he should ' have been glad if he had been in possession of any practicable formula which he could have used in designing that 73 structure'. Although not strictly a bridge it is worth mentioning briefly that in his approach to the design Barlow made
a rough test model 1/18th. of the full size of the roof ... The clear span of the model was 13 feet 4 inches, and there were two ribs, each of a width of 1.625 inch, and a depth of 4 inches, making a total sectional area of 3i inches. Railway sleepers were suspended from the arch ... and upon them pig-iron was placed. 74
Barlow's model is shown in figure 2.11. Barlow and his various ideas and experiments appear regularly in this thesis and he justified his need for the St. Pancras roof model by saying that although this 'was a rough mechanical way of treating the subject', when 'there were such differences
42 - - - The depth of the rib was 4 inches, and the rise 5 fer.t 71 inches.
W.H.Barlow's model of St. Pancras Station roof — 1870
Reference: Proc.I.C.E., Volume 31, 6 December 1870, p. 165.
- between theory and practice, where conditions of flexibility were involved, that he thought it desirable to have some experiments, or a 75 crucial test of some kind to determine the question'. This exchange at the Civils meeting epitomises the differences in the French and English attitudes to structural design.
A year later, in 1871, William Bell presented a paper which pointed the way to future small-scale experiments where strain distribution would be measured directly. He admitted;
It would be somewhat difficult, by ordinary methods, to test satisfactorily the stresses on an arch rib, so as to compare them with calculation. Observations on deflection would give some information, but a model would necessarily be on a comparatively small scale... yet ... when it is desirable to know the stress which any part of a structure of model is sustaining, it is possible to ascertain this by direct observation. 76
Bell's measurement techniques are dealt with in detail in Chapter 5.
The growth of graphical and direct measurement techniques led to the rapid decline in arch model tests and none were made after 1859 in
Britain.
43
Arch Bridges
REFERENCES and NOTES
1. For an excellent survey of eighteenth century analytical work see: Coulomb's Memoir on Statics, Jacques Heyman, Cambridge University Press, 1972.
2.. Royal Society Library, London, John Smeaton's drawings, Volume 4, folio 175v. From the bar scales the scaling factor was: middle span, Westminster bridge = 120ft. = 1.12 middle span, Blackfriars bridge 107ft. 3. Parl. Pap. Reports (2), 1801, Volume 111: Report from the Select Committee upon Improvements of the Port of London, 3 June 1801, p.265.
4. Ibid. p.265.
5. Ibid.
6. The witnesses were:
1. Dr. Maskelyne 10. Mr. Rennie 2. Professor Robertson* 11. Mr. Watt* 3. Professor Playfair 12. Mr. Southern 4. Professor Robeson 13. Mr. Reynolds 5. Dr. Milner 14. Mr. Wilkinson 6. Dr. Hutton 15. Mr. Bage* 7. Mr. Atwood 16. General Bentham* 8. Colonel Twiss 17. Mr. Wilson* 9. Mr. Jessop * Made no reference to models in their evidence.
7. Parl. Pap. op. cit. p.267.
8. Ibid.
9. Ibid. p.278: Appendix No. 1 dated 'Greenwich May 9th. 1801'.
10. Ibid.
11. Ibid.
12. Ibid.
13. Ibid. p.289: Appendix No. 3, dated 'Edinburgh College, 27 April 1801'.
14. Ibid.
15. Ibid. p.290: Appendix No.4.
16. Ibid. p.297.
17.. Ibid. 44 18. Ibid.
19. Ibid. p.310• Appendix No.6 dated 'Woolwich, April 21, 1801'.
20. Ibid.
21. Ibid. p.309.
22. Ibid. p.310.
23. Ibid.
24. Ibid. p.314: Appendix No. 7.
25. Ibid. p.318: Appendix No. 8.
26. Ibid.
27. Ibid. p.321: Appendix No. 9.
28. Ibid. p.323: Appendix No.10.
29. Ibid. p.331• Appendix No.12.
30. Ibid.
31. Ibid.
32. Ibid.
33. Ibid.
34. Ibid.
35. Ibid. p.337: Appendix No.13.
36. Ibid.
37. Ibid. p.338: Appendix No.14, dated 'Bradley, 15 April 1801'.
38. Treatise on the Construction and Properties of Arches, GeOrge Atwood, London, 1801.
39. Supplement to a Tract entitled A treatise ..., George Atwood London, 1804.
40. Ibid. Preface dated 'London 29 November 1803', pp.vi and vii.
41. Ibid. p.12.
42. Ibid. Preface
43. Report, British Association for the Advancement of Science, Newcastle meeting, August 1838, Trans. of Sections, pp.150-152.
44. Ibid.
45. The Mechanical Principles of Engineering and Architecture, Henry Moseley, London, Longmans, 1843.
45 46. Proc. I.C.E., Volume V, 1816, pp. 162-182, 'On the evidence (practically) of the line of equal Horizomtal Thrust in Arches, and the mode of determining it by Geometrical Construction', by William Henry Barlow (3 February 1846).
47. Ibid. p.163.
48. Ibid. p.164.
49. Ibid. In designing the model there was one constraint: It is necessary that the radius of curvature of the voussoirs be made within certain limits, depending on the depth of the voussoirs and the radius of the arch; if too much curvature be given, the arch will fall, before the points of contact can take up such a position, as to coincide with the line of resistance.
50. Ibid. p.166.
51. Ibid.
52. Wren Society, Volume 16, Plate 11 to which the caption reads: Section of St. Pauls with catenary chains superimposed, Drawn by E. Stanley Peach, F.R.I.B.A. In Appendix; very fine watchmaker's chains were used in the experiment'.
53. Proc. I.C.E., Volume V, 1846, p.172.
54. Ibid. p.174.
55. See Report of the Commissioners on the Application of Iron to Railway Structures where opinions on maximum span of simple cast iron beams were given: I.K. Brunel 30 - 35 feet P.W. Barlow, R. Stephenson, and W. Fairbairn 40 feet W.H. Barlow and J. Locke 40 - 45 feet J. Glynn, C. Fox and J. Cubitt 50 feet H. Grissell 50 - 60 feet
56. Thomas Fletcher Chapp‘ (1824 - 1895); b. 3 December 1824, Hulme, Manchester. 1840: Apprenticed to Fairbairn. Assisted Hodgkinson on the Britannia Bridge experiments in Manchester. 1846: Assistant Engineer on the Midland Railway. Acted as Resident Engineer under W.H. Barlow on Gloucester Docks branch, the Birmingham extension, and the Stonehouse and Gloucester line (the relevant period). 1857: Partnership with brother-in-law in cotton spinning business. 1871: Retired to London. 1895: died 14 January.
57. Proc. I.C.E., Volume XVIII, 15 March 1859, pp.349-362:'Account of Experiments upon Elliptical Cast-iron Arches', by Thomas Fletcher Chappe, M.Inst.C.E.
46 58. Ibid. p.349
59. Ibid.
60. Ibid.
61. Ibid. p.350.
62. Ibid.
63. Ibid.
64. Ibid. p.351.
65. Ibid. p.352.
66. Ibid. p.356.
67. Ibid.
68. Ibid.
69. Ibid. p.359.
70. Ibid. p.360.
71. Proc. I.C.E., Volume XXXI, 6 December 1870, pp.72-174: 'On the Theory and Details of Construction of Metal and Timber Arches', by Jules Gaudard, C.E., Lausanne (Translated from the French by William Pole, F.R.S., M.Inst.C.E.).
72. Ibid. p.163
73. Ibid.
74. Ibid. p.164
75. Ibid. p.166.
76. Proc.I.C.E., Volume XXXIII, 5 December 1871, pp. 58-165: 'On the Stresses of Rigid Arches, Continuous Beams, and Curved Structures, by William Bell - pp.123-4 'Direct Measurement of Stress'.
47
BIOGRAPHICAL NOTES
MASKELYNE Nevil (1732 - 1811) Astronomer Royal (DNB)
Ed. Westminster School and Cambridge. 1754 B.A. 1757 M.A. 1768 B.D. 1777 D.D.
PLAYFAIR John (1748 - 1819) 'Mathematician and geologist' (DNB) 1774 Elected Moderator of Synod. 1785 Joint Professor of Mathematics University of Edinburgh. 1805 Professor of Natural Philosophy University of Edinburgh. Principal mathematical work: 'Elements of Geometry' (1795) 'Illustrations of the Huttonian Theory of the Earth'. (1802)
ROBESON John (1739 - 1805) 1766 Elected lecturer in Chemistry at Glasgow University. 1773 Professor of Natural Philosophy University of Edinburgh. 1783 Royal Society of Edinburgh founded - Robeson elected Secretary. James Watt writing on Robeson's death: 'He was a man of the clearest head and the most science of anybody I have ever known'. (DNB)
MILNER Isaac (1750 - 1820) F.R.S., D.D. 'Mathematician and Divine'(DNB) 1774 Mathematical Tripos Cambridge. 1774 Made Deacon 1776 F.R.S. 1777 Ordained priest 1783 First Jacksonian Professor of Nat. Phil. Cambridge. 1786 B.D. 1791 Deanery of Carlisle. 1792 Resigned Jacksonian Professorship and elected Vice-Chancellor of Cambridge University.
HUTTON Charles (1737 - 1823) Born Newcastle-upon-Tyne, youngest son of colliery labourer. Attended evening classes there. 1760 Opened mathematical school in Newcastle. 1773 Appointed Professor of Mathematics at Royal Military Academy, Woolwich, after open competition. 1774 Elected F.R.S. 1807 Resigned Woolwich Professorship after 34 years.
48
ATWOOD George (1746 - 1807) 'Distinguished mathematician' (DNB) Designer of 'Atwood's machine' for measuring acceleration due to gravity. 'possessed musical as well as mathematical accomplishments' (DNB) 1769 B.A. Trinity College Cantab. 1772 M.A. 1776 F.R.S. 1784 Left Cambridge. Pub.! 1801 - 'Dissertation on the Construction and Properties of Arches', with a supplemeht, 1804, written at the request of a Committee of the House of Commons, then engaged in considering Telford's plan for replacing London Bridge with a one-arched construction'. (DNB p.714).
TWISS William (1745 - 1827) General, Colonel-commandant Royal Engineers. 1795 Appointed Lieutenant-governor of the Royal Military Academy, Woolwich.
SOUTHERN John Manager, Boulton and Watt, Soho. Pub.: 'On the Equilibrium of Arches', especially in bridge building, in Phil.Mag. Vol.XI pp. 97-107. (Footnote, Musson & Robinson, 'Sc. and Tech. in the Ind. Rev.' p.172 n.5) See T.N.S. XXXI, 4, 8, 11, 13, 15, 17, 26.
DOUGLASS James Worked with Telford from 1799 - 1802 when he absconded and was not heard of until 1815 when Telford received a letter from him concerning his successful career in France. ('Smiles','Lives of the Eng.' Vol.11 footnote p.362).
WILKINSON John (1728 - 1808) 'Iron mad' Wilkinson, the Quaker ironmaster of Shropshire.
JESSOP William (1745 - 1814) Pupil of John Smeaton, canal and dock engineer (W. India Docks 1800-2). Engineer of the Surrey Iron Railway (1803).
49 Chapter 3
SUSPENSION BRIDGES SUSPENSION BRIDGES
The use of suspension structures as footbridges, of modest span, has a long history which need not be repeated here. However, in the early part of the nineteenth century many bridges were built in
America, France and Britain designed for the passage of horse-drawn vehicles. Compared with footbridges such structures required a greater degree of design skill to ensure stability. Eventually the demands of the railways were to pose problems for suspension bridge designers, for which there was no precedent, and which were never to be solved in
Europe.
The suspension bridge has several advantages over the traditional masonry arch structures. Its relatively light-weight construction made large spans possible, and the structural system being above the deck left unobstructed space below. This was an important factor leading to its adoption in cases where headroom was of prime importance. As a tension structure problems of lateral instability, later to be encountered in the compression zones of metal girders, did not arise. Under the action of dead load only tension structures are inherently stable. However, the price paid for structures with such favourable strength/weight ratios is lack of stiffness and it was undoubtedly the suspension bridge which first made designers face the distinction between strength and stiffness. The calculation of the necessary sizes of suspension links and hanger rods was, after all, an easy matter after the materials strength experiments of Telford, Barlow, and others had established the tensile properties of wrought iron. But to predict the response of the structure to live load was a more complicated matter. This first became a problem with the dynamic effects of wind loading on the earlier road bridges and was the cause of 50 several bridge and pier failures. Methods of making the deck sufficiently stiff to maintain the chain geometry under the passage of moving loads were increasingly discussed and became the prime consideration in the design of railway suspension bridges.
British model experimental work in this field in the nineteenth century can be divided into two phases. Firstly, the exploitation of wrought iron in suspension bridges capable of carrying vehicular traffic. This was in response to the growth of planned road systems in the early part of the century. In this period, model experimenters were pre-occupied with the properties of the suspension chain itself. Models were used to help resolve problems arising from variations in geometry, link material, and cross-sectional area of the chain. Road bridge models were concerned, quantitatively, with strength, and the stiffening effect of the road deck was considered only in a qualitative manner. Secondly, models were resorted to by designers in their attempts to adapt the suspension bridge to railway purposes. Here the pre-occupation was with overall stiffness. Models were built to investigate the effect of combining a girder with a suspension chain. These were amongst the last model experiments recorded in Britain in the nineteenth century. The models that were made to help achieve all these objectives will be discussed here in chronological order.
The Proposed Suspension Bridge at Runcorn
The earliest reference to a model test in connection with suspension bridge design relates to the proposed bridge over the Mersey at Runcorn undertaken by Thomas Telford in 1814. A petition to
Parliament was drawn up in 1813 to bring in a Bill to establish the
51
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(Institution of Civil Engineers Library) 3.? These tests on the tensile strength of wrought iron were made 'both in regard to elementary parts, and also when combined, partly by 6 welding, and partly by jointing in a model'. Those relating to the
'elementary' parts were carried out with a hydrostatic press at 7 'Mr. Brunton's patent chain-cable manufactury, Commercial-Road, London'. The tests made with 'different degrees of curvature' were conducted • 8 with the link-polygonal apparatus shown in figure 3.3. The tests sought to establish the suitability of the material for suspension bridges and he subsequently proceeded with a design and a model - but whether the model was made at Brunton's works is not clear. Telford was assisted by James Rendel who, ' At an early age ... went to London, and obtained an engagement, as a surveyor, under ... Mr. Telford, by whom he was employed on the surveys and experiments for the proposed suspension bridge across the Mersey at Runcorn'.9
Telford's crucial statement about the model test is the prime source of evidence:
I constructed a model of 50 feet in length, and one twelve hundredth part of the strength of the intended bridge, and although composed of wire only, and of course, without proper Joints or Braces, it bore 3000 lbs. without any sympton of its parts being deranged. 10
Several questions arise from this; firstly that of the geometric scale of the model. Telford's design was for a bridge having a central span of 1,000 feet together with two side spans of 500 feet each - making it a bridge of unprecedented span. When he said ' a model of 50 feet in length' we cannot be certain if this included all three spans; although W.A. Provis was more specific saying ' a model of the central 11 opening was constructed' and this is certainly more likely and logical. 50 1 If so, the geometric scale factor was 1.455,5 _ 20 or 20:1 so far as the span was concerned, but unfortunately we have no further details of the model. Secondly, as Telford loaded this model it indicates that it was 53
B 0 C
LS V
' Here RS, TV, represent the supporting pillars upon which the wire was extended; QS, another prop, over which the wire passed; being placed at such an angle as made it coincide with the direction of the resultant of the vertical and horizontal tensions, in order to prevent any strains upon the other support, RS.
A, B, C, D, represent the places of the several weights with which the wire was loaded; C being in the centre of the length, and 8 and D at one quarter of the length from each end; and the deflections from the horizontal line RT were measured at these points, as the different weights were applied'.
Telford's Wire Test Apparatus
Reference: Life of Thomas Telford (Autobiography) Ed. by Rickman, 1838. p. 555. 3.3 not merely of the visual type, and indeed we know that another, 12 smaller, model was made presumably for this purpose. Lacking details
of the model chains it is difficult to understand what Telford meant
by describing the model as being 'one twelve hundredth part of the strength of the intended bridge'. In using the word strength we may
reasonably assume that he is concerned with the breaking stress of a
member subjected to pure tension. In which case a square law relates
the tensile stress to the geometric scale factor. If we assume 1 Telford's span scale factor to be 02th. and that this factor was also 20 used to scale down the dimension of the proposed chain then the model 1 would have been Tobth. (i.e. ) the strength of the full-sized 20 structure. The chains of this model were, however, 'composed of wire
only' and 'without proper joints' and unless the geometric scale factor 1 1 for these was it is difficult to add anything to 34.6 1200 Telford's statement relating the strength of his model to that of the
full-sized structure. The model was loaded up to c.3,000 lbs.,
'without any symptal of its parts being deranged'; in other words it was
not tested to destruction, and indeed Provis added that it 'would have 13 carried considerably more without being injured'. After the tests
Telford said: 'This far I proceeded in 1814. I was perfectly convinced
of the practicability of the scheme, and am now satisfied I went further than necessary in the quantity of material, and also as to sundry precautions in forming the plan, but I was willing to err on the 14 safe side'. Telford's design for the chains exist; they were to
consist of '16 iron cables, each formed of 36 square half inch iron
bars; and of the segments of cylinders proper for forming them into one immense cylindrical iron cable, which was to be nearly half a mile long
(including the fixings on shore), and about 41 inches diameter'. 15
54 The bridge Committee met several times in the spring of 1817
and Telford was again consulted to help them decide on various
proposals. He was convinced that a suspension bridge was the only
possible solution and reminded them that he had 'already prepared a 16 Design and Model', and offered his Report gratuitously. Telford
mentioned only one other scheme submitted:
it is that produced by CAPTAIN BROWN only which corresponds to the principle adopted by me in 1814; that is to say, Suspension by malleable Charcoal Iron, preserved as nearly as possible in straight lines ... His perpendicular Suspenders, Cross Ties, and diagonal braces, correspond precisely with mine. His main suspending lines of the upper Curve, instead of being composed of a number of flexible rods, as in mine, consist each of one Rod or Bar of malleable Iron united by Forelocks. From four of these it was proposed that the whole structure should be suspended. 17
It is interesting to note Telford's preference for charcoal smelted
iron. Captain (later Sir) Samuel Brown's interest in the applications 18 of wrought iron chains led to his Patent of 1817, relating to
suspension bridges. During 1808 he had made a series of experiments on
the 'comparative strength of bolts and bars and chains of different 19 descriptions' at his works on the Isle-of-Dogs in London. His
catenary design involved replacing ordinary chain links with long bars
having forged eyes at their ends, connected by pins in shear, reducing
both the weight of the chain and the number of connections. After the
1808 experiments he made 'drawings and calculations of the strength of
bridges of suspension' but was too busy to test the design experimentally 'on a scale commensurate to its importance' until 1813;
when I constructed a bridge of straight bars for this purpose on my own premises ... The span or extent of this bridge is one hundred and five feet, and although the whole of the ironwork weighs only thirty-seven hundred weight, it has supported loaded carts and carriages of various descriptions. 20
No further details of this small-scale bridge have emerged but we may reasonably assume that its chain configuration accorded with his 55 recommendation that they should 'rise or have a versed sine, in the 21 proportion of twenty feet in a thousand feet of length'. This gives
a very shallow curve producing a large horizontal force component on
the tops of the supporting towers. Brown claimed a favourable
strength/weight ratio for his bridge and it is worth noting that he
never used the word model in describing it. Both Telford and John
Rennie visited Brown's works and use the model in describing the bridge.
Mentioning it to the Runcorn Bridge Committee in 1817 Telford said
'Your Solicitor and I examined this model and drove a Hackney Coach over 22 it'. John Rennie, when questioned on iron suspension bridges in 1819,
said 'the only thing of that kind that I have seen is a model that was
made by Captain Brown ... over which I was drawn in a carriage, and 23 found myself perfectly safe and easy'. In addition he noticed 'very
little vibration'.
Telford and Brown met in London and exchanged ideas on
suspension bridge design. Both considered the Runcorn scheme
practicable but 'although the Committee reported favourably upon the
scheme, and subscribed liberally to a guarantee fund, nothing further 24 was done'. A thousand foot span bridge was obviously ahead of its
time and John Nicholson said; 'The size, and I may say, the daring character of this project frightened the capitalists to whom it was proposed; but it had, at least, the advantage of drawing public 25 attention to this new species of construction'. Other bridge and tunnel schemes were subsequently proposed but the Mersey was not bridged at Runcorn Gap until the transporter bridge was built in the first decade of this century. 26
56 The Proposed Suspem7ion Bridge at Montrose
The next suspension bridge design containing a brief reference to a model is that of George Buchanan - a civil engineer born in Montrose and a lecturer on mechanics at the School of Arts,
Edinburgh. In 1821 he published a 'Report on the Present State of the
Wooden Bridge at Montrose, and the practicability of Erecting a 27 Suspended Bridge of Iron in its stead'. The Report contains full details of the proposed bridge over the Esk with a single span of 420 feet and a versed sine of 60 feet - much steeper than that advocated by
Samuel Brown. Buchanan was particularly concerned with achieving adequate stiffness in his bridge and said; 'Besides that motion which takes place in suspended roadways from side to side, we must equally guard against any vertical undulation to which such a roadway may be 28 subject'. He attempted to achieve this by having vertical longitudinal iron plates beneath the decking, using the side railings, and multi-strand chains comprising 11 inch diameter rods 15 feet long.
In addition, between the vertical suspender rods he proposed to:
extend a similar series of rods horizontally ... so that these horizontal rods, interweaving with those which hang vertically, the whole space directly under the chains, and between them and the roadway, will be filled up by a kind of net or wirework, on a large scale, and which, without interrupting the view, will yet communicate a remarkable firmness and steadiness to the roadway, the reason of which may be easily shown, and has indeed been experienced in the model which I have constructed. 29
This is the only reference to the model and we therefore have no
knowledge of the scale factor, whether a load test was made, or indeed
whether this was anything more than a visual model. Even a small-scale
model would demonstrate a qualitative increase in stiffness which is all
he is claiming for his chain configuration. Buchanan's bridge was not
built and the first suspension bridge at Montrose was that of Samuel
Brown built in 1829 and destroyed in 1838.
57 The Menai Suspension Bridge - Chain Geometry Model
There is no evidence to suggest that Telford made a structural load test on a model as a preliminary to his Menai Bridge
design. He would have gained valuable information relating to strength
from his Runcorn model and tests on wrought iron a few years earlier, indeed these results were repeated in evidence to the Select Committee 30 which recommended the building of the Menai Bridge. Nevertheless, he
did make a quarter-scale model in 1823 to help resolve problems of the
chain geometry. W.A. Provis, Telford's resident engineer on the bridge, said;
In order to get the lengths of the ordinates or vertical rods which were to suspend the roadway from the main chains, a model was made of a single chain to a scale of one-fourth of the real one, and a set of boards on edge, curved to the intended rise of the roadway, were placed below it. Between these the perpendiculars were measured at every joint of the chain, which became the standards for making the rods of the vertical suspenders. 31
The model had a chord line (or span) of 142 feet 6 inches, a versed sine of 10 feet 9 inches, and the chain comprised links 2 feet 64
inches long. Provis published a 'Table showing the lengths of the
vertical suspending rods and their horizontal distances from each 32 other'. In this measuring exercise no load was applied to the chain
to simulate the decking and hence the 'intended rise of the roadway'
did not take into account change of chain profile due to its weight.
However, any differences due to this interaction could most likely be accommodated by screw thread and nut adjustment at the ends of the suspender rods. Provis explained the reason for using this type of
model very succinctly when he said; 'It is true their ordinates might
have been determined by calculation, but with a practical man an
experiment is always more simple and satisfactory than theoretical 33 deductions'. Whereas Drewry, in his Memoir of 1832 commented;
58 In reality, those lengths cannot be calculated with perfect accuracy, because, ... the chains of a bridge are neither a pure catenary nor a pure parabola, and their curve varies in every case; hence, when it is possible, the lengths of the vertical rods should be determined by experiment. 34
Nothing could illustrate more clearly the type of dilemma leading engineers.to use a model. Opinions differed as to whether calculation could provide the required data, and even Provis (a practical man) who felt that it could, nevertheless felt it 'more simple and satisfactory' to use a model. The expense of a model was justified on the grounds of the reassurance, or peace of mind, which it bought.
Wood as a Material for Suspension Chains
An episode worthy of brief mention was the model test made by Charles Drewry in order to investigate an alternative material for the chains of suspension bridges. In his well-known Memoir of 1832 he made out a case for using wood in place of wrought iron for chain links. He admitted it would rarely be desirable to seek a substitute for iron, but for bridges 'erected in remote places, particularly 35 abroad, where iron and mechanics are not easily or cheaply procured', and for lightly loaded structures, wood might be a useful material.
Wood, used as a material for making the chains of a suspension bridge, is in some respects superior, in others inferior, to iron. The advantages are, that, weight for weight, its absolute strength is greater than that of iron, and that it is worked more readily and with fewer tools. 36
He proposed joining the wooden links by means of binding with rope the tapered ends (see figure 3.4a) and it was to test the efficiency of this method that he made his experiment. As he put it:
59 No. 2.
No. 1.
C No. 2.
( a)
I J a a .1 —.A 4—
iss..•■■•■\ N
( b )
TARLE OP EXPERIMENTS ON WOOD CHAINS.
Load falling Nomb.1- of , Load in Momentum of the fardog o;■an. De cLtio • o n Remarks. Exp..; imods. 1 1. 3- Weight.ei‘tt Weight. ' ' the Platform. 15 inch- u•;, or 2tId • feet.
26 inch s. none. MO lbs. through ( ./1.5 x 8.01 x 1301bs.=) 1274 lbs. No inj:.ry. 18 inches. 11. none. 150 lbs. through 1726 lbs. One of the wood-bars tont in two. 33 inches. 26 incite.. 52 lbs. 130 lbs. through 1735 lbs. No injury done. 34 inches . 1V. 22 hudies. 52 lbs. 130 lbs. through 1645 lbs. One of the wood-birs torn in two. 30 inches. v. 21 inches. 52 lbs. 130 lbs. through ' 1735 lbs. No injury.. ' 34 inches. While the weight remained steady, no. 4 persons, thing gave way. On sw;tying up and VI. 26 inches. none. - - about 580 lbs. - - dawn, one of the wires broke. The fastenings remained sound. Same, with ad- While at rest, the bridge bore the VII. 26 inches. ditional 52 lbs. ------weight. One person jumpit:g brck4. =6321bs one of the iron wires. One of the wood-bars was torn in two VII1. 23 inches. none. 130 lbs. through 1697 lbs. .{ pieces' . The fastenings remined sound. 32 inches.
In tin• course of these trials, the fas enings of the bats, No. 1. drew considerably, but did not give way. Those of the bars No. 2., in Which the inc iliation of the ends was more rapid, (lid not show any symptom of derangement.
( c )
Reference:
A Memoir on Suspension Bridges, Charles Stewart Drewry, London, 1832, pp. 156 and 158. 4 The author has tried this mode of fastening in a model 261 feet span ... The bars of wood were 14 inches long, out and out. Of two kinds, viz. No. 1 of good pine, :1-inch square in the middle, with solid wedge ends lith.inches deep, and 1)2 long. Some of the bars No. 1 were bound together with seven turns of common cord, of barely ')/16ths of an inch diameter; others with iron wire• some had notches cut in the back, to receive the cord; others were left quite smooth. The bars (No.2) were of very common fir, 1 inch deep by iths in the middle, with solid wedge ends 2 inches deep and 2 inches long. 37
The middle 8 or 10 feet of the span was made of the wooden bars, the remainder being iron wires (see figure 3.4b). The results of his experiments are given in Table 3.4c. The model was loaded with both static and dynamic loads and it is obvious from experiments 1, 2, and 8 that he ignored the self-weight of the model in his 'Dead Weight'. He calculated the momentum of the dropped weight correctly although he expressed the result in 'lbs'.
For example: Momentum = m X v =m4 2gh
For experiment 1: 18 inches = 1.5 ft. TTE . .,.. 8.01 (gives 2 g = 32.08 ft/sec ) therefore, as he gives: momentum = 1,5 X 8.01 X 130 = 1274 lbs.
Drewry made no attempt to calculate an equivalent static load and combine it with the dead load but merely uses the relative momentum in each case for the purposes of comparison. In experiments 6 and 7 he introduces four people as loading who obligingly acted as both dead and live load. There is no evidence that Drewry's work on wooden chains had much impact even on military engineers who might have been expected to use such bridges for temporary structures.
It is interesting to note that at the same time that Drewry was discussing wood as a substitute for wrought iron, a speaker at the summer meeting of the British Association in Oxford said:
60 I am very desirous of calling the attention of the scientific world, and particularly of Civil engineers, to the serious consideration of the question, - How far ought iron to be hereafter used for suspension-bridges, since it is ascertained that a steel bridge can be built of equal strength, and superior durability, with one third or one fourth of the weight of an iron one, and at a much less expense, .... The only doubt of this being practicable on the large scale, arises from the circumstance, that in this country iron is made with mineral coal, but in Styria with charcoal of wood. 38
This echoes Telford's expressed preference for charcoal-smelted iron and the speaker added; 'I have calculated that upwards of 1000 feet span may with confidence be depended on'. This was Telford's planned span for the avant-garde Runcorn bridge but at that time the largest -- span built in Britain was 579 feet in the MenPi bridge.
James Dredge and the Taper Chain Controversy
In the 1830's a proposal to span the Avon at Bath with a suspension bridge led to an interesting discussion on chain design.
The common chain form at that time was that of Telford and Brown discussed above. They comprised an equal number of links between the pins giving the chain a uniform cross-sectional area throughout the span. In James Dredge's designs the area of the chain decreased progressively from the points of suspension towards the centre of the span. Although it can be argued that the idea of matching the area of 39 the chain to the tension was not Dredge's, his name became inextricably identified with the idea. A typical Dredge bridge is shown in figure 3.5.
The Victoria Bridge Company of Bath invited designs for a bridge in the centre of the City and two local men were the principal 40 41 contestants - James Dredge, and Thomas Motley. Dredge's design was chosen and the Victoria Bridge was built in 1836 on his Taper chain 61
■
A.
3 E
1
)1r11 i t
Typical Taper Chain Bridge of James Dredge
Reference: The Surveyor, Ennineer, and Architect, June 1840, p. 100. 3.5 principle and is indeed still standing. The span was 150 feet, versed
sine 25 feet, weight of chains 5 tons, with a platform width of 18 feet.
Motley, extremely bitter about the rejection of his scheme, entered on
a long exchange with Dredge in the Bath Journal. Dredge claimed a
superior strength/weight ratio for his system and made experimental
models to demonstrate its performance. He was a great propagandist
and the discussion extended for nearly ten years in the technical press
and elsewhere. How this west-country brewer became interested in
bridges is not clear. We know that he submitted a design in the 42 Clifton Bridge competition of 1829-30 and had erected a bridge over 43 the Leven at Balloch Ferry in 1832.
In 1836 Dredge took out a patent for 'Certain improvements in
the construction of suspension chains for bridges, viaducts, aqueducts,
and other purposes'. His improvements comprised two distinct parts,
namely; 'the construction of a chain ... which shall diminish in
breadth and weight as it recedes from the point or points of suspension;
also the construction of a bridge or other suspended erection by means
of such chains in connection with inclined suspension rods supporting 44 the platform'. Inclined suspender rods had previously been proposed
by Poyet in France and the combination of these with the taper chain in
Dredge's model tests helps confuse his argument. When the patent was
enrolled the Victoria bridge was under construction and the loyal local
press considered the structure 'well worthy the attention of the
scientific' and 'equally suitable for a large as a narrow span and the
certainty of strength insured to the satisfaction of any one who maybe 45 able to know that two and two make four'. Not everyone had such faith
in Dredge bridges. The first reference to models in connection with the design appears in a letter from the disappointed Motley to the bridge
Proprietors in July 1836: 62 You are most of you aware that the project of the bridge originated entirely with me, and that I have been more or less engaged for more than 12 months endeavouring to get the object effected, and that I have incurred considerable expense in journies to Bristol, Marlboro', &c. &c. to produce what was deemed needful information, and also that a heavy expense has been incurred for models, drawings and experiments, with which all parties appeared satisfied except James Dredge, brewer, and Isaac Wilson, dentist, to whose conduct I unquestionably attribute the rejection of my plan. 46
This gives an insight into the way in which bridge design competitions were managed at that time. No further information regarding Motley's design work has materialised, but that he was thinking in terms of a load test on a model we know from a letter written a week later urging the Proprietors to;
direct some proper disinterested party to make a model upon J.D.'s first plan, beginning with eight bars and ending with two, or his second plan of beginning with ten bars and ending with three, and another model on my plan, to contain exactly the same quantity of material, each party to have the superintendence of his own plan, then appoint a time for trial, and I will engage that my model shall sustain at least double the weight which J.D.'s will do. 47
The confident Motley added a postcript saying; 'If you object to the expense (two or three pounds) I will propose that J.D.'s model may be loaded till it breaks, and I will then arrange the same materials and 48 make it sustain double the weight'. In the subsequent argument it was never suggested that a model should represent, to scale, a particular bridge so the question of similarity does not arise. He merely proposed using two models to adjudicate the rival claims of the two protagonists.
But he was not even comparing like with like. In a Motley bridge the roadway was supported by a series of inclined parallel rods connecting the deck to the towers without a catenary. They were, in fact, not suspension bridges but highly statically indeterminate stayed-girder bridges. He built a bridge of this type over the Avon at Twerton of 120 foot span which was described as being 'Superior to the common suspension
63 bridge, in that it is more firm, and experiences much less friction, 49 owing to the absence of vibration'. After this, Motley the 'Grocer,
Tea Dealer, and Bridge Designer' 50 withdraws and we must return to the subsequent work of James Dredge.
No evidence suggests that Dredge used a. model test to justify his designs for either the Clifton or Victoria bridges, and it was not until the beginning of 1838 that he began his series of much-publicised tests. Considerable discussion followed the communication of his results to the press - invariably in a letter drom Dredge. His experiments compared the strength/weight ratio (unlike Motley he did not specifically consider stiffness) of parallel and taper chain models of the same span/versed sine ratio, each containing 9 oz. of iron wire
(exclusive of hanging rods). The first trial was made in Bath on
2 January 1838 with two models of 4 feet 6 inches span, 6 inch deflection, and a platform 2 feet wide. His amusing results were given as follows - the parallel chain model 'broke down when loaded with six sacks of horse beans' and the taper (or mathematical) chain model 'Bore six sacks of horse beans, 7 sacks of malt, 2 cwt. cast iron, and 11 men, 51 all this did not break it down'. Considering the loading material it is to be assumed that the experiment was carried out in Dredge's brewery using materials to hand - but how, in addition to the inaminate load, he got eleven men on to the platform of so small a model is difficult to imagine. This test was witnessed by 'Messrs. Worsams from 52 London, Ball, Cambridge, and others of Bath'. These unscientific results were presumably sufficiently dramatic to demonstrate something in favour of Dredge's scheme but this must surely be discounted as a serious, well-conducted, experiment.
64 In the following fortnight three further tests were made on models of the same size in Bristol, 'in the presence of several eminent, commercial, scientific, and literary men, with attendent engineers to 53 superintend the uniform loading of the model bridges'. This suggests the exercise of greater care in these tests, the result of which are given in Table 1. No additional information on the loading technique has been found but perhaps the consistently large difference in favour of the taper-chain models (approximately 2A:1) renders a detailed study unnecessary. For the experiment of January 6 (A) he commented that
'both broke on adding the subsequent 1 cwt.' which does not suggest small increments in the 'uniform loading',although the load carried is given in quarters and pounds. This trial was witnessed by 'Messrs. 54 Protheroe, Guppy, and others'. In the experiments of January 13 (B and C) the models were both broken on adding A cwt. revealing inconsistency in the loading method. The models for experiment C were
'constructed by Mr. Cross of Bristol, unknown to Mr. Dredge, in order 55 to prove that all was fair in the former trials'. These performed 56 considerably better than those made by Dredge to the identical specification and we may therefore assume that Cross was the better craftsman. These tests were witnessed by 'Messrs. Acraman, Daniels,
Hillhouse, and many others of the first merchants of Bristol, Dr. 57 Waldren and many others of Bath'. These model tests were made at a time when research was not undertaken behind the closed doors of a laboratory and Dredge's meticulous lists of those present lend the events an atmosphere of theatre. He made an important statement which may be deemed as renouncing any claim to have considered similarity between model and full-sized structure. 'It now remains for scientific men to demonstrate why the same result should not take place in the 58 largest chain piers and bridges'.
65 In the early part of 1840 Dredge came under the influential patronage of Lord Western. On Thursday April 30th. he said 'On
Saturday last I introduced Mr. Dredge, the inventor of the improvement in bridge-building, to the Marquis of Northampton, at his evening assembly; He brought his models and drawings with him and they 59 attracted great attention and admiration'. This was, presumably, a mere divertisement on a social occasion but, more importantly;
On the Monday morning following a trial of strength of the old system of building relatively to Mr. Dredge's, with two models of bridges, each formed out of the same weight of iron wire, namely six ounces, was made in the Marquis's garden, the Marquis and Lord Compton and others present. The model upon the old system was first loaded. It bore 18 half-hundred weights, and with the next half broke down. The model formed upon Mr. Dredge's principle sustained 34 half-hundreds, when upon the addition of another half-hundred, the wooden structure on which the chains were hung (answering to the towers of masonry, which form the fulcrum of suspension bridges) gave way altogether, and the bridge came down, but the chains were unbroken. 60
No further details have been found, but comparing the weight of the chain with other Dredge models the span must have been between 5 and 6 feet. Western enthusiastically embraced Dredge's principle and publicly claimed that 'Mr. Dredge can build bridges on his plan at one-third the expense of the present method; he requires only one-third the quantity of iron, and his bridge will be stronger and freer from vibration and 61 pendulous motion'. On behalf of Dredge he wrote a long letter to the
Prime Minister, Lord Melbourne, which was published in The Times, and 62 subsequently widely discussed. He described the model tests at Bristol
(giving the results a very wide audience) and mentioned the 'prudent caution' of clients:
Mr. Dredge's principle of suspension bridge building completely overthrows the theory and practice of a Telford, a Brunel, whose experience and talents we are bound highly to respect ... can we then be surprised that the public should evince some fear, and some reluctance, hastily to adopt Mr. Dredge's novel principle or theory, in substitution of that which has been so long acted upon? 63
66 He went on to say 'No human was ever exempt from error, and Messrs.
Telford, Brunel, and others, must not be considered to be infallible'.
But his main plea as Dredge's advocate was that he should be allowed
to repeat his model experiments before the Prime Minister, the Menai
Bridge Commissioners, or 'any of the most eminent engineers'. In
addition he claimed that Dredge would repair the storm-damaged Menai
bridge, at his own expense, and that the superfluous iron of the bridge
would pay him and give a balance in favour of the Government. This
dramatic claim, appearing in The Times on the last day of April 1840,
must have initiated the experiments made in London during May and June.
What information is available on these is contained in Table 1
(experiments D and E). That of May 19th. was made at the Royal Gallery
of Science, Adelaide Street, with two models somewhat larger than those
used at Bath and Bristol:
The first experiment was with a model constructed with two chains on the ordinary principle, each consisting of 3 wires laid parallel to each other ... to which by the aid of vertical wires ... a platform of wood was suspended, this platform was loaded with 7 full grown persons, and upon the eighth getting on, it broke down. The wire chains were fractured at the point of suspension. The weight of the wire in this model was 61 ounces. The next experiment was with two wire chains consisting of six wires at the point of suspension, and diminishing off to one in the centre ... these chains supported by suspension wires placed obliquely the platform which was loaded with 11 persons, without producing any fracture, until one or two of the party stamped on the platform, when it broke down, the fracture taking place at the junction of the oblique wires with the chain of suspension. The weight of the wire in this model was only 6 ounces. 64
Here, as at Bath, there was no precision in loading and this was
obviously undertaken as a dramatic public-relations exercise. The main
point of interest is that not only are the parallel and taper chains
compared, but the effect of vertical and inclined suspender rods. In
a letter of August 1840 Dredge claimed his experiments had been made '65 'before the President of the Royal Society, and other noble lords 67 and this must have been at the Royal Gallery of Science. In the following monthg he made his last experiments at the College of Civil 66 Engineers, Gordon House, Kentish Town, London. He again resorted to a human load and the parallel chain model 'gave way when only nine persons were standing still upon it, while eighteen persons standing on the tapered chain, had to jump before they could produce a fracture, the momentum of which must have been equivalent to a very considerable 67 addition of weight'. A more interesting experiment was made to demonstrate the relative performance of vertical and inclined suspender rods and was shown:
in a model constructed for that purpose. This model consisted of the chains, with a spring-beam, or steel- yard at the centre, a flexible piece of timber for the roadway, and cords for the suspension rods, which could be arranged either vertically, as in chain bridges of the old construction - or diverging from the centre as in Mr. Dredge's improvement. When the cords were arranged vertically and the roadway pressed down, the strain ... was shown by the action of the spring, which, when Mr. Dredge pressed down the roadway with both his hands, indicated a weight of 30 or 40 lbs. straining on the centre. When the suspension cords were arranged obliquely ... the whole chain was called into action; and although the roadway was pressed down with equal or even greater force than before, the spring steel-yard remained quiescent. 68
The steel-yard is the first reference to Dredge using a measuring instrument in conjunction with a model but the loading method was again hopelessly imprecise. No details of span, versed sine, or platform width were recorded for this experiment but it would seem to have been only a small demonstration model. 1840 was the year which saw the most extensive discussion of Dredge's ideas, no doubt initiated by
Lord Western's letter to The Times.
During 1841 the debate about Dredge's system continued and five modest footbridges were built to his design in Regent's park. In
July a journal published an article by Common Sense on suspension
68 TABLE 1, THE MODEL TESTS of JAMES DREDGE in BRISTOL and LONDON
MODEL INFORMATION
CHAIN DATA VERSED PARALLEL CHAIN TAPER CHAIN DATE LOCATION SPAN N 0 T E S SINE Weight Susp. Load Weight Susp, Load Iron Rods Sustained Iron Rods Sustained
cwt. Q. lb. cwt. Q. lb. 'both broke on adding the Jan. 6 Bristol 4'-G" 6" 13 3 25 34 1 25 subsequent 1 cwt', (Ref.2) 1838 (A)
Jan. 13 Bristol 4'-6" 6" 13 0 0 33 0 0 'each broke on adding the 1838 subsequent i cwt.'(Ref.2) (B)
Jan. 13 'each broke with another i cwt.' Bristol 4'-6" 6" 23 2 0 61 0 17 1838 * ** (Ref.2) (C) 'Models made by Mr. Cross of Bristol'. (Ref. 2) _/. May 19 Royal 11 persons 5'-8i" 8i" 6i oz. Vert. 7 persons 6 oz. Obl. 1840 Gallery + dynamic (D) of Science load
June 13 College of Steelyard used to measure load. 1840 Civil 9 persons Obl. 18 persons Cords used for suspender rods. (E) Engineers .
REFERENCES: 1. Bath Herald January 27 1838 p.3 . * Given as 23 cwt. in Ref. 3 2. Mechanic's Magazine March 24 1838 p.423 . ** Given as 61 cwt. in Ref. 2 • ,3. Mechanic's Magazine October 1838 p.54 4. Mechanic's Magazine July 1840 p.122 5. Civil Engineer and Architect's Journal June 1840 p.194 - bridges which extolled the virtue of Dredge bridges but had reservations about data which could only be obtained by experiment!
experiments in such matters are not always to be trusted. They are usually made by means of models vastly smaller than the structures that are to be erected. Independently of this, it is difficult to get them done by the proper parties, or in the proper manner. The experiments of engineers are but too frequently made, not for the purpose of obtaining such results might turn out, but in order, if possible, to obtain some result previously desired by the . experimenter; and in such a case, but small reliance can be placed on them. 69
Common sense indeed. The mathematical reasoning associated with the taper-chain principle is not strictly within the scope of this thesis, but it is important to note that it did receive attention. In 1841
William Turnbull published a treatise which attempted 'To trace the principle which inclined Mr. Dredge to adopt the tapering chain and the oblique suspending rods, and to prove mathematically that the principle thus adopted is strictly in accordance with the maxims of 70 accurate mechanics'. During 1843 Dredge himself published his 71 mathematical analysis and graphic statics. His mathematics was quite sophisticated and having made fundamental assumptions he showed himself adept at handling differential equations in developing his argument.
The Dredge and Clive Correspondence
During 1843 yet another resident of Bath entered into the controversy with Dredge and used models to justify his claims. This was the relatively brief exchange between Dredge and a Mr. J.H. Clive. Like
Motley, Clive was not discussing a suspension bridge but a stayed-girder bridge. His suspender rods were grouped in clusters and radiated from several points on the masonry towers (see figure 3.6). He is at least quite clear about this distinction;
70 Rltrbaitico' 1)Ziagalinc, MUSEUM, REGISTER, JOURNAL, AND GAZETTE.
No. 1050.] SATURDAY, SEPTEMBER 23, 1843. [Price 3d. Edited b. J. C. Eobertson, No. 16d, Fleet-street.
].H.Clive's Suspension Fridge
Reference: Mechanic's Magazine, 23 September, 1843. On considering my models and their indications, it appears to me, that the main chain or bearing, though one of the first and most naturally occurring modes of making a suspension bridge, is by no means the best ... My models prove that the rods alone are equal to carrying the platform and load ... therefore all the weight in the main chains which exceeds the difference between inclined and perpendicular rods is worse than useless. 72
Clive emerged in May 1843 when a letter of his was published in the 73 Mechanic's Magazine where he stated that he had seen both Dredge's and Motley's bridges over the Avon at Bath. He favoured Motley's system
'on account of its being free from any swinging motion, which chains can never be', and to test his ideas he 'constructed a rough model'. His drawing of it is shown in figure 3.7a and indicates an increasing tension in the parallel inclined suspender rods from the top to the bottom of the tower. He ended his letter with a challenge: 'If there be any fallacy in this reasoning of mine, for there is none in the model, I 74 shall be most glad to have it pointed out'. Dredge obliged in a letter a fortnight later; 'If a bracket were constructed in the manner he has shown ... with the platform curved ... the strain in the several 75 tension cords would not vary as indicated by the weights'. This drew a reply from Clive some six weeks later:
Feeling assured that Mr. Dredge ... had assumed an erroneous value for the relative forces brought into action, and thereby arrived at wrong conclusions ... I reconstructed a model of the half bridge with four loose blocks or platform compartments, just ledged on each other (which I shall be happy to show him any day) in order to furnish such a near approach as a model would give. 76
Clive's rebuilt model is shown in figure 3.7b. The- subject, as presented by Clive, is confused by his individual blocks, 'just ledged on each other'. These introduce discontinuities into the deck making it incapable of sustaining bending at the junctions, rendering the system statically determinate and capable of analysis by simple mathematics. However, if such a calculation is made by taking moments
71 a
rraNctru:s OF St S1'1 TRUDGES.-MR. MIT IN RE.14.1 TO XII. 11:11:DGF,
•( b )
J.H.Clive's Model Suspension Bridges — 1843
Reference: (a) Mechanic's Maoazine, Volume 38, 20 May 1843.
(b) Mechanic's Magazine, Volume 39, 22 July 1843. 33 about the junctions only a poor correlation with the experimental results is obtained. It is further confused by Clive's statement that the blocks were 'not of uniform texture and thickness, so as to be of 77 equal weights in all parts'. However, he admitted that in a real bridge he had no intention of letting the load 'pass over a parcel of loose blocks, merely kept on balance, but presupposed that they were to be suitably secured'. 78
Clive admitted that his model experiments were 'only intended loosely to show one mode of making a projection in imitation of the horizontal bough of a tree, which is, in my opinion, an excellent 79 example for study to all suspension bridge builders'. No evidence suggests that Clive ever built a suspension bridge and we may assume that he entered the discussion in a philosophical manner, and it must be admitted that he did not shed much light on the subject.
The Ballee Khal Bridge - Calcutta
Dredge's fame, and indeed the controversy, spread to the outposts of the British Empire when his principle was adopted by the
Royal Corps of Engineers in India. This was its first use by the military and discussion began when a Dredge bridge in Calcutta 80 collapsed during construction in 1845. The erection of the Ballee nal bridge was noted in the British technical press in October 1844 81 in an article quoting a letter dated July 1844 to James Dredge from
Captain Goodwyn, R.E. of Calcutta. Goodwyn superinteded the design and erection of the ill-fated bridge which had a span of 250 feet, a versed sine of 26 feet, and a deck 18 feet wide. He claimed to have carefully checked the preliminary design:
72 with the assistance of a very able and first rate mathemetician here, I have studied the theory of these bridges most thoroughly; and the model I have made 22 feet long, and 4 feet width of platform, is on so large a scale, that I have been able to test it in every possible way, and it has withstood the utmost efforts to derange its parts. The Governor-General, and all the scientific people here, have perfectly satisfied themselves of the efficiency of the system, and all these proofs, with my models, assure me that the theory is correct. 82
We know nothing of either the mathematician or the theory studied but we may be sure that the model mentioned was not a scale representation of the bridge. After the collapse, a three-man committee of military engineers was directed to 'investigate the circumstances of the failure
... and to report on the expediency of re-constructing it on the same 83 principles as before, . Goodwyn said the cause of failure was not one 84 of principle but lack of care during construction. Just before completion of the decking the overseer in charge, during Goodwyn's absence, placed a concentrated load of 40 tons at one end 'in innocent ignorance of the mischief he was doing' causing the horizontal iron edge-beams to buckle. The Committee accepted Goodwyn's analysis and, after making further experiments, decided that with modifications the bridge could safely be rebuilt. In describing the experiments the
Committee made an interesting comment on the role of model tests in.
General:
Useful, invaluable as models are, for rendering a particular mode of construction intelligable, all practical Engineers, as all mathematicians who are practically as well as theoretically acquainted with mechanics, know that mere models often lead to the most fallacious conclusions; and this from its being generally assumed (often without a shadow of satisfactory proof) that the dimensions of particular parts of the fabric only require to be increased in direct proportion to one of their linear dimensions, as for instance, in the case of bridges, directly in proportion to the spans; whereas extended or full-scaled experiments may be found to prove that the dimensions of some of the parts ought to be increased in some higher power than either the squares or cubes of the spans. 85
73 This acknowledges the importance of the visual model and the caution expressed almost paraphrases Smeaton's words of 1759. It also reveals an awareness of the similarity problem, albeit rather vaguely.
Experiments were made in India between October 1845 and August 1846 with the limited objective of testing the 'theory of a system based on
the "resolution of forces ".' 86Although this was a general analytical model, scaling laws were involved. The first experiment was 'on full scale as regards heights and distances, but formed of material 221-th. 0 87 of the strength of the real bridge' . It is not clear just what is
meant by strength in this case; whether a material with a lower tensile
breaking stress was used, or whether, in addition a scaling law related
the cross-sectional dimensions of model and prototype. However, in the
third experiment 'the points of suspension, the lengths of the rods
and beam, heights and distances, being to a full scale ... the sectional 88 area of the iron was ---th, part of reality'. This obviously 196 indicates a linear scale factor for the cross-sectional dimensions of 1 1 making the self-weight of the model members also- 1196-th ' of ,A96- 14 that of the prototype. The model was allegedly made to investigate
forces but how these were measured is not described and the reason for
reducing the cross-sectional area is not clear. Even though Dredge
regarded the quantity of material in the failed bridge to be 'greater 89 than was indispensibly requisite' the new bridge was rebuilt, as a
result of these experiments, with more material. The whole investigation
was confused and involved both model tests and mathematical analysis.
The Committee remarked that 'the eminent mathematician who attempted to
investigate the principles of Mr. Dredge's mode of bridge construction 90 appears only partially to have succeeded'. One mathematician showed
that suspender-rod tension increased uniformly towards the centre whilst 91 Turnbull arrived at exactly the reverse result. Indeed, Turnbull
added that 'the successful application of the principle to practice must 74 in a great measure depend on the sagacity and skill of the Engineer by 92 whom the fabric is raised'. The Committee expressed 'regret that the
profound science which has been applied to its investigation has led to 93 such an indefinite conclusion'.
Other bridges were built, and more proposed, by the Royal
Engineers in India at this time. Major Abbott of the Bengal Engineers visited a Dredge bridge of 120 feet span near Meerut (about 800 miles from Calcutta) and in a letter to Calcutta said;
on being called upon to report on a project for bridging the Jumna, with spans of 500 feet, constructed on Mr. Dredge's system I no longer delayed to inquire more fully into the soundness of the principle ... If I am troubling you with views that have been already set forth, you must attribute it to the distance which separates me, as well as many others of my brother officers from the scientific world. I am utterly destitute of the means of experimenting in support of my theory. I have referred the subject to Calcutta, where there are models, and on a large scale, but as yet I have received no reply. 94
News of Goodwyn's model tests had obviously reached remote parts and
the whole story is an interesting example of the way in which field
military engineers undertook research at this time. The army's use of
Dredge bridges in India ended with a catastrophe. Writing in October
1846, Goodwyn (now Major) said, 'A bridge on Mr. Dredge's principle, which was put up a short time since across the Kubudduck River, near 95 Jessore, has fallen'. On testing, the bridge was found to be weak even though 'guaranteed by Mr. Dredge to stand any traffic' and before its use could be restricted, 'some grand festival took place on the water, to witness which, a crowd of natives rushed on the bridge, nearly filling the platform, and after a few minutes it gave way, and drowned 96 nearly one hundred and fifty of them'.
75 Although the Bailee Khal bridge Committee, writing of Dredge's system, felt that 'the Civil Engineers of Europe have shown a marked disinclination to having any concern with its mathematical merits' one
Englishman at least expressed strong views. After the news of the
Ballee Khal bridge failure reached Britain an irate letter was published in the Civil Engineer and Architect's Journal:
Any new plan for a suspension bridge unaccompanied by its correct mathematical theory is, in my opinion, unworthy of confidence. I do not dispute the fact of Mr. Dredge's having constructed bridges with a smaller quantity of material ... but I do question their safety ... We see here a laudable desire to take every precaution to ensure success - the theory is studied, a model is made, 1/12th. of the size of the bridge, yet . somehow theory, common sense, and experience all fail, and the blame is laid on the contractor; in my opinion there was another weighty reason. 97
The writer accused Dredge of supporting his theory ' in face of its
palpable absurdities' and charged him to 'state distinctly what is given and what is to be found by theory, and also what theory it was that the 98 Indian engineer studied'.
Dredge, and his use of models in bridge design have been dealt
with here at some length, not so much because he extended model testing
techniques (that he certainly did not do) but largely because of his
considerable influence on the discussion of suspension bridge design.
A study of the literature of the period confirms this. It is true that
Dredge began his rather dramatic model experiments at a time when a
young, rapidly growing, technical press must have been looking for copy,
and he almost certainly received a greater share of attention that he
deserved. Nevertheless many Dredge bridges were built. The first of
1832 in Scotland was followed by many others in England, Ireland, India,
and some, during 1851, in Jamaica. It was during 1851 that the design
and manufacture of the bridges was put on a formal footing, although not
many were built after that date.. Messrs Charles D.Young & Co., with 76 extensive iron works in Edinburgh, published a pamphlet stating that they had 'completed arrangements with Messrs. Dredge and Stephenson
C.E., London, whereby they become the Manufacturers and Contractors for the Patent Taper Suspension Bridge invented and patented by Mr. Dredge' but that 'the entire engineering, and the immediate superintendence of the erection of all structures devolve upon Messrs. Dredge and 99 Stephenson'.
The real justification for Dredge's place in this account of structural model testing is his role in stimulating discussion on suspension bridge design - the subject for experiment in the decade
1830-1840. The engineering world divided itself into two camps - either for or against the taper chain principle. Dredge's greatest contribution to our topic was to provoke argument and keep alive the idea that a model (however crude) could be part of an engineer's analytical equipment. This he did superbly well in the years before the tubular girder problems were to arise in the mid 1840's. In later large-span suspension bridge design the development of the spun wire cables, essentially of uniform cross section, rendered the discussion obsolete. The next experiments on model suspension bridges were in the second half of the century in connection with railways.
Suspension Bridges and Railways
That the rapid growth of railways in Britain made enormous demands on structural designers is probably nowhere better demonstrated that in the attempt to adapt the suspension bridge for railway traffic.
The massive increase in loads in conjunction with the light tension structure posed problems of stiffness which were the subject of much discussion, analysis, and experiment in the middle of the century. The extreme caution felt by British engineers is reflected in the evidence
77 to the Commissioners for the Application of Iron to Railway Structures
in 1848. Only two engineers contributed opinions with respect to
suspension bridges - Robert Stephenson and Isambard Brunel. Asked
whether such bridges were applicable to railway structures, Stephenson
replied; 'I do not think, with the prospects of our weights increasing
upon railways, that you can run a locomotive engine over any chain
bridge in existence'.100 The chairman then asked if that would apply
to Dredge's bridges and he replied - 'Not so strongly perhaps'. It is worthy of note that Dredge was still considered sufficiently significant
to warrent a separate question and that Stephenson regarded his bridges with somewhat more favour than the normal. But basically Stephenson's attitude is summed up in the following;
I do not think that a railway bridge could be made on suspension principles; we have one at Stockton, which I replaced by one of these iron girder bridges, and it was fearful when the engine went on to it ... when the engine and train went over the first time ... there was a wave before the engine of something like 2 feet, just like a carpet. 101
The dramatic failure of this Tees bridge, designed by Samuel Brown, undoubtedly set back work on British Railway suspension bridges by many years. Brunel, however, was rather more sanguine and considered that they were 'applicable in the strict sense of the term, and that circumstances might arise in which they would be the best 102 construction'. However, he felt that Dredge's bridges were 'less applicable' than the normal type.
The problem of achieving adequate stiffness received considerable attention during 1857. In London during May a paper was read to the Institution of Civil Engineers 'On the Disturbances of 103 Suspension Bridges, and the modes of counteracting them'. in which the joint authors summed up the contemporary situation;
78 Suspension bridges, requiring considerably less material for their construction than girder bridges, and being practicable for far greater spans, than have ever been attempted with structures of a more rigid nature, would probably be frequently employed for railway traffic, as well as for other purposes, were they not so liable to disturbances of various kinds.104
They attempted to classify the 'various kinds' of disturbance and suggested remedies in a purely qualitative manner. During the discussion only one reference to a model was made. On the question of increased stability arising from the use of inclined suspender rods
Mr. Lukin said:
This was one of the advantages of the inclined rods. When he made experiments upon a model, it was evident, that it was altogether so much stiffer, in proportion, than would be the case with a real bridge, that he merely noticed general results but if the load caused a considerable deflection at any one point, without causing a corresponding elevation at another point, so far it might be argued, that there would be no material undulation. The model was for a span of 240 feet, at a scale of a quarter of an inch to a foot. When a truck loaded with 7 lbs. or 8 lbs. was sent across the loaded bridge, at various speeds he found that a deflection at one point did not produce an elevation at any other point; there was, in short, no undulation. 105
This small model, of five foot span, could obviously only provide the most general, unquantifiable, data, and to be fair Lukin admitted that he 'did not desire to draw any positive conclusion from such 106 experiments'. Later in the discussion P.W. Barlow rose and expressed faith in a girder-stiffened suspension bridge. As Engineer to the Londonderry and Eniskillen and Londonderry and Coleraine Railway
Companies he had recently received instructions to design a bridge crossing the river Foyle at Londonderry, forming a junction between the two lines and effecting a road improvement. He proposed a two-platform bridge - 'the upper one to carry the ordinary traffic, and the lower one 107 to support the railway carriages drawn by horses'. The limitation to horse traction was significant as it removed the hammer-blow effect
79 associated with the steam locomotive. Barlow suggested that the upper 108 deck should be 'connected with the lower platform by lattice work' resembling Roebling's Niagara bridge system. It could well be argued that the lattice stiffening system was anticipated thirty years earlier by Davies Gilbert when he said; 'to counteract and restrain undulating motion, the ballustrades may be carried to any desired 109 height, and rendered inflexible by diagonal braces'. However,
Barlow did not refer to any model tests at this stage. Stephenson, as chairman of the meeting, said the paper 'touched upon an important point, which had deeply engaged the attention of engineers - the comparison of suspension bridges with those of girder construction, for use on 110 railways'. In summing up he remarked that the 'discussion went to show, that difference of opinion existed on this subject and he trusted ... they would be able to reconcile these differences, and to 111 reduce the question to a simple form'.
P.W. Barlow's Experiments - 1857
The subject arose again at the Dublin meeting of the British
Association later in the year. Charles Vignoles introduced the topic
'as appearing to possess sufficient interest for discussion, from the circumstance of differences of opinion amongst civil engineers having thrown doubt upon the feasibility of applying the principle of suspension 112 to the purposes of railway transit'. He referred to the success in
America and considered it 'a striking set-off against the failure in this country, which occurred upwards of five and twenty years ago, under circumstances which have militated against any attempt to repeat the 113 experiment'. Like many other British engineers Vignoles was still very conscious of the Stockton bridge failure. He referred to the
Civils meeting in May - ' from which many engineers were absent', and said. the Dublin meeting would provide a further opportunity to discuss 80 'the intended application of a suspension bridge to carry a railway 114 across a navigable river in the North of Ireland'. This referred
to the Londonderry bridge and Barlow, engineer to two Irish Railway
Companies, read a lengthy paper to the meeting. He claimed great
advantages in using a suspended girder and began by comparing the
Britannia and Niagara bridges - 'the two largest railway openings yet
constructed' revealing a very adverse span/weight ratio for the 115 British bridge. Although aware of the problems of live loading he
said 'This is not, however, the subject I now submit for discussion;
the first step in the enquiry is the simple mechanical problem of the
strength and deflection with stationary loads, on which no doubt ought 116 to exist' Although he used the word strength here his experiments
really sought to establish the stiffness of the system, and for the
first time the deflection of a model suspension bridge was measured.
He claimed that his model tests 'distinctly prove that a suspended
girder, as designed for the Londonderry Bridge, is rendered equally
rigid with less than 1/25th. of the metal required in the girder 117 alone'. His experiments are of particular interest in that they were the first to attempt the consideration of similarity between a model suspension bridge and the full-scale structure. Barlow 'had the model made on a scale of 1/33rd. part of the actual span, the 118 length being 13'-6" between the bearings'. The principal object was
'to ascertain the deflection of the wave of a girder attached to a chain, as compared with the deflection of the same girder detached'.119
Barlow then made an interesting statement about the scale of the model:
My first intention was to make the experiments with a girder which was a correct model of the actual bridge, which would have indicated 1/33rd. of the actual deflection, but I found the deflection of the wave to be so small that it was difficult to measure it with sufficient accuracy, and I therefore had a wooden box made of the correct depth, with the sides as thin as it would stand, viz. deal plank, in order to obtain greater deflection of the wave, with the correct depth
81 of the girder, and with the chain attached to it as in the proposed bridge. I could no longer obtain the actual deflection of the Londonderry Bridge by multiplying the experimental deflections by 33, but knowing that the deflection of a model on the correct scale would be 1/33rd, of the Londonderry girder, and knowing by experiment how much the model was deflected when unattached, the actual deflection of the Londonderry girder is obtained by reducing the observed experimental deflection in the ratio of the rigidity of the actual model to a true model, and then multiplying by 33. 120
The crucial question here is What did he mean by a correct model of
the actual bridge? If he scaled down all dimensions by a common
geometric scale factor of 1/33 it would not, of course, have indicated
1/33rd. of the actual deflection. The wooden box girder, meant to simulate the two decks of the bridge, was described as being of the
'correct depth' but no dimensions were given. The problem is further
complicated by his reference to a 'high tower' and a 'low tower'. It
is not clear whether he was referring to a difference in height of the
tops of the towers. This would produce an unsymmetrical cable profile, 121 and was assumed to be the case by a contemporary writer, but is
rather unlikely. Even if the topography of the river Foyle provided
one tower footing higher than the other, that was no reason (and
certainly no engineering advantage would follow) for having the tops
of the towers at different levels. But here again Barlow is not explicit.
He made a series of experiments on four model girders of
progressively reduced stiffness - a wooden box girder, an angle iron girder, a wooden plank 7i inches wide X i inches thick, and a plank
6 inches wide X i inches thick. The suspended girder in each case was two-hinged and the system was therefore statically indeterminate. In each case deflection ordinates were recorded under different systems of loading and the deflected profiles are plotted in figures 3.8 to 82 3.11. lie did not say how deflection was measured but as the smallest value recorded was 0.005 inches it must have involved either a vernier or micrometer. In analysing his results he was only concerned with the maximum deflection and compared that on the simply-supported unattached girder with the maximum on the suspended girder - even though these maxima did not occur at the same point on the span. The results with the wooden box girder are shown in figure 3.8. This box girder was so stiff that there was no upward deflection at any point and to refine the experiment Barlow 'decided in order to magnify the wave and make its amount more distinct, to have a girder made of angle-iron i inch thick 122 and a quarter the depth of the former girder'. This is shown in figure 3.9. He did not describe the method of suspending the girder beyond saying that it was 'simply suspended from and not attached to 123 the chain'. This does not help and no drawing was published. Had he hung it with a leg vertical ('L') the maximum deflection would not have been in a vertical direction - this could only be achieved by supporting it symmetrically disposed in the form of an inverted 'V'. However, comparing maximum deflections he said 'The deflections here averaged
.32 inch with 168 lbs., equal to .08 inch with 42 lbs., or 1/15th. the 124 deflection of the girder without the chain'. He must have arrived at this as follows:
0.28 + 0.36 = 0.32 ins, which is 0.32 X 42 = 0.08 ins. with 42 lbs. 2 168 therefore 1.2 = 15 0.08
Barlow incorrectly assumed linear load/deflection characteristics for the system. In conclusion he said;
It was still obvious from the deflection at the centre and little rise exhibited in the wave, that the stretching of the chain to bring the metal surfaces to bear, still sensibly influenced the result, and I had another wooden girder made, consisting of a plank 7i inches in width and i of an inch thick, in order still more to magnify the wave, and to diminish the error from the stretching of the chain. 125 83
6'—g° 168 lbs. • 1 f" deal plank depth not D given 13'-6" breadth T not FLEXIBILITY MEASUREMENT (chain detached) given
HIGH TOWER 'attachedas in the LOW proposed bridge'. TpWER
ITT????
13'-61"
.030 .010 .010 First experiment. W= 56 lb.s I I I All deflections in inches.
.760 .940 W = 112 lbs
.075 .040 .010 } W = 168 lbs
.030 .020 .000 W = 56 lbs.
Second experiment. .50 .40 .?05 All deflections in inches. W = 112 lbs. 7 9
.075 .050 .005 W = 168 lbs. }
1857 — Barlow's suspended wooden box Girder.
Reference: British Association Report, Dublin Fleeting, 1857, p. 240. 3.8 61-9° m 1
42 lbs. it 8 quarter t 1.2" _,,,______,/______,_i depth of L. former 13' —6" girder 1. 1 L FLEXIBILITY MEASUREMENT (chain detached)
High Low Tower /N. Tower 227 lba. distributed
W lbs. W lbs. .05 + 56 .10
.12 112 J._
+ 168
•L8
I l' TI'TT T 1 %albs.
.06 56 .fi .15 112 .1-5------.18 + 168 .07. .36
1857 — Barlow's suspended angle girder.
Reference: British Association Report, Dublin Meeting, 1857, p. 240. 3.9 The results from this first plank/girder are shown in figure 3.10 and indicate its reduced stiffness. In addition to the concentrated load at the quarter-span point he added an increasing uniformly distributed load in experiments 2,3, and 4. Although the total load on the system increased, he showed that the damping effect of the u.d.l. was to decrease the maximum deflection. Barlow did not attempt to relate the model deflections to those of the Londonderry bridge by means of mathematical similarity. He did, however, attempt this by means of calculations involving the model deflections and actual deflections measured on three completed railway girder-bridges (without chains); 126 The Boyne Viaduct, Newark Bridge, and the Britannia Bridge.
Deflection data existed for these bridges and he reduced the average maximum deflection, when carrying a central load of 100 tons, to 33 inches. Speaking of experiment No.4 (figure 3.10) he said;
The deflection here indicated with the model loaded with a weight representing 96 tons on the bridge (which experiment was several times repeated), was .31 with 56 lbs. = .055 with 10 lbs., or 1/26th of the deflection of the girder without the chain; 33/26 1.27 is therefore the deflection of the wave indicated by the experiment of the Londonderry Bridge, with a load of 100 tons at 1/4 from the tower. 127
This is confusing. What factor related the load on the model to the
'96 tons on the bridge'? He again compared maximum deflections occurring at different parts of the span and assumed linear load/ deflection characteristics for the suspended girder. He added;
To obtain the comparative rigidity of the experimental girder we have here as - 206 lbs. : 10 lbs. :: 1 in. : .0485, the deflection of a true model with 10 lbs.; 1.48/.0485 or 1/30.5 represents the rigidity of the experimental girder; .31/30.5 X 33 = .335, the deflection by a weight on the bridge of 56 X 332= 27 tons. 27 : 100 :: .335 : 1.27, the deflection as previously calculated. 128
Here again there are difficulties. Why did he use 206 lbs., the total load in experiment 3 (i.e. 150 56), whereas the load producing the maximum deflection of 0.31 inches' in experiment No. 4 was 193 56 84 10 lbs. l ~J ..... v -r- -~ ++~ 13'-6" j f" lhick flEXI8IlITY MEASUREMENT (chain detached)
High Lew Tov r Tewar
+
70 lbs. distributed
150 lbs. distributad
193 lbs. distributad
+
1857 - Barlow's first olank girder
Reference: British Association Reoort, Dublin Meeting, 1857, p. 241. 3.10 6'-9"
8 lbll. J F;\. T 13'-6" r fLEXI8ILITY MEASUREMENT (chain detached)
High Law Tailler Tailler 193 lbs. distributld
o 56 lbll. .53 + ~------~----~~=-----~----~~
193 lbs. distributad
56 lbll. +
.30
+
.85
1857 - Barlow's second olank 9ird~r
Reference: British Association Report, Dublin Meeting, 1857, pp. 241-2. 3.11 249 lbs.? Similarly, why did he multiply the model load by the square of the geometric scale factor in relating it to the full-sized structure? Barlow made one further experiment using a plank 6 inches wide and i inches thick with the results shown in figure 3.11, and from these he concluded that;
The deflection is decreased by loading the bridge to 1/20th of that of the girder unattached, and if the chain were without weight it would be still further reduced; in practice, however, the weight on the bridge will much exceed that on a model, and 1/25th will be the least amount that will arise, a result so at variance with the preconceived notions of many engineers, that it is to be expected in some instances it will be received with incredulity. 129
Although his account is rather muddled, Barlow's experiments did draw attention to the fact that a relatively light girder might effectively spread the load over the chain providing a stiffer system.
This is quite different.from the conclusion that Stephenson arrived at in connection with the Britannia bridge.
Barlow's concluding observations were
1st. That in suspension bridges it is essential that the platform should be•stiffened with a girder to prevent vertical undulation.
2nd. That the deflection of the wave of a girder attached to a chain will not exceed 1/25th of the deflection of the same girder not attached to the chain,
3rd. That theoretically the saving of metal to give equal strength in a suspension bridge is only one-half of that of a girder ... 130
It might well be thought that this dramatic claim would have convinced the Railway Company but, despite the success of Roebling's Niagara bridge, they still had reservations about railway suspension bridges.
So they referred the question to John Hawkshaw who recommended a normal girder bridge.
In the summer of 1860 P.W. Barlow repeated his paper, with
85 additions, to the Oxford meeting of the British Association. The paper was re-published in the August issue of The Civil Engineer and 131 Architect's Journal which led to an even wider discussion of the
problem. At this time the Londonderry girder bridge was under construction and Barlow, rather bitter at Hawkshaw's decision, said;
It is no doubt the safest course for an engineer to recommend what has been done before, and to avoid experiments; but this, it is submitted, does not render it less desirable that the subject ... should be understood as a mechanical question. 132
He reproduced the results of all his experiments except that of his first wooden box girder. He recalled that when he read his paper at the Dublin meeting in 1857, 'there were several girder engineers present, but no observation was made during the discussion upon the especial object of my experiments, except by Prof. Rankine, who, ... investigated the subject on this point, and arrived at nearly the same 133 result' In fact, one of the most important results of Barlow's model experiments was to induce Rankine to develop and publish his approximate analytical technique which has been so widely used since that time. This assumed that, for a three-hinged or two-hinged stiffening girder, a concentrated load is spread uniformly over the whole span to the cable which retained a parabolic profile. This was the origin of the elastic theory - the first to attempt a rational account of the interaction between cable and girder. During the discussion of Barlow's 1860 paper his results were much contested, but he was supported by the President of the British Association - Professor Rankine. Although Barlow constantly referred to Roebling's structure 'it appeared that very little was known to the speakers of the success of the application of 134 the principle in the chief example referred to - the Niagara Bridge'.
Barlow concluded with a plea for further work;
85 It may be true that public feeling is against suspension bridges, from the repeated failures arising from want of metal, and from having no means of curing the wave: which arises. as my model has shown, by the smallest weight at any one point: but this is only a reason why men of science should look at the question, and correct an error which is a check upon useful enterprise and upon the progress of public improvement. 135
The publiCation of Barlow's paper in August 1860 led to a two-part analytical article in November and December entitled, 'Suspension
Bridges for Railway Traffic'. The anclnymous author summed up the contemporary situation;
the suitability of suspension bridges with rigid platforms to the requirements of railway traffic, is as yet to be regarded as a matter of opinion if we consult the opinions even of the men most competent to pronounce on such a question, we are led to very opposite conclusions; and until the experiment is actually made on a large scale in some railway bridge, our only remaining resource lies in experiments on models, or in theoretic deductions... Great allowances are necessary in drawing any conclusions as to a proposed work of considerable magnitude from experiments on a model, however carefully conducted ... It is therefore now proposed to inquire, what solution theory affords to the problem of the suspended girder; and while doing this it may be useful to note how far the results arrived at accord with Mr. Barlow's experiments. 136
There followed some incomplete mathematics making it impossible to follow the development of his argument. He attempted to allow for the stretching of the chains and 'the inequality in the height of the towers, which is such as to increase this wave by 1/73rd. part when the load is placed one-fourth of span from the high tower, or to reduce it by the same amount when the load is placed one-fourth of span from the 137 low tower'. None of the accounts give the relative heights ot the towers so it is impossible to check this statement. The un-named writer left the subject with a parting challenge;
87 Experiment and theory have now done their part, Each involve some known, and possibly also some unsuspected, sources of error. It remains for the practical engineer, by the bold test of some actual work, at once to correct and verify the conclusions of abstract science, and remove the question forever from the province of discussion. 138
However, no such bridges were built and the subject was not re-opened experimentally until the Astronomer Royal investigated the subject some seven years later.
George Biddell Airy's Experiments - 1867
A decade after Barlow's model experiments, Airy made a similar series of tests on an experimental rig of 11'-11" span (see figure 3.12).
Airy never used the word model to describe this apparatus and so the question of similarity was not considered. This was a general analytical model. His results were made public in a paper read at the 139 Institution of Civil Engineers in February 1867. His attention had first been drawn to the question of suspended girders some seven years earlier in discussions with Stephenson about the Britannia bridge. At that time he had thought there were better methods available for wide spans than simple tubular girders. After Britannia 'No necessity for 140 perfecting the theory arose for many years'. But in 1863/4 he had again been involved in a plan for a large-span railway bridge and had
proposed a suspended girder. It is interesting to note that by this time his mathematical analysis of the system presented 'no positive difficulty' but 'the complexity of symbols became so great' that he decided to 'refer to theory for considerations of a general class only, 141 and to rely on experiment for the numerical determinations'. If the
Astronomer Royal could publicly admit to being overwhelmed by a
'complexity of symbols' it is not surprising to find engineers reluctant to adopt the analytical approach. At no time did he refer to Barlow's experiments but he came to very similar conclusions, namely, that the 88 Chain weight = 182 lbs. 1'-11"
15 vertical Spline of wood Pin support
suspender wires
11 ,-11"
1867 — Airy's experimental model
'The upper surface of the spline was furnished with
fifteen screw—eyes, at nearly equal intervals'.
Reference: Proc. I.C.E. Vol. 26
p. 260. 3 .1 2 deflection of a suspended girder would be 1/25 to 1/30th. of that when simply supported. He did not give the mathematical reasoning leading to this result, but for his experiments,
A suspension-chain was provided, somewhat exceeding 12 feet in length, weighing 181 lbs,, attached at its ends to two pins at the distance of 11 feet 11 inches; the central dip of the chain being about 1 foot 11 inches. A spline of wood exceeding 12 feet in length (intended to represent the stiffened roadway) was lodged at its ends on pins, vertically below attachment-pins of the suspension-chain. The upper surface of the spline was furnished with fifteen screw-eyes, at nearly equal intervals, and these were connected with the suspension-chain by fifteen suspending wires, adjusted to support the spline in a horizontal position,- and to be all (as nearly as possible) in bearing at the same time. 142
No drawing was published but figure 3.12 is based on this description.
The test rig was somewhat smaller than Barlow's but his objectives were identical. The experiments were made in two groups - the first with the stiffening girder represented by a thick plank of wood (no sizes were given), and the second with a thinner plank. The results are given in figures 3.13 and 3.14. He first measured midspan deflection of the'thick spline' when simply-supported over spans varying from 3 to
5 feet (experiments 1 to 10). These showed, as was to be expected, a linear load/deflection characteristic. In experiments 11 to 20, the load was suspended directly from the catenary chain and the load/deflection characteristic is non-linear. This exposes the inherent analytical complexity of the stiffened suspension bridge problem - when a girder system with linear characteristics is attached to a non-linear chain the problem becomes statically indeterminate and, in engineering terms, only an approximate mathematical solution is possible.
Experiments 21 and 22 measured the central deflection of the thick plank over the span of 11 feet 11 inches when carrying central loads of 10 and
20 lbs., giving deflections of 44/32 and 82/32nds. of an inch respectively. If these are compared with the central deflection in
89 -
In all experiments the unit of vertical deflection = 1/32 inch
1 L/2 W lb. Flexibility measurement THICK SPLINE
Experiment Span (1) Central deflection Central deflection Number ft. in. ( W = 10 lbs.) ( W = 20 lbs.) 1 & 2 3 0 1 2 1 3 & 4 3 6 1.6 3.2 5 & 6 4 0 2 4 7 & 8 4 6 5 10 10 9 & 10 5 0 7 1 4
W (lb.) d1 (I) d2 (T) 11
10 78 42
dI 20 93 64 14 1 d1 (4, ) d (I. ) d (T) d W (lb.) 2 3 15 3
10 108 62 100
20 20 140 109 160
21 W (lb.) d1
10 44
22 20 82
W (lb.) del) 23 d 1 4 • 10 31
24 20 54
d1 (1) 25 W (lb.) d2 (T)
d 10 2 1
d 30 2 20 5 1
d d3 31 W (lb.) d1 (.1.) 2 (T)
10 4 1 2
20 8 1 4 36
George Biddell Airey — 1867
Reference: Proc.I.C.E., Volume 26, p. 261.
3.13 In aIl exoeriments the unit or vertical deflection = 1/32 inch'
rlexibility measuremant THINNER SPLINE
Experiment Span (L) Central éerlection Central cerlection Number rte in. ( III = 10 lbs.) ( III = 20 lbs.) 37 .\ 38 3 o 2.5 5.5 39 .\ 40 3 6 4 8 41 .\ 42 o 5 10
43 & 44 4 6 8 16 45 .\ 46 5 o 10.5 21
47 III (lb.)
10 138
48 20 240
49 .. L/2 L III (J,) . l 1 (lb.) -~----...-t- 1...... 1 ...... ' • 10 40 1- ~i r 50 20 60
51 III (lb.) l -~--tt-'].Dl' 1 10 6 1 td 1 III 1 d 1 2 56 20 10 2
57
10 9 3 . d 1 d ~1~----~,~~ 2 3 1d III 1 62 20 17 6
George Biddell Airey - 1857
Reference: Proe.I.e.E., Volume 26, pp. 261-2.
3.14 experiments 25 to 30 (with the plank attached to the chain by 15 suspender rods) we see that they are reduced to 2/32 and 5/32nds. respectively, giving reduction factors of 44/2 t2 22 and 82/5 16.4.
Or, as Airy said;
The comparison of the deflections in 25, 26, 51, 52, with those in 5, 6, 41, 42 shows that the central depression in the composite bridge is equal to that of a tubular or girder bridge of the same section as that in the composite bridge but of one-third of the length, or less. 143
Unlike Barlow, Airy's conclusions led him to propose a practical design method;
For planning the tube or girder of such a bridge, the rule found on known constructions is very simple. The Engineer will decide mentally on the amount of deflection that he will tolerate in the bridge as the effect of a given load. He will then, by the rules of engineering, compute the section of the tube or girder which will permit that deflection in a bridge of 1/3 of the length in question or less; and this will be the section to be used for his long bridge. 144
Here we have a model used, in the classic circumstances of analytical complexity, to provide the basis for an approximate design method to achieve a pre-determined degree of stiffness. It was the last model used in nineteenth-century suspension bridge design in Britain. Why was this? In answering this question it must be remembered that suspension bridge building largely lapsed in the last quarter of the century - in fact no purpose-built railway suspension bridge was ever constructed in Britain. The leaders in analysis and design of suspension bridges were now on the continent and in America. Another factor reducing the need for model tests was the development of the more accurate deflection theory. Although it was known in the first half of the century that the displacement of a chain, without a stiffening girder, under the action of a concentrated load was non- linear, the first mathematical statement of this non-linearity was 145 published in the British technical press of 1862. Although Airy's
90 • experiments demonstrated the effect, the first non-linear deflection theory of suspension bridges was not evolved until 1888 by J. Melan.146
What roles then did models play in the attempts to adapt the suspension bridge for railway traffic? In the decade 1857-67, connecting the experiments of Barlow and Airy, the plea was; 'Must the railway engineer forego the advantages peculiar to the suspension bridge? ... If it is in the power either of experiment or of analysis to throw any fresh light on this vexed question, the study cannot be 147 deemed unimportant or uninteresting'. British engineers were still haunted by the inadequacy of the Stockton and Darlington bridge, but as we have seen, two experimental attempts to grasp this analytical nettle were made. Barlow and Airy's small-scale tests did at least examine the system in which the future of large-span suspension bridges lay. Barlow's work is, on the whole, more interesting not only in that it preceded
Airy's by ten years, but also as it sought to provide data for the design of a particular bridge - even if not subsequently built. But even Barlow had second thoughts about his model experiments. He was present at Airy's paper and said he had
listened with attention to the Astronomer Royal's observations and experiments, the fact being that similar experiments were made by himself in the year 1857, when he ... arrived at similar results ... However, the mere result of experiments of that kind he did not think sufficient to determine the best construction of a suspension bridge. Many practical points arose which could not be determined by experiments on a small scale. 148
However, they drew the attention of others to the problem of the interaction of chain and stiffening girder, and this was perhaps their major contribution to the discussion.
91 Wind Loads on Suspension Bridges
The problem of achieving adequate stiffness in suspension bridges under dynamic loading was first encountered in the wind disturbance of road bridges. Damage to the Menai Bridge during the storm of January 1839 led to discussion of the subject following a paper read to the Institution of Civil Engineers, in 1841 by 149 W.A. Provis. Bendel said errors in bridge design arose 'from engineers theorizing too much on the properties of the catenary curve, without attending sufficiently to the practical effects of wind in the 150 peculiar localities in which the bridges were placed'. I.K. Brunel commented that 'In all suspension bridges the roadways had been made too flexible, and the slightest force was sufficient to cause 151 vibration and undulation'. But the most interesting contribution occurred when E. Cowper rose and suggested that;
The whole suspended part, when acted upon by the wind, became in some measure a pendulum, and if the gusts of wind were to recur at measured intervals, according either with the vibration of the pendulum, or with any multiples of it, such an amount of oscillation would ensue as must destroy the structure. 152
This is one of the earliest statements revealing an appreciation of the importance of the frequency of repeated live load and the possibility of resonance. The report of the discussion stated that Cowper
'illustrated this proposition by a model with chains of different curves, and at the same time pointed out the efficiency of slight brace 153 chains in checking the vibration'.
But of course controlled experiments were not possible at this time without a wind tunnel. Smeaton had used stationary air and a moving model in his experiments on the performance of windmill sails but this technique would obviously not have been suitable for model bridges.
92 SUSPENSION BRIDGES
REFERENCES and NOTES
The Proposed Suspension Bridge at Runcorn
1. Book of Reference relative to the bridge at or near Runcorn Gap. Cheshire Record Office, Chester, Ref: QDP 29, MSS dated 30 September 1813. Signed: Wm. Nicholson.
2. Salopian Journal Vol. 21 No. 1077 Wednesday 21 September 1814.
3. Mr. Telford's Reports, Estimates, and plans for improving the Road from London to Liverpool. 3 April 1829, p.7 (Warrington Reference Library).
4. Institution of Civil Engineers, London. Notebook No.2, Ref.52A.
5. Parl. Pap. 1817 Report of the Select Committee, appointed to consider the most practicable and Expedient mode of effecting the proposed BRIDGE AT RUNCORN, submitted to the General Committee on the 8th. April 1817. p.11 'Mr Telford's Report'. (I.C.E. Lib. Ref Tract 4to Vol 13 ).
6. Encyclopaedia Metropolitana Vol. 15, London 1845, p.362.
7. Life of Thomas Telford (autobiography) Ed. Rickman, p. 542 (1838).
8. Ibid. p. 555.
9. Proc. I.C.E. Vol. XV1 1856 - 7, p. 133 Memoir of James Meadows Rendel (1799 - 1856). If Rendel joined Telford in 1814 he would only have been 15 years of age.
10. Select Committee op. cit. (ref 5) p.13.
11. An historical and descriptive account of the Suspension bridge Constructed over the Menai Strait. W.A. Provis, London 1828, p.16.
12. Proc. I.C.E. Vol. CLXV, 6 March 1906, 'The Widnes and Runcorn Transporter-Bridge' by John James Webster. A footnote on p. 88, speaking of the earlier suspension bridge scheme says: Telford made a model of this bridge to a scale of 20 feet to 1 inch, and this interesting memento is still in existence in a building belonging to the Shropshire Union Canals at Ellesmere, Shropshire.
13. Provis, op. cit. p.16
14. Select Committee, op. cit. (ref. 5) p.13.
15. A Memoir on Suspension Bridges, Charles Drewry, London 1832, p.14. Details also given in Telford's autobiography .(1838) p. 550. 93 16. Select Committee, op cit. (ref. 5) p. 4.
17. Select Committee, op cit. (ref. 5) p.13.
18. Patent No. 4137 10 July 1817: Invention or Improvement in the Construction of a Bridge, by the Formation and Uniting of its Component Parts in a Manner not hitherto Practised.
19. Ibid. p.4.
20. Ibid. p.4.
21. Ibid. p.5.
22. Select Committee, op. cit. (ref. 5) p.13.
23. Tilloch's Philosophical Magazine & Journal, Vol. 54, July 1819, p. 17: Third Report from the Select Committee on the Road from London to Holyhead. 29 April 1819.
24. Proc. I.C.E. Vol. CLXV, op. cit. p.87.
25. The Operative Mechanic John Nicholson, 4th. edition, London 1853, p. 805.
26. See Proc. I.C.E. Vol. CLVX. op. cit. p.87.
The Proposed Suspension Bridge at Montrose
27. Edinburgh Philosophical Journal. Vol. 5, 1821. pp. 140 - 156 and 267 - 281.
28. Ibid. p. 268.
29. Ibid. p. 268.
The Menai Suspension Bridge - Chain Geometry Model
30. Parl. Pap. 1819 (256). Vol. 5, P. 138: Third Report from the Select Committee on the Road from London to Holyhead.
31. Provis, op. cit. p.48.
32. Provis op. cit. p.89: Appendix No. 5.
33. Provis op. cit. p.48.
34. A Memoir on Suspension Bridges, Charles Drewry, London 1832. p. 160.
Wood as a Material for Suspension Chains
35. A Memoir on Suspension Bridges, Charles Stewart Drewry, London 1832. pp. 154 - 158: 'Of the Use of Wood for the Supporting Chains of Suspension Bridges'.
36. Ibid. p.154.
94 37. Ibid. p.156.
38. Report of the British Association for the Advancement of Science. Oxford meeting, 1832. pp. 608 - 610: 'On the Steel Suspension Bridge recently built over an arm of the Danube at Vienna; and on the mode by which the exceeding tough steel employed was manufactured in Styria, at a small advance upon the cost of Iron'. by James J. Hawkins.
James Dredge and the Taper Chain Controversy
39. See Phil. Trans. 1826 part 111, p. 202: 'On the Mathematical Theory of Suspension Bridges, with tables for facilitating their construction', by Davies Gilbert, in which he demonstrates the varying tension in a catenary. Several subsequent authors acknowledge this paper.
40. James Dredge (1794 - 1863) of Walcot is described as a brewer in his patent specification of 1836.
41. Thomas Motley, a grocer, gives his address as 'Mount Pleasant Cottage, Beechen Cliff' in his correspondence with the Bath Journal.
42. See Surveyor, Engineer, and Architect. 1 September 1840, P.174: letter from J.D. dated Bath, 11 August 1840, gives details of his Clifton bridge design. See also Mechanic's Magazine Vol. 30, No, 794, October 1838, p. 54.
43. The bridge had one span of 200 feet, platform width of 20 feet, and was erected for Sir James Colquhoun.
44. Patent No. 7120 dated 17 June 1836.
45. Bath Journal. Monday 11 July, 1836, p.2.
46. Bath Journal. Monday 18 July 1836, p. 2: open letter from Motley.
47. Bath Journal. Monday 25 July 1836, p. 2: open letter from Motley.
48. Ibid.
49. British Association Report, Newcastle Meeting, 1838, p.157. A great deal of confusion exists over this bridge. It is invariably described in the technical press as 'Tiverton' bridge. The confusion is possibly explained in Collinson's History of Somerset (Taunton, 1898) where the Bath place-' name is given as 'Twiverton or Twerton'.
95 50. Be was so addressed in a letter from William Turner (the Bath engineer who made the Victoria Bridge chains) published in the Bath Journal for 15 August 1836. This letter appears to end the acrimonious exchanges in this newspaper.
51. Mechanic's Magazine, Vol.30, No.794, October 1838, p.54: letter from J.D. dated Bath, October 19 1838.
52. The Times, Thursday 30 April 1840, p.6: letter from Lord Western.
53. Mechanic's Magazine, Vo1,28, 24 March 1838, p.422: letter to Editor from J.D. dated Bath 14 March 1838.
54. The Times, Thursday 30 April 1840, p. 6. The 'Guppy' mentioned must be Thomas Richard Guppy, the Bristol merchant who was a principal promoter of the Great Western Railway.
55. Ibid.
56. Both Cross's models performed better than Dredge's and if the load (in quarters) which they carried is compared a performance quotient can be obtained: 94 Parallel chain model: Cross 1.8 Dredge 52 Cross 244 Taper chain model: - 1.85 Dredge 132
57. Surveyor, Engineer, and Architect, No. V, 1 June 1840, p.101
58. Mechanic's Magazine, Vol. 28, 24 March 1838, p. 433:letter from J.D., dated 14 March.
59. The Times, Thursday 30 April 1840, p. 6 preamble to Western's letter to Melbourne.
60. Ibid.
61. Ibid.
62. The Times, Thursday 30 April 1840, p. 6: Lord Western's letter to Lord Melbourne. This letter was also published in full, but not in its original sequence, with illustrations and editorial appendix in: Civil Engineer and Architect's Journal, Volume 3, No. 33, 1 June 1840, pp.193 - 4. An abridged version of the letter was also published in the Mechanic's Magazine, volume 32.
63. The Times, Ibid.
64. Civil Engineer and Architect's Journal, Volume 3, No.33, June 1840, p. 194 (Editor's appendix to Western's letter).
65. Surveyor, Engineer, and Architect, 1 September 1840, p. 174: letter from James Dredge dated 'Bath, August 11 1840'.
96 66 This recently-formed College had only appointed its staff in the spring of 1840 and received considerable adverse criticism in the press. See the Surveyor, Engineer, and Architect for September 1840.
67. Mechanic's Magazine, Volume 33, No. 884, 18 July 1840, p.122.
68. Ibid.
69. Surveyor, Engineer, and 'trchitect, Volume 2, 1 July 1841, p. 131: Article, "Common Sense" on Suspension Bridges'.
70. The Mathematical Principle of Dredge's Suspension Bridge, William Turnbull C.E., London, John Peale, 1841.
71. See Mechanic's Magazine, Volume 38, 18 March 1843, pp. 213-215: 'Mathematical demonstration of the Principles of Dredge's Patent iron bridges, by the Inventor'. (Article dated: 'Bath Feb. 15 1843'). Article completed in the issue of 28 March 1843, pp. 234-239.
The Dredge and Clive Correspondence
72. Mechanic's Magazine, Vol.39, 19 August 1843, pp. 133-134.
73. Mechanic's Magazine, Vol.38, 20 May 1843, pp. 406-407.
74. Ibid.
75. Mechanic's Magazine, Vol.38, 3 June 1843, p.463.
76. Mechanic's Magazine, Vol.39, 22 July 1843 pp. 57-58.
77. Ibid. p.57.
78. Ibid. p.58.
79. Ibid. p.58.
The Ballee Khal Bridge, Calcutta
80. See Professional Papers of the Royal Corps of Engineers, Vol. 1X, 1847, pp.83-144: 'The Taper Chain Tension Bridge at Ballee Khal, near Calcutta, in its renewed form after the Failure in June 1845. by Captain Goodwyn, E.I.C. Engineers'.
81. Mechanic's Magazine, No. 1106, 19 October 1844, pp. 258-261: 'Description of a Suspension Bridge on Mr. Dredge's principle, erected over the Ballee Khal, for the Indian Government, from the designs, and under the superintendence of Captain Goodwyn, R.B.E.'. (A woodcut of the bridge appears on the front cover of this issue).
82. Ibid. p.261.
97 83. The committee comprised Lieut-Colonel E. Garstin, Superintending Engineer, L.Ps.; Lieut-Colonel W.N. Forbes, Engineers, Mint Master; and Lieut-Colonel A. Irvine, C.B., Engineers, and was convened by an order dated: 'Fort William, 18th. June, 1845. Their report was dated: Calcutta 6 September 1845' but was not published in Britain until 1847 (see Professional Papers op.cit.)
84. Professional Papers op. cit. pp. 126-130 Appendix to report signed (rather surprisingly) 'H. Goodwyn, Captain, Civil Architect'.
85. Professional Papers op. cit. Report p. 121.
86. Professional Papers op. cit. pp. 130-136: 'Letter from Captain Goodwyn to Major Greene, Secretary to the Military Board'. Dated: 'Iron Bridge Department, Fort William, 28th.August 1846'
87. Ibid. p.132.
88. Ibid. p.134.
89. Ibid. p.115.
90. Ibid. p.114.
91. Mathematical Principle of Dredge's Suspension Bridge. William Turnbull, C.E., John Weale, London. 1841.
92. Turnbull op. cit. p.35.
93. Professional Papers op. cit. p.115.
94. Professional Papers of the Royal Corps of Engineers, Vol. 1, 184 pp.24-26: 'An Insquiry into the Principle of Mr. Dredge's Tension Bridge' by Major F. Abbott, Bengal Engineers. p.24: Letter from Abbott to Captain Denison, R.E., 13 June 184
95. Professional Papers Vol. 1X, op. cit. p. 138: Letter dated, 'Calcutta, October 1846'.
96. Ibid.
97. Civil Engineer and Architect's Journal, October 1845. p.313: 'on Dredge's Suspension Bridges' by F. Bashforth, B.A., Fellow of St. John's College Cambridge and of the Cambridge Philosophical Soc.
98. Ibid.
99. I.C.E. Tract, Vol.69: Pamphlet - 'Description of Suspension Bridges on Dredge's Patent taper principle', published by Charles D. Young & Co., 1851, London & Edinburgh, p.5.
98 Suspension Bridges and Railways.
100. Parl.Pap. 1849 (1123) XXIX. Report of the Commissioners appointed to inquire into the Application 01 Iron to Railway Structures. p.357: Robert Stephenson giving evidence on 16 March 1848.
101. Ibid.
102. Parl. Pap. 1849 (1123) XXIX op.cit. P.376: I.K. Brunel giving evidence on 13 April 1848.
103. Proc. I.C.E., Volume XVI, 19 May 1857, pp.458-478: paper by A.S. Lukin and C.E. Conder.
104. Ibid. p.458.
105. Ibid. p.474.
106. Ibid.
107. Ibid. p.476.
108. Ibid.
109. Phil. Trans., 1826 Part 111,p.211.
110. Proc. I.C.E., Volume XVI, op.cit. p.473.
111. Ibid. p.478.
112. British Association Report, Dublin 1857, pp. 154-8: 'On the Adaptation of Suspension Bridges to Sustain the Passage of Railway Trains', by C.Vignoles, C.E., F.R.S. p.154.
113. Ibid.
114. Ibid.
115. British Association Report, Dublin 1857, pp.238-48: 'On the. Mechanical Effect of combining Girders and Suspension Chains, and a comparison of the weight of Metal in Ordinary and Suspension Girders, to produce equal deflections with a given load', by Peter W. Barlow, F.R.S. p.239: Barlow made the comparison:
Span Weight of Material
Niagara Bridge 820 feet 1,000 tons
Britannia Bridge 460 feet 3,000 tons
116. Ibid. p.246
117. Ibid. p.239
118. Ibid.
119. Ibid.
120.. Ibid. p.240 99 121. See The Civil Engineer and Architect's Journal, December 1860, p.352, article by anonymous author - ' Suspension Girder Bridges for Railway Traffic '.
122. British Association Report, 1857, op. cit. p.240.
123. Ibid.
124. Ibid.
125. Ibid. p.241
126. Ibid. p.246: Appendix A.
127. Ibid. p.241
128. Ibid.
129. Ibid. p.242.
130. Ibid. pp.244-5.
131. The Civil Engineer and Architect's Journal, August 1860, pp.225-30.
132. Ibid. p.226.
133. Ibid. p.229.
134. Ibid.
135. Ibid.
136. The Civil Engineer and Architect's Journal, November 1860, pp. 317-8.
137. The Civil Engineer and Architect's Journal, December 1860, p.352.
138. Ibid. p.356
139. Proc.I.C.E., Volume 26, 19 February 1867, pp. 258-64: 'On the Use of the Suspension Bridge with Stiffened Roadway, for Railway and other Bridges of Great Span'. By George Biddell Airy.
140. Ibid.
141. Ibid.
142. Ibid.
143, Ibid. p.263.
144. Ibid.
145. The Civil Engineer and Architect's Journal, August 1862, pp.236-7: 'The Statics of Bridges - The Suspension Chain'.
100 146. Hanbuch der Ingenieuwissenschaffen, Leipzig, 2nd. Edition, 1688, 'Theorie der eisernen Bogenbrucken and der Hangebrucken'. by J. Melan.
147. The Civil Engineer and Architect's Journal, November 1860, p.318 Article: 'Suspension Girder Bridges for Railway Traffic'. Anon.
148. Proc. I.C.E., Volume 26, Airy, op. cit. p.278.
149. Proc. I.C.E., Vold, pp. 74-80: 'Observations on the effect of wind on the Suspension Bridge over the Menai Strait, more especially with reference to the injuries which its roadway sustained during the storm of January 1839'. by W.A. Provis, M.Inst.C.E.
150. Ibid. p.79
151. Ibid. p.78
152. Ibid. p.77
153. Ibid. p.77
101 BIOGRAPHICAL NOTES
LAMB, William (1779 - 1843) Second Viscount MELBOURNE
Childhood at Brocket Hall, Herts.
1790 Eton
1796 Commoner Trinity College, Cambridge
1806 M.P. for Leominster (Whig) 1807 M.P. for Portarlington 1816 M.P. for Northampton 1819 M.P. for Hertfordshire 1827 M.P. for Newport I.O.W. 1830 Home Secretary d. 24 November 1848
WESTERN Charles Collis (1767 - 1844)
Ed. Newcombe's School, Hackney, at Eton, and Cambridge (without graduating).
June 1790 M.P. for Maldon, Essex until 1812 when he obtained a seat for County - retained for 20 years.
28 January 1833 Lord Melbourne created him Baron Wester of Rivenhall.
d. Felix Hall, Kelvedon, 4 November 1844 buried Rivenhall Church.
Unmarried.
Author of several pamphlets particularly on agriculture.
102 Chapter 4
BEAM AND GIRDER BRIDGES BEAM AND GIRDER BRIDGES
INTRODUCTION
The introduction of beam-bridges on railways had impressed upon the profession, the necessity of considering the true nature of a beam and the strains to which it was subjected and ... the laws by which it resisted those strains. 1
Robert Stephenson (1855)
The need to understand the mechanism of beam behaviour was
forced upon British engineers by the problems posed by the railways and
the increased use of metal in bridges to solve such problems. By 1840
cast iron was unchallenged as the principal structural material used in
bridges and yet by 1850 it had been almost entirely superseded by
wrought iron for the spanning elements of bridges. During this decade
various attempts were made to increase the practicable spans of cast
iron beams. These included wrought iron strips let into slots to
reinforce the tension flange and the use of inclined wrought iron rods 2 to truss solid cast iron beams. Small-scale experiments were made at
this time to establish the relative strength/weight ratios of various 3 forms of 'model' cast iron beams. With cast iron the principal
structural problems occurred in regions of tension, but with the
introduction of wrought iron the problem shifted and it was compressive
stresses and the onset of buckling which became crucial. Another
problem which emerged in the design of wrought iron beams and lattice
girders was one resulting from a lack of understanding of shear effects.
Although engineers had an adequate method of calculating the stresses
in the flanges of solid girders and the boom members of lattice girders
they had no satisfactory theory to explain web loading and the behaviour
of web members. Consequently models were used to study the behaviour of
the walls of wrought iron tubular girders, the webs of plate girders,
and the inclined members of lattice girders. Models were also used to study the statically indeterminate problems arising from continuity in 103 girders over supports. The neutral axis question was investigated using
photoelasticity but the technique's analytical possibilities were not developed in the nineteenth century. The use of structural models in
the design of beam bridges can really be said to begin with the
experiments of William Fairbairn and Eaton Hodgkinson for Robert
Stephenson and the Chester and Holyhead Railway Company.
WROUGHT IRON TUBULAR GIRDERS
The Conway and Britannia Bridges
The problem of carrying the Chester and Holyhead railway over
the Conway estuary and the Menai Straits demanded a unique solution
where;
The plan devised by Mr. Robert Stephenson for a railway bridge consisting of a wrought iron tube 450 feet long, is so bold in itself, and suggests such very important and instructive lessons respecting the theory of girders, that an investigation of the principles on which it is proposed to construct the Menai Bridge, and the form which it will be necessary to give it in order that its strength may be uniform in every part, cannot fail to be interesting. 4
This contemporary comment is indicative of the enormous public interest
in the details of such a vast project. In addition to many articles in
the technical press, two major accounts were published - one by William 5 6 Fairbairn, the other by Stephenson's resident engineer Edwin Clark,
the latter's account being described as 'one of the most magnificent 7 speciments of engineering literature in existence'. The Britannia
Bridge was the most widely discussed nineteenth-century engineering
structure prior to the Forth Bridge. Various writers have considered
the mass of information published; one, in 1874, described the Britannia
Bridge as a topic 'about which an immense amount of nonsense has been 8 written', whilst twenty years later Dr. William Anderson remarked;
'It is difficult, from the published histories of such enterprises as the
Conway and Britannia bridges, to arrive at any conclusion as to the •
104 extent of knowledge, or rather ignorance, which existed among engineers
before these works were commenced'. 9
It is, therefore, important when studying the evidence relating to the design of these bridges to bear in mind the nature of the collaboration between Stephenson, Fairbairn, Hodgkinson and Clark.
The unprecedented role of 'model' tests and other experimental work in the evolution of the form and proportions of the tubes makes it important to establish and assess the relative contributions of each individual. This is the more necessary in view of the conflicting claims made by each. The exercise also tells us much about the management of company-sponsored engineering research in the middle of last century. A contemporary civil engineer, referring to the respective roles of Stephenson and Fairbairn said;
It is seldom that the invention of works of new design and skilful mechanical arrangement is due entirely to one mind, any more than their construction is due to one pair of hands: hence great difficulty arises in assigning to each contributor his fair share of merit in their production. It must, however, be admitted, that to Mr. Robert Stephenson alone we are in this instance indebted for the original suggestion. 10
This is not in question and although Stephenson, as Engineer to the railway company, was in ultimate control it should be remembered that he was extremely busy at this time and could devote little time to the detailed analysis and design. Having decided on the tubular form (before any experiments were made) Stephenson found himself without a precedent,no fundamental data, and little knowledge of the mode of. failure which the design method should seek to prevent. Stephenson's choice of a tubular girder needs explanation. His first choice, an arched structure, was overruled by navigation constraints and predjudice against the suspension bridge for railway purposes precluded its serious consideration.
The remaining alternative was the beam or girder form and having rejected timber as the structural material Stephenson had to consider 'the best 105 11 mode of obtaining a rigid platform of iron'. It is interestincinteresting, to
note, in view of the subsequent development of the metal lattice girder, that he 'considered well the means of trussing iron together in a similar way to wood' but came to the conclusion that 'there was no way so simple, so cheap, or so rigid, as throwing the iron-work into 12 the form of a tube'. At this time (May 1845) Stephenson was thinking in terms of an elliptical tube some 25 feet by 15 feet and in order to
play down its novelty to the Select Committee on the railway Bill he said, 'it is nothing but putting an arch over a wooden bridge, which is 13 very common, for the purpose of protecting them from the weather'.
Stephenson was undoubtedly indebted to his knowledge of iron shipbuilding
for the idea of the wrought iron tube and said to the Select Committee
that it had been ascertained that ' a vessel of 250 feet in length, supported at its ends, will not yield with all the machinery in the 14 middle'. This link between shipbuilding and bridge building in
Stephenson's mind was clearly revealed in his reply to the Select
Committee's question as to whether there was a precedent for a tubular girder when he admitted, 'No, there is no experience of it; nor was 15 there of the iron vessel some time ago:. Despite this Stephenson was
confident of the tube's practicability. In may 1845, before the question of buckling had emerged, he was bold enough to say, 'I feel it necessary
to make a series of experiments: not that it will convince me more than
I am at present, but that it shall convey confidence to the Board of
Directors under whom I am acting; not that I have any doubt in my own 16 mind of it'. After the experiments were completed Stephenson evidently
regarded them somewhat differently. Speaking in 1848 he explained
that, with the consent of the railway directors, he had instituted
'a very laborious, and elaborate, and expensive series of experiments, in order, most thoroughly, to test experimentally the theory I had formed, and also to add suggestions for its full development'.17
106 • To implement this Stephenson consulted William Fairbairn
(1789-1874) in April 1845 and the collaboration continued until the
opening of the Conway Bridge in 1848. Fairbairn resigned in May, four
days after Stephenson's speech during the opening celebrations, in which
Fairbairn felt he had not been given sufficient credit. He was led, in
1849, to the publication of his book (see reference 5), the first full account of the works. He named two objectives in this account; 'first,
to establish my claim to a considerable portion of the merit of the
construction of the Conway and Britannia Bridges; and, secondly, to
give an accurate and faithful record of all the proceedings connected with the progress of these stupendous structures, from their origin to 18 their successful completion'. The extent to which these objectives were realised is questionable, and it must be admitted that his account
is partisan and written in a prevailing mood of pique. Fairbairn's
version disappointed Stephenson who supported Clark's two-volume work
published in 1850. Fairbairn's relationship with Stephenson does not 19 emerge clearly from either of these works, but from unpublished letters we know that he was unpopular with both Hodgkinson and Clark. Fairbairn's own establishments were used for the experiments - a general engineering works in Manchester established in 1817, and a shipbuilding yard at
Millwall on the Thames opened in 1835.
Eaton Hodgkinson (1789-1861) became involved, at Fairbairn's request, in August 1845 to 'deduce if that were possible, a formula which, from the observed strength of a tube of a lesser, might enable me to 20 calculate the strength of one of greater size'. Hodgkinson and
Fairbairn were both 56 years old and had previously collaborated in
107 Manchester, and although Hodgkinson habitually referred to Fairbairn as 'my friend', or indeed 'my valued friend' he was obviously unhappy about his position in relation to Fairbairn. Writing to Stephenson in ,
March 1846 he said, 'As I have no direct correspondence with you, ...
I should, perhaps, have acquiesed in my friend Wm. Fairbairn
continuing to be the medium of communication, had I conceived that he 21 could in all cases have been so with propriety'. He also conveyed severe strictures on the recent Millwall experiments;
I feel deeply obliged to you for the confidence you have placed in my friend, though I doubt much whether, with his slender stock of experimental knowledge he ought to have undertaken such a trust. You will see from looking over his published papers that his experiments have been confined to the transverse strength of rectangular bars of one inch square. He no doubt relied on me, but had it not been that I was bound to him by gratitude for the liberality he has shown me in furnishing the means of experiment I should not have accepted the offer to act under him in the case. It is the first time I have been engaged in experiments of which I have not had the direction and I believe I have made and published more than any man living. 22
This certainly gives an idea of the relationship between the two men, and explaining the delay in making his objections he said 'although consulted I was not called in at the commencement; but after the 1 apparatus was formed, and about /3rd. of the experiments were made.: and 23 then not to direct but to advise and compute'. Stephenson's reply was such that, a week later, Hodgkinson felt it better 'to be at the trouble and expense of a visit to London, than leave any misunderstanding as to 24 what I had said or done'. Obviously chastened, Hodgkinson continued;
I do not wish to exclude Mr. Fairbairn, except from taking the lead in these matters which his want of education and experience render him wholly incapable of ... Mr. Fairbairn has represented me as a mathematical person, not as an experimenter, he forgets that I directed or made many, perhaps most, of his experiments: and if I am known to the public it is for my experiments, and those alone, or nearly so. 25
108 Matters were eased by his visit to London and only eight days later he wrote to Stephenson from Manchester saying, 'As my friend Mr. Fairbairn is going to London he has kindly undertaken to be the bearer of this letter, and he has promised to render every assistance which his great practical knowledge will enable him to do in carrying out my views in 26 the further experiments'. But by July 1846, after the first experiments on the large tube at Millwall, he complained of the delay in getting his own experimental tubes made in Manchester: 'My friends consider me to have been very ill used by Mr. Fairbairn in this matter, but I do not intend to let that interfere with my efforts to render you 27 any service I can in this matter'. A little later he expressed the hope that;
Mr. Fairbairn will bear better the intrusion of his friend, into the sanctum sanctorum of an inquiry which he conceives he has an exclusive right to, than he has hitherto done. I am sure that as a friend to both he ought not to object ... I cannot help feeling a deep regret that Mr. Fairbairn should still persist in his dislike to my procedure in the investigation of a matter in which information seems to be so all important, and a failure would be so serious. Could you do any thing to reform Mr. Fairbairn's antipathy? 28
These extracts illustrate the background to the experimental work in
London and Manchester. Hodgkinson's experimental and mathematical contribution will be considered later.
The youngest member of the team was Edwin Clark (1814-1894) who met StephensoninMarch 1846. In his determination to arrange a meeting he continually called at the Great George Street office and was eventually granted an interview with Stephenson who, learning of his mathematical knowledge;
offered him a few day's work in regard to a problem on which he was then engaged, namely, the nature of the strains on the great Britannia Bridge tubes, under certain hypothetical conditions ... Mr. Stephenson was so struck with the criticisms and
109 suggestions offered by Mr. Clark, that he at once placed the matter in his hands. A room was provided for him in the Great George Street office. 29
Clark wrote to his friends conveying his excitement at his good fortune;
I have got put into my hands by Mr. Robert Stephenson all his ideas and wishes about the intended bridge ... All is at present in embryo. I am sole manager of the plans and sole calculator of all the mathematical work, and have liberty to perform experiments ... I have made a model of the bridge for Mr. Stephenson, and we spend every day two or three hours in chatting together on the subject. He is a delightful fellow and a very clever practical man. 30
Thus he became Stephenson's resident engineer and represented him in all matters relating to the experimental and site work. Writing to
Stephenson a little later he said, ' I have seen Fairbairn & Hodgkinson and commenced my mediative commission with little success at present. 31 They continue to hate each other most enthusiastically'. Early in
1847 the question of continuing the Manchester experiments was raised.
In January Clark wrote to Stephenson from Manchester;
Mr. Fairbairn is here, all in a pickle about the complaints made against him, and protesting against farther experiments ... I have not seen Hodgkinson. I should like to know your wishes as to his making more experiments which after his present rest he will no doubt be anxious to do and to continue till doomsday if you like. 32
In February Clark relayed Hodgkinson's 'personal longings after farther experiments on his darling subject 'elasticity' to come out with at the 33 University'. By March pressure to terminate the experiments was such that Hodgkinson complained of Stephenson being 'uncourteous'. Stephenson considered Hodgkinson ' a great deal too thin skinned - tell him if I had my own way he should go experimenting until the last days, but I am 34 driven by many considerations to put an end to them now'. Clark offered to ease the situation in Manchester;
I am going to dine with him and put him in a good humour which is easily done by a little salve applied to his vanity bumps - He says all 110 TUBULAR GIRDER EX PERIMENTS for the CONWAY and BRITANNIA BRIDG ES
184 5 1846 181 7 n :3 -1 Ap r May I·Jun J ul IAUg Se p Oct Nov IDe Jan Feb Mar Ap r May Jun Jul iAug Se p Oct Nov Dec J an Fe b Mar Apr IMa y l 1-" C ::0 1-' O' 0 f ~ C STEP II ENSON 3 4 z E 1-' 0 ru PJ r- I-' '1 0 1-' FAl nOAI RN l Cl Cl -< ~ 1-" ::J '1 IIODG KINSON 2 Cl. I0. CD :3 '1 PJ CLAR K 5 ::J r'1 [) X CD EXPE RIME NTS '1 1-" at 3 CD MIL LWALL I~ :J ("t" EX PEI1 IM ENTS on LARGE MODEL (Il 1 l' l~ l' ::r ~ Wfi//h' Dmmn Rmnm ~~"'~ J.~ JI EXPE RUŒNT S nt MANCIIEST ER
~ 1 MI. 11 111 11 11111 11 111111 1. Fairbairn cons ult ed by St ephenson- ~ Cylindrical Tubes 2. Ho dgkinson consulted by Fairbairn 3. Stephenson in Ita ly ~ Elliptical Tubes 4 . Re port to Ch este r and lIo1yhead Railway Directors
, fa Rolled 1 beams 5. Edwi n Clark interviewed by Stephenson
" mn. Rectangular Tubes the first mathematicians living acknowledge his greatness and importance and never treat with him as a mere man of business assigning specific dates to his calculations or limits to his enquiries. 35
Stephenson came to rely greatly on Clark and in 1848 recommended him to the Parliamentary Commissioners on the Application of Iron to Railway
Structures as 'the person most competent to give them information upon 36 the subject of tubular bridges'. Edwin Clark's personal copy of 37 Fairbairn's book has survived and is a fascinating source regarding his feelings about Fairbairn. He added extensive marginalia, some of which is merely exasperated comment such as 'ignorance is bliss', 'bosh', 38 'how patronising', or 'a mass of egotistic misrepresentations'. But in other cases Clark adds his first-hand knowledge of particular events and so corrects Fairbairn's account. In 1850 Clark published his own account of the bridges -. 'with the sanction, and under the supervision, 39 of Robert Stephenson'. This is certainly the better technical account and includes general material on beams and the properties of materials of construction.
So much then for the background to the model tests and the relationships between Stephenson, Fairbrairn, Hodgkinson, and Clark from July 1845 to April 1847, the period during which the experiments were made in London and Manchester. It is important to bear these personal feelings in mind in the following discussion of decision-making and the role of model testing in the design of the tubular bridges.
Experiments in London and Manchester 1845 - 1847
The experiments on the transverse strength of tubes fall into three groups; firstly, there were the preliminary series made by Fairbairn at Millwall between July and October 1845. These were made on simply- supported circular, elliptical, and rectangular tubes, together with some 111 on rolled '1' beams. Secondly there were Hodgkinson's experiments in
Manchester between January 1846 and April 1847 made on simple rectangular tubes. And thirdly there were the experiments on the large tube with a cellular compression flange made by Fairbairn at Millwall between July
1846 and April 1847 (see figure 4.1). Before discussing the experiments in detail we should consider the stated motives for making them. 'Before any experiments were started Stephenson had already made an approximate calculation of the strength of a tube which William Pole considered
'though necessarily very imperfect, gave confidence in the feasibility of the design'•40 Stephenson said the calculation was made by
'assimilating the tube to a cast iron girder' and applying Hodgkinson's formula for such girders. Stephenson added, 'although this was not strictly correct reasoning, it was for practical purposes a near approximation to the truth; and as it disregarded the sides as an 41 element of strength, it appeared to lead to unquestionably safe results'.
This type of calculation based on flange areas and depth completely overlooks the possibility of buckling - it was an important role of the subsequent model experiments to demonstrate the possibility of this latter failure mode. Nevertheless, Stephenson's satisfaction with a sufficiently-strong structure is understandable at this early stage - it was after all only a rough check, but Stephenson continued this attitude into the design programme. It is typical of the engineer's approach and is clearly distinguishable from that of Hodgkinson, who was seeking the best tube cross-section. Writing later of this early stage in the investigation Stephenson said 'I could not at that time avail myself of the generally received theories of tubes, viz. that their strength was directly as their sectional areas and depth, and inversely as their length, for no experiments had been made confirmatory of such 42 theory, or which furnished any data for practical purposes'. This is a curious and misleading statement - there was obviously no 'generally 112 received' theory of tubes, had there been the whole story, certainly as regards the experimental models, would have been very different.
Stephenson is obviously referring to the contemporary beam formula and his assumption that it applies to tubes again ignores lateral instability as a limiting parameter. The formula states that the breaking load
W = A.d.C. where A = cross-sectional area, d = depth of section, L = L span, and C = experimentally-determined constant for a particular form of section. This equation (discussed further in chapter 6) had certainly been used from the 1820's and that Stephenson could not 'avail' himself of it is indicative of the confusion surrounding the design of the tubular bridges. As we have seen, Stephenson wished to make experiments even if only to inspire confidence in the railway directors. Fairbairn on the other hand considered, perhaps with hindsight, that 'new developments, as well as correct results, are only obtained by repeated trials of an experimental and inductive character. It shall be my special province to ascertain the facts, and determine the law which 43 governs the strength and form of this important structure'. Hodgkinson was more explicit and exposed the real issue;
The tendency to undulation in compressed plates presented a difficulty which had not previously been felt, and of which theory could offer no solution ... the laws of resistance of plates to • wrinkling were utterly unknown, and if they had been known would probably, as I thought, have been too complex to be useful in the prosecution of the present enquiry. 44
This is an interesting statement implying as it does that mathematical laws, even if available, might not be of much use in such an engineering design problem. Moreover he considered, 'The obtaining of a proper proportion between the thickness of the plates at the top and bottom of 45 the tubes is only to be determined by experiment'. Whereas Edwin
Clark considered the preliminary experiments at Millwall exploratory and conducted 'not so much with any particularly definite object as to
113 find out what information was required and they were made simply to see, by breaking a few tubes, what would be the course of inquiry 46 necessary for making a larger tube'. At one level, the need for fundamental data about an entirely new structural form is obvious, what is less obvious from the accounts is the extent to which they thought the experimental tubes were models of the full size structure.
This obscure but fundamentally important issue is discussed further in chapter 6 in relation to scaling laws. First we should establish how each of the principal parties used the word model. Fairbairn reserved 1 the term model for the 75 foot span tube ( /6th. full size) but nevertheless said, 'The whole of the experiments had a direct reference to the proposed bridges ... and the diameters, lengths, depths, and thicknesses of each tube may be considered as certain proportional 47 fractions of those structures'. This is not entirely true. Hodgkinson on the other hand did not regard any of the tubes as models and felt the preliminary experiments were 'on too small a scale to be useful as 48 models of the intended bridge', and speaking of the last experiments on the large girder; 'This tube has been called the 'Model Tube'; but it was not a model of the bridge, either in the form of the bottom or of 49 its tubular top'. This is certainly true. Clark however uses the word model indiscriminately in describing all the experimental tubes, and furthermore said;
In determining the size of the models, it must be remembered that Mr. Stephenson had already, on other grounds than the proportions necessary for strength, decided approximately on the dimensions of this bridge. Its height was to be sufficient for the locomotive, while a much greater height would have endangered the sides; a .good proportion for the depth of large cast-iron beams had been found to be about one-fifteenth of their length, and therefore the same proportion had been provisionally fixed for the tube, while the breadth was governed by the space necessary for the passage of the trains. The dimensions, then, were 450 feet length, 30 feet height, 15 feet breadth ... It will be found that these proportions are maintained in the models with such 114 variations as would give data for testing theories of the effect of change of any particular dimension. 50
Clark confuses the issue here somewhat. It was surely the necessary
15:1 span/depth ratio which decided that it was possible for locomotives to travel inside the tube. However from the foregoing uses of the word model (and from other evidence) it is clear that theie were
basically two schools of thought. Hodgkinson obviously felt that he was undertaking analytical experiments to provide parameters for an eventual theory of tube behaviour, whereas Fairbairn, Clark, and Stephenson considered that they were testing models to prove that a given design was likely to be sufficiently strong and adequately stiff.
Having mentioned briefly the motives for making the tests and the means of arriving at the sizes of the experimental tubes, the apparatus and techniques will next be described.
Apparatus and Experimental Techniques
Fairbairn's Preliminary Tests at Millwall
This series of experiments began in July 1845 on a simply- supported cylindrical tube. This was supported on stacks of'timber
(AA in figures 4.2 and 4.3) which Fairbairn loosely described as 'two 51 solid blocks' but which Clark more accurately referred to as timber 52 packing adapted to the shape of the tube'. The load was applied to the centre of the tube on a suspended platform carrying blocks of pig iron loaded incrementally and the corresponding deflection noted.
To enable the load to be removed at intervals and gradually re-applied, a transverse cast iron lever (H), operated by a screw jack, was used
(figures 4.2 and 4.3). The permanent set induced in the latter stages of loading could be measured with the load temporarily removed by means of the lever. As the deflection increased, the fulcrum of the lever could
115 U E ilk 716
J T i Z- L_ 1 7- -J
Reference: An Account ... of the Britannia and Conway Tubular Bridges,
William Fairbaira, London, 1849. 4.2 1
Reference: The Britannia and Conway Tubular Bricoes , Edwin Clark,
London, 1850. 3 be lowered by means of the nuts on the screwed studs. Although these experiments were made on quite simple apparatus, Hodgkinson generously admitted that it was;
very ingeniously constructed: and well adapted to avoid shaking, in loading and unloading the tube; but the tensile force being, from the nature of the apparatus, always exerted in one vertical line, the tendency of the weight was to draw the tube in that direction only, and to prevent it getting out of the vertical line; which is so frequent a cause of failure in wrought iron girders ... in the future experiments it will be desirable to apply the pressure so as to allow the tube to yield in the direction of greatest weakness. 53
It is not quite clear what Hodgkinson is getting at here. He appears to be concerned about lateral stiffness and implies that by loading the tension flange this inhibited horizontal movement. But this system surely simulated the real loading more accurately than Hodgkinson's lever-loading method adopted in Manchester.
Hodgkinson's Experiments in Manchester
Hodgkinson visited Millwall in August 1845 in connection with
Fairbairn's work and feeling that it left much to be desired obtained
Stephenson's consent to make his own experiments in Manchester. He had no facilities for fabricating experimental tubes or premises for conducting tests and in these respects he was doubly reliant on Fairbairn.
This placed him, as he felt, at a distinct disadvantage;
The experiments were made upon a plot of ground, taken for the purpose, very near to Mr. Fairbairn's engineering works in Manchester. The tubes were mostly executed by him, from my directions,.under Mr. Stephenson's orders, and I had men from his works to assist in making the experiments. He had, therefore, every means of knowing the objects of the experiments, and the results arrived at; and of advising Mr. Stephenson conformably to them. 54
The accounts in the correspondence (figure 4.4) show that the rent for this land was £112 for the nine months ending at Christmas 1846, and that Hodgkinson received a fee of £50 per month for 'professional work'. 116
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The handwritten copy in Edwin Clark's diary is dated 8 January 1847.
Reference: Autooraph Letters, Institution of Civil Engineers, London.
Diary No. 2, Edwin Clark, Institution of Civil Engineers, London. 4.4
For these experiments he had 'an apparatus of a very superior kind 55 constructed' employing the lever-loading system previously used in 56 his tests on the cast iron girders of the Salford railway viaduct.
Figure 4.5 shows the engraving he sent to Stephenson in March 1846,
but, at Stephenson's suggestion, the iron base beam was replaced by
'six baulks of timber for the platform to break the tubes upon:
and the lever apparatus ... will be rendered stronger and adapted for 57 the present purpose'. Figure 4.6 shows the apparatus as modified for
the Manchester experiments made between May 1846 and April 1847. The
timber base comprised 'two parallel rows of baulks of timber, three in 58 height, between which the tube was laid'. This platform was stiffened
by inclined timber struts fitted into cast iron sockets secured to the
base by wrought iron straps and nuts. The advantage of the lever loading
system was, of course, the multiplying effect extending the load range
whilst minimising the handling of pig iron. In the apparatus as drawn
(figure 4.6) the leverage is 7:1. Therefore, if the weight on the
platform is W, the load applied at one end of the tube is 8W - the end
reaction on a beam due to a central load of 16W. Hodgkinson's system
did not accurately simulate the symmetrical bending of Fairbairn's
Millwall system as the central load and one end of the tube remained on
the same horizontal line. But more importantly, his system of loading
severely inhibited the buckling mode in the compression flange (now on
the underside). This is the more surprising in view of his criticism of
Fairbairn's loading system. Hodgkinson experimented on rectangular
tubes, without cellular flanges, on spans ranging from 3'9" to 45'-0".
Increments of load and corresponding deflection were recorded. Throughout,
characteristically, he complained of delays in getting tubes made and in
July 1846 said to Stephenson 'my experiments ... are not as yet of that
important character which I wished for - through Mr. Fairbairn's neglect 59 to prepare the tubes'. Again in the autumn he wrote; 'I have only 117 •••
/ J .1 • is S[•24/ 4 e
'The accompanying drawing is a sketch of that engraved in my unpublished aaditions to Tredgold on cast iron'. Hodgkinson to Stephenson, 26 March 1846 (Autograph letters, I.C.E.)
Beam - under test
Loading lever
Experimental load (w) a
If a : b = 6 : 1 then reaction (r) = 7w
Therefore applied load W = 14w.
Reference: Autograph letters, I.C.E.
4 4, (Joone Aq umeapa8)
- M CD 0
184 9 (11 9
23 ) XX1X )
, A , • i ppend - M , , x AA x 0 :eguaaaja Cross beam spans from3'-9"to45'-0" Six baulksof timber Timber Strut Hodokinaon's Lever Apparatus through post Load appliedcentrally under test Wrought irontube lever Load multiplying platform Loading today been able to recommence the experiments, partly because the
weather has been very wet and I have a very imperfect shelter; but 60 principally because I have had nothing prepared'. In the last
stages of his tubular girder tests Hodgkinson attempted to stiffen the
compression zone with cast iron plates, but it was too late to influence
the design of the bridges. Clark was a frequent visitor to Manchester
and his diary contains a sketch of such a composite tube failure
(figure 4.7). Apart from the transverse tests on rectangular tubes,
which attempted to model the structural action of the bridge, Hodgkinson
made other experiments as part of his investigations. These included
axial compression tests on tubular wrought iron columns of square, 61 circular, and rectangular cross section. In addition, experiments
were made to compare the strengths of cast and wrought iron solid
columns 10 feet high and 1 inch square, and on the resistance of 62 horizontal tubes to side impact. But in the circumstances perhaps the
most important were a series of forty experiments on the resistance of
isolated rectangular plates of wrought iron to compression along their
long axis. Hodgkinson found the buckling resistance was proportional to 2.878 t where t is the plate thickness- A century earlier Euler had 3 established the resistance as being proportional to t . It is clear
from this that Hodgkinson was not imbued with the same sense of urgency
about the bridge design as Stephenson and the rest of the team and
indeed seems incapable, or unwilling, to separate research from design.
Experiments on the Large Tube at Millwall
Fairbairn's last experiments in London overlapped to some
extent with those of Hodgkinson in Manchester previously described (see
figure 4.1). As the techniques employed were similar to those of
Fairbairn's preliminary experiments it is only necessary here to mention
the method of determining the model dimensions. Their role in the 118 ^
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Reference: mss Diary, Edwin Clark, Library of Institution of Civil Engineers.
Letter dated 28 April 1847. 4.7 decision-making will be dealt with later.
In December 1845 Stephenson decided to test an experimental girder of one-sixth the linear dimensions of the main tubes of the
Britannia Bridge, 'corresponding, as nearly as possible, in every respect with what it was then supposed might be the best ultimate form to adopt. The proportions of this model were thoroughly discussed'. 63
The dimensions were:
Clear span: 450 = 75 feet
Depth at mid-span: 27= 4 feet 6 inches 16 Width: = 2 feet 8 inches
The plate thickness was similarly determined; 'the same proportion was maintained, i.e. six times the thickness of the plates of the model gives 64 the thickness then proposed for the Britannia Tube'. Construction of the tube began in April 1846 and was completed in July. The tube was simply-supported between baulks of timber as in the previous Millwall experiments and Clark, aware of Hodgkinson's practice, said; In so important an experiment it was determined to break the tube by actual 65 weight suspended from its centre without the medium of a lever'. The
Millwall system simulated more accurately the real loading of the bridge by being applied through the bottom flange. Figure 4.8 shows the arrangement adopted at Millwall. A transverse timber beam (CC) could be raised by two powerful screw jacks to relieve the tube of load at intervals. DD were temporary supports to arrest the falling load when the tube failed. Weights were laid on in increments of about one ton and the corresponding deflection recorded. The difficulties encountered in this procedure are described in chapter 5. We must now consider the contribution of this mass of experimental data to the design of the
Conway, and more particularly, the Britannia Bridge.
119 ipparalan for Eaperimenling on the Jilodel Fig. 67.
Fig. 68.
Reference: An Account ... of the Britannia and Conway Tubular Bridges,
William Fairbairnt London, 1849. 4.8 The Role of Experiment in the Design of the Britannia Bridge
From the conflicting statements in the published accounts,
(although sometimes resolvable from the manuscript sources) it is
surprisingly difficult to establish precisely how the model tests
contributed to the design of the Britannia Bridge. What specific
questions for example were answied by the experiments and to what
extent were the small tubes genuinely models of the bridge? Indeed the
ultimate and crucial question is whether the Britannia Bridge could
have been safely designed without model tests at all. The whole issue
is probably best considered by looking at some specific problems which
arose during the course of the investigation and thereby assess the
contribution of the experiments to the final decisions.
Having chosen a possible span/depth ratio for the tube one of
the first decisions concerned the need for supporting chains. Did the
models contribute anything to this decision? Stephenson had originally
thought of a tube with chains (at least for erection purposes) but in
giving evidence to the Select Committee in May 1845, before any tube
experiments had been made, he said 'in going into the calculation of the
strength of the tube, I found that I did not require the chains
themselves, and therefore I have since proceeded upon the idea of the 66 plating merely and simple tubes'. However, in his Report to the
railway Directors of February 1846, although still reasonably sure that
the chains could be dispensed with, he stated that the question 'will be 67 determined by the proposed additional experiments'. To this Report
were attached those of Fairbairn and Hodgkinson where differing views
were expressed. Fairbairn at that time felt that chains would be useful
during site erection (as did Stephenson) but added, 'provided the parts are well proportioned, and the plates properly riveted, you may strip off
the chains, 68 Hodgkinson on the other hand felt'obliged to 'recommend 120 that suspension chains be employed as an auxiliary, otherwise great thickness of metal would be required to provide adequate stiffness and 69 strength'. The future tube experiments were to remove any doubt on the subject, but it is interesting to note that Stephenson had convinced himself of their dispensibility, by calculation, in May 1845.
The model tubes merely reassured and provided additional confirmation.
This was not only a characteristic role for model tests but fundamentally the basic philosophy - indeed the idea of the true structural model had not yet dawned.
But undoubtedly the principal subject of investigation concerned the best form and proportions of the tubular girders.
Stephenson had decided on a tubular girder before any experiments were made but not on the cross-sectional form of the tube. Fairbairn's preliminary experiments at Millwall on tubes of circular, elliptical, and rectangular cross-section convinced him that the latter;
indicate a considerably increased strength when compared with the cylindrical and elliptical forms: and considering the many advantages which they possess over every other yet experimented upon, I am inclined to think them not only the strongest but the best adapted (either as regard lightness or security) for the proposed bridge. 70
The rectangular form was irrevocably chosen by the time of the progress report to the railway Directors in February 1846 when Stephenson said,
'Another instructive lesson which the experiments have disclosed is, that the rectangular tube is by far the strongest, and that the circular 71 and elliptical should be discarded altogether'. It is important to note that it was the experiments which decided this issue of the form of the tube. The 1846 Report comprised contributions from Stephenson,
Fairbairn, and Hodgkinson. In his report, Hodgkinson introduced some analysis and gave equations relating 'f', the bending stress (although he did not call it this), the load, and the cross-sectional dimensions of
121 the tubes. On checking his equations it is clear that they are based on the elastic simple bending theory. For example, for the rectangular tube he gives:
3 w 1 d f = ------3 3 2(b.d -b.'d' )
Where w . the breaking weight 1 .= the span d = the overall depth d'= the internal depth (symmetrical about neutral axis) b = the overall breadth b'= the internal breadth
If we substitute the above notation in the simple bending equation we have: Applied bending moment (M) x Extreme fibre distance(y) Bending stress (f) . Second moment of area (I) w.1 d 3 3 where: M = 7--4 y = . - and I = .Th- (b d - b' d' ) then Hodgkinson's equation satisfies the simple bending equation. The difficulty however lay in the meaning given to the symbol 'f'.
Hodgkinson said;
The value of f, which represents the strain upon the top or bottom of the tube when it gives way, is the quantity per square inch which the material will bear either before it becomes crushed at the top side or torn asunder at the bottom. But it has been mentioned before, that thin sheets of iron take a corrugated form with a much less pressure than would be required to tear them asunder; and therefore, the value of f, as obtained from the preceding experiments, is generally the resistance of the material to crushing. 72
Crushing is not the best word to use in this context and is in fact misleading. 'f' is really the maximum bending stress in the flange of the girder and in those tubes that failed in tension at the bottom its value would, and did, approximate to the known tensile strength of 2 wrought iron (about 20 tons/in )• This value had been established in tensile tests on the material, particularly in connection with the design of suspension bridges (see chapter 3). It was an appropriate parameter in those cases as material breakdown initiated the failure. But
122 for those tubes which failed by buckling of the compression flange the value of f, as a stress, is essentially irrelevant as the compressive stress thus established would be well below the crushing strength of wrought iron. It is surprising to think that Hodgkinson did not
understand that the simple bending formula was not applicable to beams suffering lateral instability failure. It is possible (and Hodgkinson does this) to regard 'f' simply as an experimentally-determined constant
connecting the buckling load and the cross-sectional dimensions of the tube, limited to that particular tube. Later in the same report
Hodgkinson said; 'The determination of the value of 'f', which can only
be determined by experiment, forms the chief obstacle to obtaining a formula for the strength of tubes of every form. When f is known the 73 rest appears to depend upon received principles'. Edwin Clark certainly appears to appreciate the difficulty as, writing later, he said;
With respect to those experiments in which failure took place by the buckling of the top, f only represents in each experiment the resistance to buckling in a tube of that particular thickness of plate, and would not apply as a constant to tubes of other dimensions. This was really all the information directly obtainable from these experiments. 74
But in the 1846 Report Hodgkinson did say that the first of his objectives in the experiments was to 'ascertain how far this value of 'f' would be affected by changing the thickness of the metal, the other dimensions of 75 the tube being the same'. This relationship he established by experiments on individual plates as mentioned previously. The Report certainly convinced the railway Directors of the need for further experiments and was a watershed in the experimental investigations.
Before the Report the concern had been to establish the best form for the tube, whilst the subsequent experiments were principally concerned to optimise the proportions of the tube in terms of simultaneous tension and compression failure in the flanges. More of this a little later.
Nevertheless, one last question of form had to be resolved namely, 123 whether to use a thick plate or a cellular flange to achieve adequate stiffness. There was the usual argument about who suggested the modification which was first used at the end of the preliminary experiments at Millwall of which Hodgkinson said;
I suggested the introduction of circular cells into the top of the wrought-iron tubes. This idea I urged strongly on Mr. Fairbairn, and mentioned it in the presence of Mr. Stephenson's assistants, during the first experiments in London, and he made a drawing of it in his note-book. After this, he had an experiment made on a tube with a corrugated top. Mr. Stephenson informs me, that he thought of stiffening the tops of the tubes by cells at the same time; a matter so obvious, that it is no wonder that two, or even three persons, should think of it at once. 76
This is further evidence both of Hodgkinson's continuing sensitivity and of Fairbairn's tendency to claim ideas as his own. Nevertheless, the changes which the cells, particularly in the compression flange, underwent during 1846 tells us much of the role of 'model' tests in the decision-making process. Although Hodgkinson's experiments on isolated tubes under axial compression demonstrated the superior resistance of those of circular cross-section, other considerations governed the final form of the cells. Hodgkinson said;
since rectangular tubes are weaker than square ones to resist compression, and these much weaker than cylindrical ones, I hope the latter will be substituted for the former, as it would, according to the preceding experiments, effect a saving of one-fourth of the metal in the top, leaving the strength the same. This matter is of the more consequence, as the weight of the tubular bridge will bear so large a proportion to the breaking weight. 77
Nevertheless, Stephenson wrote to Fairbairn in December 1846 saying;
'The more I think of the circular cells, the more the practical difficulties increase. If you can see your way to riveting the rectangular cells effectively, I have no question about their being the 78 most eligible, notwithstanding their comparative weakness'. So here experimental evidence was overruled by practical constructional and 124 maintenance considerations. Furthermore, the decision to use a cellular flange made of thin plates was forced on the designers by the limitations of the rolling mill, as William Pole said;
to collect the necessary quantity of material of the top and bottom in single plates would have required the former to be 2.7 inches, and the latter 2.3 inches thick; and had such plates been procurable, nothing better could have been desired, and the cells would have been unnecessary. At that time, however, it was impossible to procure plates of such a thickness, whose quality could be depended on; and the engineer in this, as in numberless other details, had to adopt what he could obtain. 79
It was this alone that led Stephenson to adopt a cellular tension
flange where stiffness was not an issue.
We should now consider the question of proportion. The
preliminary experiments at Millwall quickly revealed the two principal
failure modes as being either in tension (the bottom plate tearing
between the rivet holes), or in compression where the top plate became
'wrinkled'. Writing to Stephenson in March 1846 Hodgkinson commented
on these experiments and shrewdly observed that providing the thickness
of the sides was sufficient to maintain the form of the tube (a separate
issue, discussed later) then they should aim at 'the top and bottom
being of sufficient strength for the purpose required, and adapted to 0 each other, so that both should be ready to give way at the same time'8
This is an interesting, and in this form early, statement of what was
to become known as the 'critical', or 'balanced', or 'economic' section.
Although the concept of balancing the areas of the tension and
compression flanges of cast iron beams had been considered earlier by
Hodgkinson, and others, it is worth noting that buckling failure of the
compression flange had not been a problem. The main reason for this is
a purely practical foundry matter. The ideal beam section would require
a tension/compression flange area ratio of about 6:1. This would mean 125 a thick tension flange, connected by a thin web, to a small compression
flange and such a casting would suffer from differential cooling
effects leading to serious internal stresses. Practicable castings would
have a flange area ratio of something like 3:1 giving an excess
compression area. In addition, in building structure, as opposed to
bridges the compression flange would usually have been adequately
restrained by the flooring medium. In the wrought iron tubes the
compression flange was relatively unrestrained and the early experiments
quickly revealed this weakness. Once the need to optimise the flange
area ratio was established the subsequent experiments were largely
directed to this end and this represents the principal contribution of
the model tests to the design procedure. The extent to which the introduction of wrought iron represented a departure from established
practice is clearly revealed in Clark's comment on the early tests at
Millwall;
In conformity with the rule for cast-iron girders, the first experiments were made with the thickest plates at the bottom, and subsequently these same models were repaired and used with the thickest plates at the top, with much better results, as might naturally be expected with thin tubes; but the buckling of the top in thin models, as with the circular and elliptical tube, still interfered in all the results. 81
This echoes Stephenson's Report of February 1846 when he said that the early experiments demonstrated that 'rigidity and strength are best obtained by throwing the greatest thickness of metal into the upper 82 side'. A month later Hodgkinson, anxious to continue his experiments in Manchester, warned Stephenson;
You conclude in your Report that the form of the tube and the distribution of the material have been finally determined ... Finding that you had drawn these conclusions, I felt some alarm lest they should not be borne out by the facts when fully explained ... The experiments made by Mr. Fairbairn on circular, elliptical, and rectangular sections are numerous, and I hope good; but do not; I think, show, except 126 approximately the proper distribution of the material. 83
Various ratios of flange area were tried in the ensuing experiments and in the large tube the top flange comprised six rectangular cells (the area constant throughout the span) whilst the bottom flange was made of 84 flat plates of varying cross-section. Its flange area ratios (top/ bottom) varied from 24.024/8.8 (2.75:1) in the first experiment to
26.56/22.45 (1.2:1) in the sixth and last experiment. Apart from the flange proportions the other issue which emerged was the importance of the proportions of the sides of the tubes. Here was a much more complex
problem because web loading, both in tubes and lattice girders, far from being understood was hardly even recognised as an issue by Stephenson and his contemporaries. Edwin Clark's manuscript diary shows the simple moment method of calculating the load, and hence stress, in the flanges of the large experimental tube (figure 4.9) but no such simple method was available for evaluating the shear loading effects on webs. In the
1846 Report only Fairbairn mentioned the problem specifically;
we shall have to consider not only the due and perfect proportion of the top and bottom sides of the tube, but also the stiffening of the sides with those parts, in order to effect the required rigidity for retaining the whole in shape. These are considerations which require attention. 85 S Some four year later Edwin Clark commented;
here again, as with the top, we have evidence of the great caution necessary in arguing from models to large structures; for whereas with the top the fears that first arose were afterwards proved to be groundless, so with the sides, the confidence their behaviour in these experiments at first inspired was subsequently discovered to be unfounded. And while little difficulty was experienced in the construction of the enlarged top, the greatest caution was necessary in properly proportioning and stiffening the sides; which, indeed, will be found the limit to any much greater extension of the magnitude of such structures. 86
127
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Reference: mss Diary, Edwin Clark Library of Institution of Civil Engineers. Hodgkinson did at least attempt an analysis of this problem. He wrote to Stephenson in March 1846 about some proposed new tube experiments saying;
The thickness of the metal I propose to be reduced from the middle towards the ends in each tube, in the following ratio, dividing the length of the tube into 3 equal parts, and making it of equal height throughout. 8 8 12 15 16 15 12 8 8 The thickness of the tube at half the distance between the middle and each end will be 12/16 or 34 of that in the middle. The thickness at of the distance from the middle to the ends will be 15/16 of the middle thickness, being but little reduced; and the thickness near to the ends I have proposed reducing to 8/16 or that in the middle. The theoretical scale of resistances would require the strength of the tube in different parts to be as below. 0 7 12 15 16 15 12 7 0 ... The dimensions given in at present are for the sides of tubes only. 87
This is a confusing statement. He was obviously using a parabolic demand-curve for the distribution of plate thickness which leads one to suppose that he was considering the bending moment curve due to a uniformly distributed load. But the loading was applied as a concentrated load at mid-span to which was added that portion of the self-weight of the tube which would produce an equivalent mid-span bending moment.
In any case bending moment was not the criterion. It is clear that
Hodgkinson was confused at this stage (at least) and certainly he was not using shear as the criterion for side-wall loading. Hodgkinson added nothing to this aspect of the analysis and design in his contribution to the Iron Commissioners Report some three years later. It was by observing the signs of structural distress; the onset of buckling and even cracking in the paint on the sides of the tube, that the problems were overcome in a practical manner. Stiffeners and gussets were added, not only at the points indicated by the failure of the model tubes under simulated working load conditions, but also to enable the tube to withstand the abnormal support conditions encountered during the 128 floating and lifting into position. William Pole said 'The sides of the tubes weigh nearly forty per cent of the whole weight. Had they
been constructed in situ, this weight might have been considerably 88 reduced. In the matter of web buckling the experiments added little to the understanding of the problem and did not lead directly to an analytical technique. The last experiment on the large tube was made on the 15th, of April 1847 - 'too late to be of much service in 89 assisting in the design for the tubes', In addition, the large tube was only to a very limited degree a geometrically similar model of the full-size structure. In particular, the one-sixth scale model had six rectangular cells in the compression flange whereas the Britannia tube had eight square cells. Hodgkinson warned of problems after the first experiment on the large tube saying;
Had the bridge been made after that model, its top cells would have been from 2ft.6in. to 3 feet square, and would have been crushed with a very small pressure, as is evident from my experiments on the resistance of rectangular cells ... This I mentioned strongly to Mr. Fairbairn at the time, urging that, if he succeeded in persuading Mr. Stephenson to have the bridge made with these large cells, the project would, I conceived, be a failure. 90
In addition, the model did not have a cellular tension flange whereas the full-size structure did. But this was not crucial as, providing there was sufficient area to resist tension, there were no instability problems in this zone. This brings us back to the important issue of buckling and here the geometric scale factor of 1/6th. was applied to the thickness of the model plates. This meant that in scaling up the plate thickness by a factor of six the bridge had a factor of safety 6 x 63 against buckling of 36 (i.e. 2 ) on unrestrained lengths of plate. 6 As Hodgkinson found that the scaling law for the strength of mathematically similar tubes was approximately 1.9 (see chapter 6 and figure 6.3) then the buckling issue, with its square scaling law, was safely contained within this parameter. 129 From a cursory acquaintance with the mass of published material relating to the design of the Britannia and Conway Bridges it would be easy to conclude that the model experiments played a central and crucial role. Fairbairn, in his account, was obviously concerned to maximise his part in the design process (it is this that mars his book), and he elevates his 'model' experiments to a position of prime MI■111..11■1, importance. Although Edwin Clark was an interested party his account is more detached, is broader in scope, and indeed volume one could be regarded as a textbook on beam analysis. Eaton Hodgkinson was not an engineer at heart and did not feel himself subject to the pressures of demands for decisions made under the stimulus of deadlines. He was concerned to develop a theory of tube behaviour and wished to extend his experimental work. Had he been able to insist on a full investigation of some issues, such as the buckling of the sides of the tube, the bridge completion would have been severely delayed to the cost of the Railway Company. However interesting in themselves the importance of the model tests has, as we have seen, been somewhat exaggerated over the years. In many 'cases the data resulting from the experiments was overruled by considerations of expediency, facility of construction, erection, and maintenance. Very few further tubular bridges were built as they were quickly superseded by plate girder and lattice trusses, but the enormous publicity and discussion attending the design and construction of the prototype tubular bridges ensured at least an acceptance of the possibility of using models to solve other bridge design problems.
130 Lattice Girders
The general opinion of engineers appears to be that the cast-iron arch is the best form for an iron bridge when it can be selected without regard to expense or to the height above the river or road which is to be crossed. For low bridges the bowstring girder is also strongly recommended. Lattice bridges appear to be of doubtful merit.
Iron Commissioners Report 1849.
Despite this prediction it was not long before the superior
strength/weight ratio of the lattice girder, for a given span and load,
led many railway bridge designers to adopt this form to solve their high
load, large span problems. Although timber trussed roofs and road bridges
had been designed for centuries 91 the introduction of metal lattice
girders presented certain analytical problems. Before the widespread 92 adoption of Clerk Maxwell's graphical methods in the 1860's it was
considered necessary,or at least desirable, even with simple
triangulated pin-jointed structures, to verify experimentally the
results obtained by mathematical analysis. Here again it was the
problems facing railway bridge designers that led to the widespread
adoption of the open-web trussed girder in Britain. These railway bridge 93 lattice girders fall into two main categories:
(a) Those of constant depth (parallel booms), and
(b) Those with a varying depth/span ratio ('bowstring').
Experiments on both types were made in the middle of the nineteenth
century.
Doyne and Blood's Model Warren Girders - 1851
In November of 1851 a paper was read to the Institution of
Civil Engineers which compared a small-scale model test with mathematical analysis. The paper, entitled; 'An Investigation of the Strains upon 94 the Diagonals of Lattice Beams, with the resulting Formulae', was the work of W.T. Doyne95 96 and W.B. Blood. The avowed object of the 131 experiment was for 'illustrating, practically, the truth of the mathematical reasoning, upon the strains to which the different parts 97 of a lattice beam were subjected'. It is interesting to note that although it was the forces (or 'strains') in the 'different parts of a lattice beam' which were to be studied, the investigation confined itself to the diagonal, or web, members. This reveals yet again the contemporary lack of understanding of....._ web loading conditions. More of this later and we should first consider the apparatus. Although the authors used the term model throughout it was not intended to be a replica of a particular bridge and scaling laws were not considered. The experiment merely involved the replacement of individual members of a 98 small Warren girder by a 'dynamometer' and comparison of its reading with the calculated value of the force in the member. Although straightforward, a degree of ingenuity was displayed in making the diagonal members:
those acting as struts, in the model being made of mahogany bars 14 inches long by li inches wide and I inch thick, with their ends simply let into the top and bottom strings, but not made fast in any way; while the ties are made of light hoop iron chains, each in three parts, put together with loose pins passing through them, and fastened to the top and bottom by the iron pins, which connect the parts of which they are formed; this arrangement preventing the possibility of the struts acting as ties, and vice versa. The length of the model, between the points of support, is 154 inches (12 feet 10 inches), the triangles formed by the lattice bars are equilateral, each side being 14 inches long, making the depth from centre to centre of the top and bottom 12.124 inches. Its total weight is 22 lbs.. and any portion of it can be taken out, so that a dynamometer can be inserted, by which means the strains upon all the parts have been measured, and compared with those calculated. 99
Figure 4.10 is a drawing based on this description, The authors did not describe, in detail, the method of force measurement but a few years later William Humber said "The strains were measured by inserting - a dynamometer in place of the different rods in succession and carefully
132 3 2 4 6 8 10 member 2 3 5 7 9 11 numbers
self—weight (2) 12.124 only (22 lbs.)
-12 equal (14") panels = 154"
Doyne and Blood — model Warren girder 1851
W = 77 lbs. O
11 + 38.5 = 49.5 lbs. 49.5 lb.
U = 14 lbs. O
11 + 77 = 88 lbs. 88 lb.
W = 14 lbs. O
11 + 70 - 81 lb. 81 lb.
W = 7 lbs. O
11 + 35 + 38.5 = 84.5 lb.
Reference: Proc.I.C.E., Volume Xl, November 1851, pp. 1-14. 4.10 100 screwing it up to the required length'. It must, therefore, have been a spring balance device with adjusting screws. Whether the one dynamometer could work both in tension and compression, or whether separate ones were used, is not clear. Again, whereas Doyne and Blood only gave details of the diagonal members in the model, Humber added;
'The top and bottom members were formed of mahogany rods connected like the chains of a suspension bridge, so that the nature of the strains 101 might not be affected by the stiffness of these parts'. In other words, the booms were not continuous but comprised pin jointed members.
Experiments were made under five different load conditions and the diagonals were numbered from the centre of the span outwards to the supports (see figure 4.10). The results are given in Table 4.11.
The authors were aware that under symmetrical loading the distribution of struts and ties would also be symmetrical;
With a load at the centre, the horizontal strains are greatest at the centre, decreasing towards the ends, in the ratio of the distance from the centre, while the strains upon the diagonals are uniform throughout the beam. With a uniform load, the horizontal strains are greatest at the centre, decreasing towards the ends, in the ratio of the ordinates of a parabola, while the strains upon the diagonals commence at the centre, increasing towards the ends, as their distances from the centre. 102
This is quite correct, and to a present-day reader clearly indicates the bending-moment and shear-force origins of the loading of boom and web members respectively. But we must not impute this knowledge to Doyne and Blood - in 1851 the issue was confused, at least as far as the web members were concerned. That the forces in the boom members could be found by taking moments about the appropriate panel point was understood, and indeed a similar technique had been used by Edwin Clark in working up the results of the large Britannia tube model (see figure 4.9). Doyne and Blood gave general formulae for the forces, which in the case of the 133 STRAINS upon the Diagonals of the Monm, as calculated by the Formula, and as indicated by the Dynamometer.
Strain with Strain with Strain a oh 14 Iln.Strain with 14 %a l, ,,in w ith 711n. its 0%11 771bs. at at each point I at each point at inch point of Weight. Centre. of Top. I of Bottom Ter ..n1 Bottom.
'd. •
-a t 01 1 711 11 la 101 a lm' = = 01 Ca
'6 44.6 .11} 8. 7 .• '6 4.6 2 1.7 45 45.7 9.8 17 17'5 13 13.8 3 2.9 .• 146.9 27.1 •• t 1.9-1 23.1 4 4.0 47 48.0 981 28.25 34 36.3 ‘11 32.3 5 5.2 •• 49.2 •• 45.6 41.6 6 6'3 481 50.3 46 46.7 54 54'S 50.8 7 7.5 •• 51.5 .• 64.1 • 56:0 60.0 8 8'7 511 52.7 651 65.3 73 73.4 69 69.3 9 9.8 •• 53.8 S2.5 74.5 78.5 10 11'0 571 55'0 87 S3•7 95/ 91'8 9! 87.8 11 12'1 •• 56.1 101.0 • • 92.9 97.0
Results from Doyne and Blood's model Warren girder
Reference: Proc. I.C.E. , Volume Xl, 1851,.pp. 1-14. 4.11 boom members were taken as understood, and for the diagonals, the subject of the model experiment, were deduced from them. As an example of these equations the authors said that for a central load on the top
boom (loading case 2 in figure 4.10);
the horizontal strain at the centre is WL 2x s WL and at any other point s =---. --, where 4D 4D L W = the weight, L = the length, D = depth, and x = the distance of the point from the abutment; and the strain upon any diagonal is y = Wb/2D, where y = the strain, b the length of the diagonal, and W D as before. 103
The general equation for boom member forces is clearly based on moments,
and when Doyne and Blood describe x as 'the distance of the point from
the abutment' they obviously refer to the panel point appropriate to
the member concerned. But the diagonal members were not so easily dealt with. They said that the diagonals could be analysed 'by the medium of
the resolution of forces' and their equation for the force in a diagonal was based on the fact that 'the strain upon each lattice being uniform, and equal to half the load applied, increased by as much as the lattice
bar is longer,than the perpendicular of the triangle of which it is the 104 hypotenuse'. Although this is effectively saying that the vertical
component of the diagonal force is equal to the shear force across a
panel (in this case 2) they did not use the term shear force at any time.
Neither did they use the term bending moment although in the graphic
construction showing how the forces in the members changed across the
span it was, in effect, the bending moment and shear force diagrams
that they produced. However, at this time the concept of a shear force
diagram was not used by engineering designers. Doyne was a practising
engineer and said that his advocacy of lattice girders was;
based upon careful theoretical investigation and practical experience, both by experiments on a sufficiently large scale and by the construction of bridges of considerable span. He had determined to enter thoroughly into the investigation of the 134 subject, and therefore had ... so constructed the large model that ... the strain in any part could be measured. The experiments were in all cases made before the calculations and the coincidence between the results was remarkable. 105
He went on to claim important advantages for the lattice girders
compared with wrought iron tubes. Several eminent engineers were present at the discussicn including Hawkshaw, Bendel, and I.K. Brunel who agreed
that the Warren girder was a most efficient system. Doyne and Blood's 106 model girder does not appear to have survived. Their use of a model
is an interesting example of the confirmatory experiment. The high
degree of correlation between the experimental and calculated results
rendered further experiments unnecessary and in any case drawing-office
techniques were soon to largely supersede the mathematical and
experimental analysis of such straightforward lattice girder systems.
107 Earlier in 1851 R.H. Bow produced his important book on
the analysis of braced structural frames which contributed significantly
to the spread of analytical and graphical techniques for the solution of statically determinate structures. This led directly to a reduction of
the need for model experiments. A reviewer of the book summed up the
contemporary situation;
Lattice bridges appear to afford great facilities for spanning very wide intervals, and the limit of their capabilities in this respect do not appear to have been as yet nearly attained. In simplicity of construction they have great advantages as compared with their rivals - suspension, tubular, compound girder, and arch bridges. Their rigidity adapts them to the requirements of railway and other heavy traffic. Lastly, the statical strains to which braced or latticed structures may be subjected by assigned loads, are capable of being investigated with close approximation to mathematical exactness. The absence of theoretical information ... and of general experimental knowledge of the strength of large lattice bridges, are possibly the reasons that those structures have not been more frequently employed than they have been, in modern engineering 108
135 At this period the lattice girder really began to challenge the tubular variety and their relative merits was a frequent topic of discussion.
The reviewer felt that the intrinsic merits of the tubular bridge had not been accurately defined and cautiously added, 'there are those who
believe that tubular bridges are not so economical as lattice 109 bridges'. The subject was raised in 1852 at the Belfast meeting of the British Association when James Barton, engineer to the Belfast 110 Junction Railway, read a paper on lattice girder analysis. He had compared tubular and lattice girders in connection with his design of the Boyne Viaduct and made experiments on girders of both types having the same weight, span,and depth. Details of the girders were not given but Mr. W, Coates, of Belfast, said that he had 'constructed the experimental girders exactly as directed by Mr. Barton'and 'the lattice bore slightly more than the tubular' and added moreover that he 'could construct lattice-girders at from 10 to 20 per cent, less cost than 111 tubular girders'. Fairbairn was present at the meeting and said he could not account for the poor performance of the tubular girders and felt that they 'must have been peculiarly constructed'. However, he had the grace to add that he 'adopted tubular bridges believing them to be the best, but if shown that a lattice-bridge is better he would adopt 112 it'. The lattice bridge quickly challenged the tubular form (even after the triumph of the Britannia bridge) and with increasingly simple analytical techniques for the statically determinate lattice girder they were widely adopted. But this still left analytical problems with the statically indeterminate lattice girder and here again model tests were used.
Airy's Bowstring Girder Model - 1868
By far the most novel and ingenious experimental method of measuring forces in members of model lattice girders was that used by 136 Wilfred Airy in his model bowstring girder - the last recorded structural model test in Britain in the nineteenth century. He described his experiment to Members of the Institution of Civil Engineers in 113 April 1868 where he suggested that his technique was applicable to
'other instances of mechanical structures with complex bracing, where the labour and uncertainty of a theoretical calculation render an 114 experimental investigation exceedingly desirable'. He described his model in the following words:
The bow was of steel a inch square, span 6 feet, rise 1 foot; the string was constructed of two slips of oak each 4 inch deep by a inch wide. These two slips were inch apart, and embraced at each end a small block of oak, to which they were rigidly fastened, and into which the two ends of the bow were let and wedged up. The suspension ties were of steel-wire No.6 gauge (96 feet to the ounce); these wires were attached at the top to strong loops rigidly fastened to the bow, and at the bottom to the eyes of small eyebolts, which passed between the two slips composing the string, and were secured by nuts to small wooden blocks nailed at each joint on the under side of the string. By means of these nuts each tie could be accurately adjusted as to tightness. 115
His drawing of the apparatus, and one based on this description, are given in figure 4.12. Although Airy termed it a 'bowstring girder, as 116 ordinarily constructed' the curved compression member was continuous through the panel points as was the horizontal 'string' or tie. This had the effect of making the structural action more like that of a statically indeterminate tied arch, with wire members in the spandrel, rather than a girder. The experiment was only concerned with the spandrel, or web, members and Airy explained that he had been engaged on the analysis of a bowstring girder and after 'easily determining the strains on the bow and string' had found himself 'totally at a loss for a correct or reliable method of determining the strains on the ties, and, by reason of the difficulty of the theoretical investigation, had found 117 himself driven to adopt the experimental method described'. This is somewhat confusing. Airy does not give the method of calculating the
137 ZTRA LA 3 • ©fl 'J3 (cr VTr acy©el II'2 Ti
FI:e1.• 2. 7=1;•-1 PLAN OF STRING.
“ 3 square steel bow 8 3
steel wire No. 6 gauge (96 feet/ounce)
oak string
eyebolts and wooden blocks nailed nuts to underside of string
Airy's model bowstring girder — 1868
Reference: Proc. I.C.E. , Volume 27, 1868, pp. 443-453. •I2 bow and string forces. As a tied arch it would not respond to simple statical analysis and even if he regarded the booms as articulated at the panel points he could not use the panel-point moment method previously described as the panels were counterbraced and this rendered the problem statically indeterminate. Nevertheless his experimental method produced good results for the web members.
Airy considered that the load on these web members depended on the stiffness (or flexibility) of the bow and string and he began by measuring the transverse flexibility of each separately:
The bow being set on end vertically sagged 5/32 inch from its span, when lying flat on a table, by its own weight, and deflected further, pretty uniformly, at the rate of 3/32 inch per lb. hung from the top. Again a straight piece of steel, of the same section as the bow, being laid on two supports 6 feet apart, deflected at the rate of 5/32 inch per lb. laid on at the centre. The string being laid on supports 6 feet apart deflected uniformly at the rate of 1/4 inch per lb. laid on at the centre. 118 Having determined these flexibilities (see figure 4.13) he made no further use of them. The real interest in his experiments lies in the method of measuring the forces in the wire members under varying load 119 conditions. Airy said that the thin steel wire in tension;
gave, on being sounded, a good resonant musical note; and advantage was taken of this to compare the note of any string with that of a free string suspended in a frame made for the purpose, and cut off by a sliding bridge to the length of the string under comparison. The free string supported a small scale-pan, and this scale-pan was loaded with weights till the note of the free string and that of the string under comparison exactly coincided. 120
He said that this comparison of notes was easily made by ear but the only quantitative data Airy gave was in the statement that 'the effect 121 of oz. in 80 oz. being clearly perceptible'. If this was his smallest discernible increment the accuracy of matching would be 1 in
160 or 0.625% - almost certainly better than spring balance accuracy. 138 3" square steel bowN„ 8 3" per lb. 1 32
/
3" square steel \ 8 5" per lb. 32 f
3 X 3 73 oak . 1 " per lb. f 4 w
Flexibility measurement
Load applied at each lower node in turn (11 experiments)
Loading method
Equal loads applied simultaneously to each lower node
Reference: Proc. I.C.E., Volume 27, 1868, pp. 443-453. 4.13 The wires in the web of the model vary from about 12 inches to 6 inches in length and it is possible to calculate the increase in frequency produced by a 1 oz. increment on a tesion of 80 oz. A 12 inch wire tensioned to 80 oz. will produce a frequency of 250 cycles/sec. (a pitch close to middle 'C' on a piano) and an increment of 1 oz. would increase 122 this by only 0.62 cycles/sec, whereas on the 6 inch long wire the frequency would increase from 500 to 501.24 cycles/sec. Some people would find the slow 'beat' (0.62 cycles/sec) of the long wire difficult to hear but the shorter wires would have presented less difficulty.
Airy's 'monochord frame' used for the comparisons is shown in figure 4.14.
The problem of measuring the force in compression members by this method,
'which at first appeared a great obstacle' was solved by his discovery that a uniformly distributed load placed all the wires in tension. He, therefore, applied a blanket uniform load (see figure 4.13) placing, in addition, the travelling point load at each of the lower panel points in succession. The effect was to reduce the tension produced by the distributed load in some members but providing there was residual tension the method was satisfactory.
Thus;
if T = tension in any wire produced by the distributed load only.
t = tension in any wire when a load additional to the distributed load is placed on any one node; if t< T, then the additional single load has created a compression C in that tie, where C = (T - t). The effect of this blanket distributed load would be to raise the datum of pitch at which the experiment was conducted and ease the problem of matching the pitch of the wire with . the 'monochord'. From these results Airy produced a series of practical design rules for proportioning the members of bowstring girders. In enumerating these he stated two important fundamental ideas; firstly that of linear-elastic behaviour when he said 'the tension, or thrust 139 MONOCITORD FRAME FOR COMFAU.IcoM OF MUSICAL NOTES.
AA. Upright legs of frame graduated with inches and parts, measured from the upper end of the wire.
BB. The sliding bridge, which can be moved up or down the legs AA, and clamped fast in any position.
CC. The comparison wire, made of.the same material as the ties of the girder: it can be cut off to any required length by the sliding—bridge BB, and weighted to any required tension by means of. weights laid in the small scale—pan.
K. A small block running under the back edge of the base, so as to tilt the frame slightly forwards, and cause the wire to bear steadily, though lightly, against the sliding—bridge.
Wilfred Airy's 'Monochord' — 1868
Reference: Proc. I.C.E., Volume 27, p. 447. 4.14 .Fig :8.
1.1mufes of the Institution of Civil En6ineers Vol 1.2(VII Scssian 1867_68.
Specimen results from Airy's model bowstring girder
( unite = ounces 'T' = thrust )
Reference: Proc. I.C.E., Volume XXV11. x.15 is proportional to the weight causing it' and, more importantly, an
early statement of the principle of superposition - 'When several
weights are applied at the same time, the effect on every string is
that due to the sum of the effects which would be produced by each of 123 the weights separately'. Airy felt that his musical technique was
'novel. elegant, safe, and applicable to a great number of
complicated structures, such as lattice-girders, station-roofs, and
trussed arches' and concluded by giving his reason for using
experiments;
It was no unusual thing for an engineer, with an important and extraordinary work on his hands, to have a model made of the intended structure for the purposes of experiment, if it was thought that thereby results might be arrived at affecting the security and expense of the work. This, then, was what he had done in the present instance; he had shown how such a model could be constructed, so as to obtain important results, which could scarcely be obtained except by direct experiment. 124
This is a classic statement of motive but it did not lead to the adoption of his method in future work. Airy regarded his experiment as
'simply an accurate investigation in one single instance of a very
difficult problem, and was not framed to exhibit a complete theory on 125 the subject'. The system was statically indeterminate whether his
bowstring girder (with double diagonal bracing) was considered as a
pin-jointed girder, or as a tied arch. W.H. Barlow was at the discussion of Airy's paper and although he considered the acoustic method 'at once
novel and interesting' he expressed doubts about the continuity of the
bow and the use of steel and wood and their effect on the wire tensions.
Airy felt however that this would not affect the result to any degree when compared to a truly pin-jointed girder. Nevertheless, two years later in 1870, a paper translated from the French was read at the
Institution of Civil Engineers in which the author, Jules Gaudard, said;
140 The ingenious musical contrivance employed by Mr. Airy to measure, on a small scale, the strains of the lattice of a bow-string girder has given results different from thoa?.obtained by calculation based upon the hypothesis of articulated members. This ought to be a matter for surprise; it is an additional proof that in these matters, where there are an accumulation of organs capable of affording mutual aid, calculation is insufficient to decide upon the real distribution of the efforts. 126
This is a somewhat puzzling statement as Airy did not offer any calculations for comparison with the experimental results. Such a calculation would have been extremely laborious and although the analytical problem of the statically indeterminate truss had just begun 127 to receive attention in France it did not even begin to become available to engineers until the work of Mohr and subsequently of
Castigliano. It is interesting to note that Airy's bowstring model came under the notice of a French analysist - even if he was critical.
Gaudard did not condemn the experiment out of hand however and said;
Nevertheless, it does not on that account lose all its utility; for it indicates distribution, possible or virtual, if not effective. It ought to be generally admitted as a principle of resistance, that a construction sustains itself as long as it has not expended the whole of its possible conditions of stability; it suffices, then, to prove that a certain state of stability is realisable, in order to be assured that the work will not perish. 128
The role of a model in predicting a sufficiently safe structure was_one of the most important aspects of model testing and the fact that Airy's model experiment was the last one mentioned in the nineteenth-century
Proceedings of the Institution of Civil Engineers reflects the fact that the growth of mathematical and graphical analytical techniques for lattice girders soon rendered them unnecessary.
Web Buckling in Plate Girders
The buckling of thin vertical web plates was first investigated experimentally by engineers in the experiments relating to the Britannia
141 Bridge design (see earlier part of this chapter). The problem remained however when engineers developed the wrought iron plate girder of I section. The first use of models, with paper webs and cardboard stiffeners, in the study of this problem was made by D.J. Jourawski in 129 Russia in his extensive criticism of the Britannia Bridge design.
In Britain, Benjamin Baker made use of a similar technique to study web buckling in plate girders. Speaking of the nature of the problem in 1870 he explained; 'The laws governing the strains on the flanges are so well defined and easy of application that but little variety of opinion has ever existed as to the required strength of those portions; 130 but the same cannot be said with reference to the web'. He referred to the earlier work of Fairbairn and Hodgkinson by saying, 'the experiments on the model tube for the Britannia Bridge indicated clearly that diagonal strains, both compressive and tensile, occurred in the webs of the tube; the direction was evidenced by the wave of buckling following an angle o131 of 45 Baker referred, in 1880, to some experiments he had made on five iron plate girders of equal size, but with varying proportions of flange and web and in addition;
He also made models of the girders to scale, with wooden flanges and stiffeners, and paper webs. Testing these little wooden girders to destruction, the lines of stress were indicated with conspicuous clearness; and the phenomena exhibited by the full- sized girders were exhibited also, in an exaggerated degree, by the models. Indeed, the latter experiments proved more suggestive than all the experiments on the iron girders, and all the mathematical investigations on the subject; and, after witnessing them, there was no difficulty in forming a clear idea of the nature and intensity of the strains in a plate web as ordinarily constructed. 132
Baker did not give his scale factor, or factors, or reveal whether he was aware of the proportionality of the buckling load to the cube of the web thickness (shown to be so by Hodgkinson) and although he obtained a clear idea 'of the nature and intensity of the strains' there can be little doubt his models were merely qualitative in nature.
142 Continuity in Seams and Girders
In the middle of the nineteenth century structural designers began consciously to introduce continuity into bridge girders, that is bridges having two or more spans in which the girders were continuous over the intermediate supports. This achieved the desirable objectives of reduction in mid-span bending moments and deflections but the technique was attended by consequent analytical difficulties. The system was inherently statically indeterminate and thus the support reactions could not be determined by statics alone. The other, related, difficulty lay in predicting the deflected curve of the continuous girder and hence the location of the points of contraflexure and the consequent zones of tension and compression in the flanges. The differential equation of the elastic curve was, of course, known to mathematicians and although Navier was the first to tackle the continuous beam problem the method had little currency amongst practising bridge designers in Britain at the time. In any case solutions using this 2 d y equation (-M = EI 2)were laborious and although two French analysists dx- Bertot (1855) and Clapeyron (1857) developed the three moment equation the techniques remained cumbersome until Professor Hardy Cross introduced his relaxation technique of moment distribution in the 1930's.
Prior to this various graphical techniques were evolved in order to avoid the mathematics. In the 1850's simple model tests were considered desirable to check the calculated results and to reassure engineers of the deflection mode of continuous girders. In addition quite drastic confirmatory experiments were made on completed bridges prior to opening 133 them to traffic. Undoubtedly the widest discussion of the problem was that initiated by the refusal of the Railway Commissioners to allow the opening of a two-span continuous girder bridge over the Trent at
Torksey in Lincolnshire.
143 The Torksey Bridge
Early in 1850 the Torksey Bridge case was extensively discussed at the Institution of Civil Engineers in London. The bridge, comprising a continuous girder of two spans each of 130 feet, had been designed by John Fowler, engineer to the Manchester, Sheffield, and
Lincolnshire Railway Company, and constructed by William Fairbairn.
The structure is usually described as a 'tubular bridge' although it was not of the Britannia type but was an over bridge with wrought iron box girders at the sides. The matter was brought before the Civils in
January and February but the principal discussion occurred in March in connection with a paper by Fairbairn 'On Tubular Girder Bridges'. 134
It was said that 'the Torksey Bridge had excited the attention of the profession, from the fact of the Commissioners of Railways having objected to the opening of the bridge for traffic, on the plea of care 135 for the safety of the public'. Fairbairn began by enumerating three points on which differences of opinion existed; firstly, 'the application of a given formula for computing the strength of wrought iron tubular girders', secondly, 'the excess of strength that should be given to a tubular-girder bridge, over the greatest load that can be brought upon it', and thirdly, 'the effects of impact, and the best mode of testing 136 the strength, and proving the security, of the bridge'. Only the first two points need concern us here. Fairbairn referred to his
Millwall experiments which he claimed established, for girders having a cellular top, the relative sectional areas of the top and bottom to be as 11 and 12. Using these proportions he claimed that the usual beam aA.C. formula W _ was valid (see the earlier part of this chapter).
But the relevant discussion in this case really turned on the fact that the two-span girder at Torksey was continuous over the central support, a consideration which Fairbairn blatantly ignored;
144 It is considered by some engineers, as very important to the strength of these bridges, that the girders should be continuous, or extending over two, or more, spans. This is, no doubt, correct to a certain extent, and although the fact is admitted, yet this consideration is nevertheless purposely neglected, in these calculations; any auxiliary support of that kind acting merely as a counterpoise. It is considered safer, to treat the subject on the principle of compassing each of the spans with simple and perfectly independent girders. 137
This is not altogether surprising as Fairbairn totally failed to
understand the effects of continuity on the Britannia Bridge tubes and
it means that he had no contribution to make to the Torksey bridge
discussion.
138 Captain Simmons, the Government Inspector of Railways,
objected to the Torksey bridge design and said;
I do not consider, that the viaduct can be opened for the continuous passage of trains, with safety to the public, and that it will not be in a condition to be opened, until it shall have been so strengthened, that a load of about 400 tons, (including the weight of the beams themselves, and all the standing parts of the bridge), distributed equally over the platform of one span, shall not produce a greater pressure upon the top plate of the girders, than five tons per square inch. 139
Fowler requested C.H. Wild to determine the compressive stress in the
top of the girder under the conditions prescribed by Simmons. That
Fairbairn was not highly regarded is clear from Wild's condemnation of
Fairbairn's neglect of continuity as 'not only unphilosophical, but
positively dangerous' and he added 'The importance of continuity was acknowledged by all authorities, so that it could not be admitted, that this was an element, the consideration of which might, with any 140 propriety, be neglected'. Wild was aware of the importance of knowing the position of the points of contraflexure in the analysis of a two-span continuous beam and
145 In order to check, practically, the calculated position of the point of contrary flexure, the experiment was tried on a large wooden model, by loading it, first with such weights as represented the constant load due to the structure. The model then took the form shown by the dotted line ... and the point of contrary flexure was found to be 301- inches from the point B. The model was then severed and hinged at that point, when the curve and the deflection were found, as might have been expected, the same as before. 141
The experimental results are given in figure 4.16. The scale of the
'large wooden model' was not given but in determining the position of the contraflexure points on the full-scale structure it is obvious that
Wild was using a geometric scale-factor of 1/12, giving the model two equal spans of 130 inches,•or 10 feet 10 inches. Providing the bridge girder and the model were both uniform in cross-section this would be perfectly satisfactory. In addition, no elaborate scaling laws were necessary as only ratios of deflections between the continuous and discontinuous cases were considered. The second experiment was made
to ascertain the point of contrary flexure in a beam loaded as prescribed by the Government Inspector, over one span only, an additional weight was added, having to the weight previously applied on that span, the same proportion as 400 tons, the prescribed load, had to 150 tons, the weight of the structure; the point of contrary flexure then approached to within 214 inches of the central support. The beam was again severed and hinged at that point, and the curve was formed as regularly as before, thei deflection on the heavily-loaded side being 573 inches. 142
The third, and last experiment, was made to compare the continuous beam with two adjacent simply-supported beams;
The beam was then cut in half, making it into two detached beams, the ends meeting on the central , pier, when it was found on the heavilWoaded side that the deflection was increased to 9/3 inches. As much weight was then removed, as reduced the deflection to the same amount as had, in the continuous beam, been produced by the weight representing 400 tons, and the proportion borne by the weight requisite to produce a given deflection in the detached beam, was to that requisite to produce the same deflection in the continuous beam as 651 to 120. Having found the 146 c
Torksey Bridga - Continuity modal 1B50
• 1 ~ 11111" 1" 11111 1 111111 1 1 1 1 1 1 l "* *1 -. 1 1 continuous - 21:- . L-k--- -~=~- ~IIIIIIIIIIIIIIII~,,,, !lI'111 "* ;- -- -- 1 1 u: 1 1 . 5 continuous
L-~---- 1 __--.1._ 11111 " Il " III " 1il1 Il " i 1111 i 91- ~-... -~------~ ~ ~k i 1 discontinuoui 1
Determination of ceints or centra flexure and deflection ------_._----
Reference: Proc.I.C.E., Volume IX, 1850 pp. 233-287. 4.16 position of the point of contrary flexure in a beam, loaded in the proportions prescribed by the Government Inspector, it was easy to calculate the strain upon the top cells of the Torksey bridge, 143
This last statement is central to this account in which the physical cutting and hinging of a wooden model played such a reassuring role.
Wild used this knowledge to compute the compressive stress in the top cells as 4.67 tons/in2. He concluded in a tone which seems to sum up the mood of the civil engineers;
The experiments, therefore, fully corroborated the truth of the calculations previously made, and showed the compressive strain per square inch, on the top cell of the girder, to be less than that for exceeding which the Government Inspector had condemned the bridge, and thus an important line had remained for some considerable period closed at a great pecuniary sacrifice, the Railway Company had been, and were still deprived of the use of their property, and the public convenience suffered, not in consequence of any omission on the part of the engineer to provide adequate strength for the public security, but from the pernicious effects of Government interference, and from the necessary consequence of the want of practical skill, always demonstrated when officers whose duties were strictly military were entrusted with the control of civil works. 144
William Pole was requested by Fowler to analyse the strength and stiffness of the Torksey bridge and said;
It is remarkable, how closely the results obtained by Mr. Wild's experiments agree with the results of mathematical investigation, the general form of the deflexion curve being nearly identical in both cases, although the two results were obtained entirely independent of, and uninfluenced by each other. The experimental distance of the point of contrary flexure, where the model beam was cut across, from the centre pier, is a little less than 22 feet; as calculated, it is 22 feet 11 inches. For the unloaded beam, the calculation gives the distance of this point = 32 feet 6 inches; the experiment = 30 feet 6 inches. 145
Using these distances from the 1/12th. scale model span he found that,
'the experiment gives the greatest compressive strain = 4.67 tons; the 146 calculation = 4.55 tons'.
147 John Scott Russell, who first brought the Torksey bridge ban to the notice of the Civils, thought that the mathematics of Pole and the experiments of Wild both demonstrated the advantages of continuity and added;
The model exhibited the form of the girder in its actual condition, and demonstrated the enormous addition to its strength at the expense of a very small quantity of material; it was certainly, then, a radical error to omit so important a consideration as the continuity over the central pier, and any formula which neglected that element could not be accepted by the profession; but it was even less excusable, that a structure, which had been shown, both theoretically and practically, to possess the requisite amount of strength, should have been rejected because an officer of the Government, acting under the sanction of an Act of Parliament, had applied to a comparatively new system of construction, an antiquated formula, for which it was never intended. 147
Even after this discussion the Railway Commissioners were not entirely satisfied and on 26 March 1850 Fowler obtained the assistance of Mr.Pole and Mr. Wild in some experiments on the bridge itself. These were carried out in the presence of Captains Simmons and Laffan with the result that the Commissioners finally gave their permission for the line to be opened in April.
The Torksey bridge discussion made such an impression on the Civil 148 Engineering profession that it was still referred to in 1886. The bridge still stands, having been strengthened by a central steel lattice girder, but the line is disused.
Although the Torksey Bridge was the most widely discussed, there were other cases where British engineers turnedto models to help with continuity problems.
Brunel's Continuity Model
I.K. Brunel investigated the problem of continuity in connection with the design of his Chepstow Bridge (opened in 1852). Although
148 Brunel's son described the bridge as comprising 'virtually continuous 149 beams of five unequal spans' Brunel's experiment was made on a continuous beam of three equal spans, Here again it was considered desirable to check the results of mathematical analysis by means of small-scale experiments. Brunel's son described his father's simple experiments thus;
A deal rod, exactly half an inch square and 38 feet long, quite free from knots, was supported on props of equal height, above the perfectly horizontal and planed surface of a large beam of timber. The props were placed so as to correspond relatively to the actual spans,and the rod was loaded uniformly by means of a chain. It was thus bent into an elastic curve, the ordinates of which were very carefully measured, at every foot along the length, by a finely divided scale and magnifier. 150
The measured elastic curve was compared with that predicted by mathematics and the correlation was 'so close as to leave no doubt that a true knowledge of the nature of the strains had been arrived at .
Edwin Clark was the first to publish details of this experiment in 1850 152 (see figure 4.17) including a deflection diagram. A certain refinement of technique was revealed by the statement that the rod was
'turned over on each of its four sides, the experiments were repeated, and the average taken, in order to eliminate the effects of initial 153 curvature, or of unequal elasticity'. In addition to plotting the elastic curve Brunel measured the support reactions;
The pressure on each prop was also determined, by removing any particular one, and suspending the point of the rod immediately over it to a steel-yard, the weight being observed when the point of the rod was exactly at the same level as before the prop was removed. The obvious condition, that the sum of the pressures on the props should be equal to the weight of the rod and its load, furnished a satisfactory means of testing the results of these weighings. 154
Edwin Clark added some details of the weighing method;
The pressures on the supports of the model beam were measured by a steel-yard, applied at each bearing of the beam in succession. The distance 149 ::tl -..ro CD t1 ro ::J r.f8Fl~EI_:'TlO!1 (1!-1 (.: r__ 1 :;-:':1 i'; C)U;~ }~F.J~v::3. 0 CD B\.::llll o'lp'P'-.rte'l "J.t l"_1U' pûln'_f III en:J"~I~ C t11ro 1:J a 1:J en o t1 al t1 c: .... t1 cT #u.~"'~ 0 cT C .... ru ::l c :J ro 3 :J .... ro ...... ru III ru U1 th, of fi","," ",' ::l cT , ; ;, Th, 'ffi'Ü=l=Fm'" ''''',l' 1:J 0.. ru co"u"~f • ro CI .... ~ 0 1 m :J N e: III • ru t1 1. Points of Thcorclical < a. Observatio; Ob.crvcd Dl'flc,·tion Dcflcction. ~ I(or value of ï') (or value of y), c .... rr c c ...... 0 Inche •. Inche •. ru t1 Support on the outer prop •• '0 + 0'000 + 0'00 t1 C 3 '1 + 0'772 + '75 al t1 \il. ''2 + 1'4'22 + 1'38 .... 1'870 )'84 1 '3 + + 1 0. D '4 + 2'08 + 2'OG ru Centre of outer span ...... '5 2'OG '2.'06 III + + '.. '6 + \'77 + 1'8~j r1 '7 + )'39 + )'4) 0. '8 ' + 0'87 + 0'89 (;: ru t1 c: .g .... ~ x ru ru + 0-:36 + 0'37 ::J '0 n t1 .... ro 0 .... Support on the inner prop .. 1'0 + 0'00 + 0·00 n 0' t1 t1 ru 1'1 - 0'12 - 0'13 .... • .... D, 0' 01 3 ro .... 1'2 -0'09 - 0'08 t1 E ro a. ro 1 1'3 0'01 0'03 A CD :J + + 1 .... cT a. a. 1'4 0'07 + 0')'2. ,\0 c .... + r :r t1 (JI Centre of middlc span .•.. )'5 + 0'11 + O'IG 0 ...... H) 0'07 0'12 :J :J ru + + ~~ a. 10 :J 1 1 7 + 0'01 + 0'03 0 o 1 )·s 0 ::J CD - 0'09 - 0'08 ~ .. I·g - 0'12 - 0'13
1 Support ...... 1 2'0 + 0'00 + 0'00 1
~ . - A 8 C D
R E A C T 1 0 N Experiment Calculation
Support A 0.210 0.217
B 0.605 0.598
C 0.605 0.598
0 0.210 0.217
Total: 1.630 1.630
Brunel's Continuity Model
Reference: Britannia and Conway Tubular-Bridges, Edwin Clark, Volume 1, p.464. 4.18 from the fulcrum to the point of support of the beam was always 18 inches, and the weight on the steel-yard half a pound. The leverage,or distance of this weight from the fulcrum, was carefully recorded as the lever was applied to the different points of support. 155
A sketch based on this description is given in figure 4.17 and figure
4.18 shows the correlation between the experimental and calculated
reactions.
Edwin Clark's Britannia Bridge Continuity Model
Clark made an experiment very similar to Brunel's in order 156 to 'imitate the conditions of the Britannia Bridge'.
A rod of uniform red Memel deal, 1 inch square, and 33 feet long, was supported at five points. The two central spans were 11 feet each, and the side spans 5'6" each. Each face of the rod was placed alternately uppermost, and the deflections were measured from a straight edge beneath the rod. 157
The observed deflection was compared with the computed deflection and
the results are shown in figure 4.19. Unlike Brunel, Clark did not
measure the support reactions, but once the points of contraflexure are
established (shown ringed in the diagram) the calculation of the reactions
is a simple matter.
W.H. Barlow's Continuity Experiments - 1858
During 1858 William Henry Barlow made some small scale
experiments on continuous beams of cast iron. These are of interest as
they involved both beams of uniform section and those where the sectional
area was increased over the supports. As usual, deflections were measured
but a unique feature was that they were also tested to destruction. In
his introduction of the topic at the Institution of Civil Engineers Barlow
said, 'The experiments extended to a comparison of strengths and stiffness 158 of four descriptions of bars'. The range of beams is shown in figure
4.20. He used a single simply-supported span of 6 feet for comparison 150 a 0 0 0 cn • 0 awnT0A 40;96
VI ng aeT ncini o3 pue aTuueq T38 aqj :aduaaaja8 4 MIET3UT P3 pi enu
s B s rk' a Cl rit wi Ed nni a n n a B a
qTnuTquo3 a rid / z 4
S
Tht proportauuofdtr.... 6'
7
8 Centre support C Support 13 Support A Middle oflargespan Middle ofsmallspan
.9
10 11.131415 ,
:t.vm
1. beam ::•_11,por.tcdatfive
r.C.1, ismar of Obser- Number vation. '2 5 7 6 8 .5 9 4 0 8 2 3 0 6 4 3 7 ie
i ldflea totheupperfi4ure20 17 port
from sup- Distance 132 120 108 Inches. 96 84 19 66 60 72 36 55 48 66 22 24 44 33 12 II (=x). 0 - points. — •010 — .038 — .039 — •044 — .031 + .076 Deflection. observed Inches. • .031 • .294 . .408 .428 .374 . . • -359 '000 000 348 437 100 20') 000 tum•L.,th - — .035 — .023 — — .003 + .090 Computed Deflection
Inches. (=!/). . • • .'256 .35'2 . .431 . . • .318 .000 . -035 -0IG 000 041 139 418 436 398 208 000 wer une 53 tunes. Ha 6
.4
Ft:II: 7.
a 4 a fig a a a TRIAL REAMS.
W. H. Barlow — Continuous beam experiments — 1858
Reference: Proc. I.C.E., Volume 26, 1867, 4.20 •
TANI/ showing the Dsstxenon with 100 lbs. uniformly Distributed over CE-NTIIE Erns.
No. 2. \o3 Condition Continuous 1lesen. mcreasud three Continuous It om Int-msg.' to tin tarhe.l Ibsen toiled calt:-mty No. I. of times in smith over the I'..rs, doutle the d: pct over the hen. Length of 1. •rlr g equal to antra Span Uniform ContMiaow Beam. Loading. the weight of Peam biting 10. the **richt of Beam being in- of Beams. B,.g. I, 1.3. creased 25 per cent. 1 creased 50 per cent.
Inch. l inn h. inch Experiment No. 1 . •1703 Experiment Na 1 . • inl.03h8 Experiment Na 1 •1114 Experimer.t No. 1 • • •3;'5 • . .32...; Loaded only . 2 . •1572 2 . • 1274 „ 2 •1090 on centre " ,I 0, VP » ' . 3 • • •3449 span, the . . 3 . •1501 i . . 3 . •13.81 3 •1066 » :, 4 • • •35n5 ends being ; • . 4 . .1663 I •1167 fastened •• • P 4 Mean • . .3199 down. Mean . . . •1611 I Mean . . • 1321 Mean • • • 1114 . Summary shuts Inc the 11.2,41:ma as mo- wed • ith a deusubed &ans.
inch Inch. Inch . • 0979 Experiment No. 1 . • 0795 The load per Experiment•No. 1 . •1428 l Experiment No. 1 No. foot on • » 2 •1317 ▪ . 2 . •0935 2 . *0788 Condition of Loading, of centre span !Beam being twice . 3 . •1317 ▪ . 3 . • 0916 . 3 • '0723 that on side • 4 . • 0955 • 4 • '0723 1246 Loaded only on .1 1 46414 span'. centre spin. the I „ Mean . . . -1327 Mean . . . • 0946 Mean . . "0757 ends being f.J.stened , j 3 37-75 down . . . . .) 31 SS Inch. Inch. Inch. The load per f.vot on •1 Experiment No. 1 . -0S43 Experiment No. 1 . • 0496 Experiment No. 1 . :002228 1 37.92 Beam loaded centre elan being . , 27.0i ., 2 . .0823 . 2 . • 0477 0250 twice that on aide : 3 uniformly " " 21.63 over its . 3 . •0799 . . 3 . •0472 ▪ 3 . :002:39 whole ., 4 . •0799 . . 4 . :0497 Beam loaded nni- • 1 23.31 length. - formly over It& 2 13 • sti Mean . . . '0816 Mean . . . .0485 Mean . . *0250 whole length . . i 3 7.11
TABU of Entrain-re on Carr-now Gnats, showing the Weight on the en-rcE Sens at the Tnrc of Fr.scryst.
• No. I. No, 2. No:3. Condition Uniform Continuous Beam. I inch A similar Timm. II:acreaged three A similar Beam increased to double Detached Beam. 1 Inch omen, lowed of square. 15 feet long. supp,lnd times an width over the piers, the depth over the piers, the uniformly. Loading, at the ends. and on pl.r. 4 feet the weight of Beam being in- atucht of Dcaro being a:creased Length of baring 6 feel. equal to centre 6 Inchei on each sale the centre. cresuid Si) per cent. 25 per cent. span of Beams, sou. 1.2. 3.
lbs. II, lbs. lbs. Experiment No. 1 1,032.0 Experiment No. 1 1,567.2 Experiment No.1 1,569.6 Experiment No. 1 . . 696.0 „ „ 2 . : . 717.6 Loaded only 2 1,254'4 ,. . 2 1,656•0 » . 2 1,636•0 on centre " „ „ • 3 . . 662.1 . 3 1,186.4 . . 3 1.567.2 » . 3 1,636•2 „ „ 4 . . 494•4 span, the •• . ends being ,. . 4 1,054.2 „ . 4 .. . 4 1.658.4 fastened " Mean . . 642.52 down. Mean . . 1,131.7: Mean . . 1,596'8 Mean . . 1,675-05 _ Summary shoeing the Breaking Weights - - --- as compared • ath a detached Beam. Tbs. lbs. tin Experiment No. 1 1.411.4 Experiment No. 1 1,682 •4 Experiment No. 1 2,062.4 I 1,2.T:47.1%r The load per i No. of each 1r ro: Condition of Loadirg. ; of 1,,,N,..,...... ,, fixA on . . 2 1.637.G » . 2 2.107.2 . . 2 2,712.8 ri...en.ws-a centre span 1,433'6 1,726.4 1 Br:lb.:mg being twice " ,.3 . . 3 . . 3 2.916.8 that on side . . 4 1,411.4 . . 4 1,949.0 . . 4 2,420•0 Loaded only on .1 'Palm • ___ 1 1 1.7614 Mean . . 1,473.5 Mean . . 1,916.25 Mean . . 2.528 • 0 centre span, the . 0 2.4,,33 end being fastened 'I 3 •••••n•*-0 down . . . . 1 " -'
lbs. Ib.. lbs. The Ifidd per foot on . Experiment .19G7 centre span being 2 2. l.,824 Beam loaded . 2 1,300'8 .. . 2 2,284•6 . . 2 3,212.4 twice that on side ■ 3 3.3336 uniformly " !pans over its . „ 3 1,=3•6 . „ 3 1,9721 " . 3 2,510.4 ' • • • 1 whole . . 4 1,277'6 . . 4 2,356.0 « . 4 3,094.4 Brim loaded ani- 1 2.912i length. formly over its 2 3.5327 Mean . . 1,306.35 Mean . . 2,263.8 Mean . . 2,813.5 whole length - . , 3 4.42.36
W. H. Barlow - Continuous beam experiments - 1858
Reference: Proc. I.C.E., Volume 26, 1867, PP. 254-5. 4.21 with the 15 foot long continuous beams. Three loading systems were
used (figure 4.21). The beam systems were not intended to represent,
as far as we can tell, any particular bridge so scaling laws and
similarity problems did not arise - he was merely comparing the
relative performance of uniform and non-uniform beams. His results are
given in figure 4.21. Barlow summarised the results of beam number 4
(the best performer) by comparing its behaviour, under each of the
three load conditions, with that of the simply supported beam both in
terms of strength and stiffness: 'The mean relative strength of the bar,
in the three conditions of loading, that of the detached bar being 159 taken as 1, were as follows:-'
relative strength load case 1 = 2.6 2 = 3.93 3 = 4.42
He added that, 'The stiffness was increased in a still higher proportion,
for, taking the deflection of a detached beam at 100, the deflections
of the continuous beam under the three conditions of loading, were 31, 160 21, and 7 res pectively'. His conclusion was that, 'In a continuous
girder, if, instead of using an equal depth throughout, a greater depth and a greater sectional area be given over the piers ... an increase of strength is obtained in a much higher ratio than that of the increased 161 weight of metal employed'.
Stoney's Analytical Textbook
Bindon Stoney published his highly theoretical textbook on the 162 analysis of girders in 1873. It is somewhat surprising, therefore., to find him advocating, in the chapter devoted to continuous girders, a method for finding the points of inflexion depending 'partly on theory,
partly on experiment'. His technique appears to owe much to that of
Brunei and Clark: 151 Take along rod of clean yellow pine or other suitable material to represent the continuous girder, and let it be supported at intervals corresponding to the spans of the real girder. Next, load this model uniformly all over, or each span separately, or in pairs, or make any other disposition of the load which can occur in practice. Now, it is clear that, if the model and its load be a tolerably accurate representation of the girder and its load, the points of inflexion of the former will correspond with those of the latter; they might therefore be at once obtained by projecting the curves of the model on a vertical plane. It is difficult, however, to do this so as to determine the points of inflexion with the requisite accuracy, for the exact place where the curvature alters is never very precisely defined to the eye. The pressure on the points of support may, however, be measured with considerable accuracy, taking the precaution of keeping them all in the same horizontal line. 163
He does not say anything about the model loading method or of the
technique of measuring the support reactions, but he did echo Brunel in
saying; 'It it a safe precaution to measure the pressures on the points
of support with the rod turned upside down as well as erect, and then 164 take the mean measurement as the true result'. Having found the
reactions experimentally the ensuing analysis was straightforward. Later
textbooks treated the subject of continuous beams in an entirely
mathematical (or occasionally graphical) manner - the need to verify
results experimentally naturally diminished as engineering designers
understood, and gained confidence in, other analytical techniques. So
another aspect of structural analysis left the experimental area for that
of mathematical analysis and standard solutions.
Polarised Light and Model Structures
From the seventeenth century scientists had been interested
in refraction, bi-refringence, diffraction, and the optical properties
of various crystals and both Huyghens and Newton made observations of
importance. But it was Sir David Brewster who first suggested the
possibilities of the application of polarised light and transparent models to structural analysis. In 1816 he communicated the results of 152 165 some important experiments to the Royal Society, in which he
demonstrated that double defraction was not only a property of certain
crystals; it could also be induced in some transparent materials when
these were stressed. This stress could be produced by unequal heating,
or, of more relevance to our present purpose, by external loading. He
was able to 'communicate to glass, and many other substances, by the
mere pressure of the hand, all the properties of the different classes 166 of doubly refracting crystals'. But, unlike previous scientists,
Brewster suggested;
There is one practical application of these views which is particularly deserving of notice ... If the arch stones of models are made of glass, or any other simply refracting substance, such as gum copal, &c. the intensity and direction of all the forces which are excited by a superincumbent load in different parts of the arch, will be rendered visible by exposing the model to polarised light. If different degrees of roughness are given to the touching surfaces of the glass voussoirs, the results may be observed for any degree of friction at the joints. The intensity of direction of the compressing and dilating forces which are excited in loaded framings of carpentry, may be rendered visible in a similar manner. 167
This is, of course,not true as stated; it was not forces but stress
differences which produced the fringes. But the relationship between
optical fringes and principal stresses was not understood at this time.
Nevertheless, the notion of the potential engineering use of the
technique is typical of Brewster who considered 'the application of
science to the practical purposes of life' important 'in a commercial
country like ours, which depends so much on the improvement of its 168 manufactures, and the progress of the useful arts'. Brewster's
suggestion might have marked the beginning of the engineering use of
'photoelasticity' but this was not the case - largely for the reasons
given above. Even after the clarifying work of Clerk Maxwell the
nineteenth century can really only be regarded as revealing the pre-
history of this important model technique. The_ engineering Institutions, when concerned with optical techniques at all, were principally 153 interested in photometry and the artificial lighting of buildings.
Moreover there is no reference to the subject at all in the nineteenth century Transactions of the Institution of Mechanical Engineers - the 169 first reference occurring in 1911. The Institution of Civil
Engineers had occasional brief extracts from foreign scientific journals (which would have meant little to structural engineers). There was, however, one reference to Brewster's work in 1844 in connection with the question of the neutral axis in beams under flexure. It was with the study of beams that the link with the engineering world was first made and this takes us back to the work of Brewster.
Brewster's Model Beam Experiments - 1816.
His paper to the Royal Society contained a series of
propositions and experiments relating to loaded glass beams exposed to
polarised light in which he observed;
The convex, or dilated side of the plate affords one set of coloured fringes, similar to those produced by one class of doubly refracting crystals; and the concave or compressed side,. exhibits another set of fringes similar to those produced by the other class. These two sets of fringes are separated by a deep black line where there is neither compression or dilation. 170
Of these fringes he added, 'the tints are a maximum at the point where the pressure is applied, and ascend gradually in the scale of colours 171 towards the point of support'. Figure 4.22 is a copy of plate 1X which accompanied his paper. He described his technique thus;
I took a plate of glass ABCD, Fig.11 (p1.1X) six inches long, li broad, and 0.28 thick, and having placed its extremities, upon the points of support C, D, I bent it by a screw applied to the surface at M. Seven orders of colours were now distinctly seen on each side of the black fringe in the section Mm. In the section 1 1, the first order of colours only was developed; between the section 1 1, and 2 2, the second order of colours appeared, and so on with the succeeding orders, till the seventh was seen near Mm. Scholium 154 NID(111NT. "de TX' I
David Brewster's Experiments — 1816
Reference: Phil. Trans., 1816, Part 1, Plate 9. ©2 2 It follows from the preceeding experiments, that the mechanical contractions and dilations at the points, l 1,2,3,4,5,6, are as the numbers 7 /5, 13 /20,22, 292/3, 38, 454/5, the values of the corresponding tints in Newton's scale. 172
This optical-mechanical correlation was to become part of the quantitative
basis of the subject. Another important experiment was performed on a
glass cantilever beam (fig. 12, p1.1X) which investigated the effect of
combining direct and bending stresses, The result he expressed in an
optical version of the principle of superposition; 'If a plate of glass
is subject to compressions or dilations exerted in different directions,
the same effects are produced as when separate plates influenced by the 173 same forces are combined in a similar manner'. In describing the
experiment he said;
I took a plate of glass AB, Fig.12, (pl, lx) and having compressed its extremity A by means of the screw S, a bright white of the first order emerged from the points of pressure P, Q. By a force applied at B, I now bent the glass so as to make the lower side concave, and to produce the white tints on each side of the interjacent black space m, n. The effects of bending were now combined towards m, with the effects of compression, so that in the line mo, a black fringe appeared, the compressed structure produced by bending having acted in opposition to the compressed structure produced by the screw S; while in the line mp, a yellow tint emerged, the dilated structure produced by bending, acting in conjunction with the compressed structure produced by the screw. 174
Brewster's work, with its potential importance to the engineer, was ahead of its time and remained in the province of the scientists.
The next reference, in an engineering context, to Brewster's work was made, nearly thirty years later, at a meeting of the Civils in connection with Colthurst's paper on the position of the neutral axis in
beams, In 1841 Colthurst attempted to measure this by mechanical means
(see the section on this). In a written contribution three years later
Dr. Schafhaeutl, dismissing Colthursts methods, felt that 'a pencil of polarised light was the most delicate test, for ascertaining the position 155 175 of the neutral axis in a transparent body'. Having described
Brewster's experiments he;
wished to direct the attention of the Institution to this, not only because he believed Sir David Brewster's discoveries, and his remarks upon them, were very highly interesting, and formed a good comment on Mr. Colthurst's paper, but particularly as the results of these discoveries allowed of a wider application, than that of ascertaining the position of the neutral axis of beams or bars only, and had been published so long ago by an Honorary Member of the Institution, and who was a bright ornament of every scientific body, which had the good fortune to rank him amongst its members. 176
But apparantly this advocacy fell on deaf ears as no further reference
to the subject is to be found in the nineteenth century Proceedings of
the Civils.
In an encyclopaedia published in 1845, Sir John Herschel said
Brewster's glass experiment 'affords an exceedingly beautiful illustration of the action of compressing and bending forces on solids, and furnishes ocular evidence of the state of strain into which their 177 several parts are brought by external:violence'. This seems an odd description of the carefully controlled loading necessary on glass beams.
Here again, however, we have an advocate of the practical uses of the technique as he added;
The ingenuity of Dr. Brewster has not overlooked its application to the useful and important object of ascertaining the state of strain and pressure on the different parts of architectural structures, as stone bridges, timber framings, &c., by the use of glass models actually put together as the buildings themselves. 178
This material appeared in the encyclopaedia in a lengthy article on
'Light' and would not, therefore, have readily attracted the attention of engineers.
156 Similarly inaccessible were the writings of scientists like 179 Stokes and the germinal work of Clerk Maxwell. In 1850 he read 180 a paper (published in 1853) 'On the Equilibrium of Elastic Solids',
one section of which was devoted to 'the determination of the pressures
which act in the interior of transparent solids, from observations of 181 the action of the solid on polarized light'. As we might expect,
Clerk Maxwell was well aware of earlier work saying, 'Sir David Brewster
has pointed out the method by which polarized light might be made to
indicate the strain in elastic solids; and his experiments on bent glass 182 confirm the theories of the bending of beams'. He then proceeded to
analyse experimentally the extremely complicated problem of a loaded
triangular plate. In the course of this he made the important step of
developing the technique whereby 'The direction of the principal axes of
pressure at any point is found by transmitting plane polarized light, and 183 analysing it in the plane perpendicular to that ofpolarization'.
From these experimentally-determined strain trajectories he then showed
the principal tensile and compressive stresses (p and q) could be
evaluated. But, again, this paper of exciting potential failed to attract the attention of engineers or to suggest techniques for solving
practical problems.
Little or no mention was made of the subject in engineering
circles for something like another quarter of a century. But in 1871
Spon's Dictionary of Engineering referred in a long article, yet again, to Brewster's experiments with reference to the neutral axis in beams, and the article added details of experiments made by an American engineer named Nickerson. This must be the first reference to an engineer making use of experiments in photoelasticity. He used glass beams and hollow glass columns from which he drew practical conclusions for design purposes. This reference in an engineering dictionary, in English, still 158 does not appear to have made an impact on structural analysis in this country.
However, in the last decade or so of the century two papers were published in a scientific journal which, although strictly outside our period, are worthy of brief mention here. The first records details 184 of experiments made in the summer of 1888 by Dr. John Kerr of Glasgow.
He studied a portion of a small glass beam, remote from the central load, in the loading frame shown in figure 4.23; the load being applied by two wing-nuts through semi-circular bearings of ebony. His beams were
10 to 12 inches long, ith to thick, and 1 to 2 inches wide. The paper is concerned with the relationships of relative and absolute strain-generated retardations of polarised light and he extended the knowledge that these were sensibly proportional to the strain. However, a practical engineer looking at Kerr's paper would not be struck with its relevance to his own problems. In 1891 Professor Carus-Wilson published the results of experiments in which he investigated the effect 185 of what he called 'surface loading' on the bending of beams. He based his work on three assumptions;
(1) The true state of strain at the centre of the beam may be found by superposing on the state of strain due to bending only, that due to surface- loading without bending. (2) The state of strain due to surface-loading only may be found, with close approximation to truth, by resting the beam on a flat plane instead of on two supports. (3) The strains due to bending only may be obtained from the Bernoulli-Saint-Venant results. 186
His first assumption had been shown to be true, as we have seen, by .
Brewster in 1816. Carus-Wilson's principal concern was with the fact that a beam under central loading is not in a state of pure bending due to the co-existance of shear (which he consciously ignored) and the local stress in the region of the load. His experimental apparatus, which was 159 Kerr's glass beam and straining frame — 1888
Fi a 3
Fi . 4
Carus—L2ilson's experiments on glass beams — 1891
References: a) Pilosophical Magazine, 5th. Series, Volume XXV1, p.324.
b) Philosophical Magazine,5th. Series, Volume XXX11, P1. 2. 4 73 refined, consisted of;
a steel straining-frame in which the beam to be examined is placed; the beam rests - for flexure - on two steel rollers, and is loaded by a micrometer-screw which bears on a third central roller. The base of the frame is divided, from the centre, in divisions of 2 millim. so that the supports can be set for any required span. A micrometer-screw is placed in the base of the frame opposite the load, so that deflexions can be measured to one ten thousandth of an inch, Two screws in the sides of the frame enable lateral pressure to be applied. The whole frame can be moved in any direction in its own plane, so that all parts of the beam can be examined ... The beams used were marked on one side with 2 millim. squares; they were covered with paraffin and marked in a dividing-engine and then etched; the lines thus formed enabled the position of dark bands to be determined with accuracy. 187
These dark bands were examined through a microscope with a micrometer- eyepiece divided to thousandths of an inch and the bandswere 'plotted 188 on squared paper corresponding to the squares on the glass beam',
These curves are shown in figure 4.23 (his fig.3) from which he used
Clerk maxwell's method to plot the principal stresses (his fig.4). The curves shown are for a glass beam of 60 mm. span, depth 19 mm., and thickness 5.5 mm., supported on, and loaded through, steel rollers of
2 mm diameter. In his conclusions Carus-Wilson pointed out that surface- loading effects really only became important for span/depth ratios of less than 4 to 1. This means of course that the problem could be ignored in beams having the range of span/depth ratios applicable to engineering structures.
The story of photoelasticity, which could be said to have been pioneered by Sir David Brewster in 1816, took over a century to develop into a tool of practical use to the engineer. Sir William Anderson, speaking at the Institution of Civil Engineers in 1893 said, 'The history of scientific research teems with instances of discoveries which at first seemed to have had no practical value, but which nevertheless have 189 ultimately proved to be of the utmost importance to the engineer'. 160 It is noteworthy that although his subject was the Interdependence of
Abstract Science and Engineering he did not even mention Brewster's or
Clerk Maxwell's work on photoelasticity. The modern development of the subject occurred in this country with the work of men like Professor
E.G. Coker who set up a laboratory at University College London where
he trained many young research workers. The publication, with 190 L.N.G. Filon, of his Treatise on Photo-elasticity in 1931 could be said to mark the beginning of the widespread use of the technique by
engineers.
161 BEAM AND GIRDER BRIDGES
REFERENCES and NOTES
Introduction:
1. Proc. I.C.E., Volume XIV, p. 468: Stephenson speaking on 24 April 1855 in discussion of James Barton's paper - 'On the Economic Distribution of Material in the Sides, or Vertical Portion, of Wrought-Iron Beams'.
2. . For an account of this transitional period see Trans. Newcomen Society, Volume XXXV1, 4 March 1964, pp. 67-84: 'The Introduction of Structural Wrought Iron', by R.J.M. Sutherland.
3. The most extensive and best documented of these were made by two architects; Charles Parker and his colleague Goerge Cooper. See R.I.B.A. Library, MS. SP 5 No.12: 'Experiments on Cast - Iron Beams - 1845', by Charles Parker. 22 MS. foolscap sheets of results of experiments on cast iron beams of 22 inch span. Pencil note: 'paper read 23 June 1845'. See also; The Builder, 11 December 1847, p. 593: 'Experiments on the Form of Cast-Iron Girders, by George B. Cooper. Tests made on 13 different beams of 24 inches span. Article continued in The Builder, 18 December 1847, pp. 600-1, and The Builder, 25 December 1847, pp. 612-3.
Wrought Iron Tubular Girders
The Conway and Britannia Bridges:
4. Civil Engineer and Architect's Journal, Volume 9, April 1846, p.100.
5. An Account of the Construction of the Britannia and Conway Tubular Bridges, with a complete History of their progress, from the conception of the original idea, to the conclusion of the Elaborate experiments which determined the exact form and mode of construction ultimately adopted, by William Fairbairn, London, 1849.
6. The Britannia and Conway Tubular Bridges with general inquiries on beams and on the properties of materials used in construction, by Edwin Clark, 2 volumes, London, 1850.
7. Proc. I.C.E., Volume CXX, p. 347: Edwin Clark obituary.
8. Dictionary of Engineering, Spon, Volume 1, London, 1874: p.740: article - 'Bridge'.
9. Proc. I.C.E., Volume CX1V, Part 1V, 4 May 1893, p. 265: 'The Interdependence of Abstract Science and Engineering', by Sir William Anderson.
162 10. Tubular and other Iron Girder Bridges, G. Drysdale Dempsey, London, 1S64 - Introduction.
11. Clark, op. cit., volume 1, p.57. Stephenson giving evidence to the Select Committee, 6 May 1845.
12. Ibid.
13. Ibid. p.49, Stephenson giving evidence to the Select Committee, 5 May 1845.
14. Ibid. p.48
15. Ibid. p.50
16. Ibid. p.60
17. Fairbairn, op. cit., p.175, Stephenson's speech, 17 May 1848
18. Fairbairn, op. cit., Preface: p.v.
19. Bound volume of autograph letters in Institution of Civil Engineers Library (presented to I.C.E. 24 October 1916). Contents: Stephenson to Clark 43 letters Clark to Stephenson 48 letters Hodgkinson to Stephenson 22 letters Hodgkinson to Clark 1 letter Total: 114 letters
20. Fairbairn, op, cit., p.13.
21. Autograph Letters, I.C.E. Library; Hodgkinson to Stephenson, 10 March 1846. Also published by Fairbairn op. cit., p.55.
22. Autograph Letters, Hodgkinson to Stephenson, 10 March 1846; covering letter to above (unpublished).
23. Autograph Letters, Ibid. A little later however, Hodgkinson said 'I had been consulted privately on the matter from the commencement, or nearly so' (Iron Commissioners Report, Appendix AA, p. 115).
24. Autograph Letters, Hodgkinson to Stephenson, 18 March 1846.
25. Ibid.
26. Autograph Letters, Hodgkinson to Stephenson, 26 March 1846.
27. Autograph Letters, Hodgkinson to Stephenson, 18 July 1846.
28. Autograph Letters, Hodgkinson to Stephenson, 28 July 1846.
29. Proc. I.C.E., Volume CXX, p. 346: Edwin Clark obituary.
30. Ibid.
31. Autograph Letters, Clark to Stephenson, 28 October 1846. 163 32. Autograph Letters, Clark to Stephenson, 15 January 1847.
33. Autograph Letters, Clark to Stephenson, 25 February 1847.
34. Autograph Letters, Stephenson to Clark, 1 March 1847.
35. Autograph Letters, Clark to Stephenson, 2 March 1847.
36. Parl.Pap. (1123) XX1X, Report ... Commissioners ... on the Application of Iron to Railway Structures. p.377: Edwin Clark examined 10 June 1848.
37. Fairbairn op. cit., copy owned by J.G. James (member of Council of Newcomen Society) to whom I am indebted for an extended loan.
38. Ibid., pp 21, 283, 89, and 32.
39. The Britannia and Conway Tubular Bridges, Edwin Clark, op. cit., Title page.
40. The Life of Robert Stephenson, J.C. Jeaffreson, London, 1864 volume 2, p.82 (Chapter contributed by William Pole).
41. Clark, op. cit., p.26
42. Ibid., Volume 1, p.26
43. Fairbairn op. cit., p.9
44. Parl. Pap., 1849 (1123) XX1X, p.133.
45. Ibid.
46. Ibid., p.377.
47. Fairbairn, op. cit., p.213
48. Parl. Pap. 1849 (1123) XX1X, p.115.
49. Ibid.,p.178.
50. Clark, op. cit., Vol.1, p.85.
Apparatus and Experimental Techniques
Fairbairn's Preliminary Tests at Millwall:
51. Fairbairn, op. cit., p.211.
52. Clark, op. cit., p.87
53. Autograph Letters, Hodgkinson to Stephenson, 10 March 1846.
164 Hodgkinson's Eyperinents in Manchester:
54. Parl. Pap., 1849, op. cit., p.136.
55. Ibid., p.117.
56. Autograph Letters, Hodgkinson to Stephenson, 26 March 1846.
57. Ibid.
58. Pail.. Pap., 1849, op. cit., p.198.
59. Autograph Letters, Hodgkinson to Stephenson, 16 July 1846.
60. Ibid., 24 October 1846.
61. Parl. Pap., 1849, op. cit., pp. 138-9.
62. Ibid., pp. 122-3.
Experiments on the Large Tube at Millwall:
63. Clark, op. cit., p.157.
64. Ibid.
65. Ibid., p.161.
The Role of Experiment in the Design of the Britannia Bridge:
66. Ibid. p.50
67. Ibid. p.138.
68. Ibid. p.147.
69. Ibid. p.154.
70. Ibid. p.143.
71. Ibid. p.137.
72. Ibid. p.151.
73. Ibid. p.153.
74. Ibid. p.104.
75. Ibid. p.151.
76. Parl. Pap. 1849 op. cit. p.137.
77. Ibid.p.142.
78. Fairbairn, op. cit., p.122
79. Jeaffreson, op. cit., p.105.
80. Autograph Letters, Hodgkinson to Stephenson, 10 March 1846. 165 81. Clark, op. cit., p.117.
82. Ibid. p.137.
83. Autograph Letters, Hodgkinson to Stephenson, 10 March 1846.
84. See Clark, op. cit., and Fairbairn, op, cit., for details.
85. Clark, op. cit., p.146.
86. Ibid. p.134
87. Autograph Letters, Hodgkinson to Stephenson, 26 March 1846.
88. Jeaffreson, op. cit., p,104
89. Clark, op. cit., p.178
90. Parl.Pap. 1849. op. cit., p.178
Lattice Girders.
91. For drawings of well detailed timber lattice girder bridges see The Four Books of Architecture, Andrea Palladio, (Venice 1570), Dover, New York, 1965, Chapter V111, plates 111, 1V, and V.
92. See Philosophical Magazine, Volume XXV11, 1864, pp.250-261: 'On Reciprocal Figures and Diagrams of Forces', by James Clerk Maxwell, and British Association Report, Volume XXXV11, Dundee meeting 1867, p. 156: 'On the Theory of Diagrams of Forces as Applied to Roofs and Bridges', by J. Clerk Maxwell where he says; The advantage of this method is that its construction requires only a parallel ruler, and that every force is represented to the eye at once by a separate line, which may be measured with sufficient accuracy for all purposes with less trouble than the forces can be found by calculation. It also affords security against error, as, if any mistake is made, the diagram cannot be completed.
93. There is some confusion in the use of the term Lattice Girder; some writers in the nineteenth century reserved the term exclusively for the true lattice of counterbraced panels, whilst other deemed it to include all triangulated open-web girders. The present author uses it in the latter sense.
Doyne and Blood's Model Warren Girder
94. Proc. I.C.E., Volume Xl, pp.1-14, 11 November 1851.
95. William Thomas Doyne (1823-1877) for Memoir see Proc. I.C.E., Volume 52, pp. 270-3.
96. William Bindon Blood was Professor of Civil Engineering at Queen's College, Galway.
97.• Proc. I.C.E., op. cit., p.1. 166 98. Patented by Captain James Warren, Patent No. 12,242, 15 August 1848: 'Construction of bridges, aqueducts, and roofings'.
99. Proc. I.C.E., op. cit., pp.1-2.
100. A Practical Treatise of Cast and Wrought Iron Bridges and Girders. William Humber, London, 1857, p.56.
101. Ibid.
102. Proc. I.C.E., op. cit., p.2.
103. Ibid. pp.4-5.
104. Ibid. p.3.
105. Ibid. p.10.
106. The model may have been referred to by William Anderson, speaking at the Institution of Civil Engineers in May 1894: In the museum of Trinity College, Dublin,* there has existed since, I believe 1854, a model of a Warren girder, 12 feet 6 inches long and 12 inches deep, in which the tension members both of the flanges and diagonal bracing are so arranged and articulated that any one section can be taken out and a spring balance inserted, by means of which it can be demonstrated that the stresses calculated for any disposition of load do actually arise. * This model was sent over and exhibited at the lecture.
Reference: Proc. I.C.E., Volume CX1V, 4 May 1893; 'The Interdependence of Abstract Science and Engineering', William Anderson (The 'James Forrest' lecture) p. 267. (A letter to Trinity College in 1973 revealed that the model cannot now be found).
107. A Treatise on Bracing, with its application to Bridges and other Structures of Wood and Iron, Robert Hebry Bow, London, Weale, 1851, 8vo. pp.54; five plates.
108. Civil Engineer's and Architect's Journal, 2 August 1851, pp. 414-6.
109. Ibid. p.414.
110. British Association Report, Belfast September 1852, pp.23-4: 'On the Calculation of Strains in Lattice Girders, with Practical deduction therefrom', by James Barton.
111. Ibid.
112. Ibid.
167 Airy's Bowstring Girder Model - 1868
113. Proc. I.C.E., Volume 27, 7 April 1868, pp. 443-453: 'On the Experimental Determination of the Strains on the Suspension Ties of a Bowstring Girder', by Wilfred Airy.
114. Ibid. p.443,
115. Ibid. p.444.
116. Ibid. p.443,
117. Ibid. P.448.
118. Ibid. p.444.
119. Taking the specific gravity of steel as 7.83, the diameter of the wire, at 96 feet to the ounce, will be:
V 4 1728 d = 96 12 Ti 62.4 16 7.83 0.0156 ins.
120. Proc. I.C.E., Volume 27, op. cit. p.444,
121. Ibid. p.444.
122. In a vibrating string the frequency is proportional to the square root of the tension;
thus f = k VT where f = frequency and T = tension to find the increase in frequency produced by an increase of oz. on a tension of 80 oz.; 161 Atuff if T ---,T. = K -.- T 160 ff' 160 161 i 1 = --- f.(160) = f. ( 160 )1 161
= f.( 1 ) 1 1 161
f.( 1 uiTo
323 f f. 322
Also f.)%= where: f = frequency A" X = wavelength = 2.L T = string tension = mass/unit length If we consider the longest string (wire) where Length (L) = 12" then:
168 12 x 2.54 L - - 0.3048 m. 100 80 T = 6 x 2 1 2 x 9.8 = 22.27 N. -2 1.56 x 2.54 x 10 2 -4 3 = 2 ) x 10 x 7.83 x 10 = -5 96.5046 x 10 1 x f = j 22.27 2 x 0.3048 96.5046 x 10 approx. f = 250 c/sec.
Then the increased frequencies will be;
12" wire for a 6" wire 323 f' = 250 x 323 f' = 500 x 322 322 = 250.62 c/sec, = 501.24 c/sec.
123. Proc. I.C.E., volume 27, op. cit., p.445.
124. Ibid. p.448.
125. Ibid.
126. Proc. I.C.E., volume 31, 6 December 1870, pp. 72-174: 'On the Theory and Details of Construction of Metal and Timber Arches', by Jules Gaudard, C.E., Lausanne (Translated from the French by William Pole).
127. Particularly in the work of A. Clebsch (1833-1872) in the 1860's.
128. Proc. I.C.E., volume 31, op.. cit.
Web Buckling in Plate Girders
129. These were described in Ann. Ponts et Chausses, Volume 20, 1860, p. 113.
130. On the Strengths of Beams, Columns, and Arches, Benjamin Baker, Spon, London, 1870, p.289.
131. Ibid.
132. Proc. I.C.E., Volume 62, 23 June 1880, pp. 251-271: 'The Practical Strength of Beams', by Benjamin Baker.
Continuity in Beams and Girders
The Torksey Bridge 1 aw Iva/ trompl4 erpeethwni DP. Boyoe $140 d et. 11414 4 4`g""" 133. aim spa., , peeh• g..a ArnieWIli 'Gm% 910r/bpe/Qh doP'*4 cl'• IC04"14 Apdan 442,noitthehr a PonO avter4tAwrifet 134. Proc. I.C.E., Volume 1X, 12 March 1850, pp. 233-287: No.826 - 'On Tubular Girder Bridges', by William Fairbairn. The importance of the discussion in relation to the paper may be judged from the fact that the paper occupied pp.233-241 whilst the discussion occupied pp.242 -287. Amongst those taking part 169 were; Vignoles, Scott Russell, Bidder, Hodgkinson, Wild, Pole, Paslcy, Rennie, Fowler, and Simmons.
135. Ibid. p.246, Bidder in discussion.
136.. Ibid. p.233.
137. Ibid, footnote p.237.
138. Captain J.L.A. Simmons (1821-1903), studied at R.M.A. Woolwich, was commissioned 2nd. Lieut. R.E. in 1837, spent his early career in railways, subsequently spent many years abroad finally achieving the rank of Field Marshall. (obit. Proc. I.C.E., Volume 152, pp.312-5).
139. Proc. I.C.E., op. cit., PP.253-254.
140. Ibid. p.254.
141. Ibid, Pp.254-6,
142. Ibid. p.256.
143. Ibid.
144, Ibid, Pp.256-7,
145, Ibid.p.261.
146, Ibid.
147. Ibid. p.271.
148. British Association Report, Birmingham meeting 1886, p.477: 'On some points for the consideration of English Engineers with reference to the design of Girder Bridges', by W. Shelford and A.H. Shield.
Brunel's Chepstow Bridge:
149, The Life of Isambard Kingdom Brunel, Isambard Brunel, London, Longmans, 1870. p.229.
150. Ibid.
151, Ibid,
152, The Britannia and Conway Tubular Bridges, Edwin Clark, London, 1850 p.462
153. Brunel, op. cit., p.229
154. Ibid.
155. Clark, op, cit., p.463,
170 Edwin Clark's Britannia Bridge Continuity Model:
156. The Britannia and Conway Tubular Bridges, Edwin Clark, London, 1850, Volume 1, p.464.
157.. Ibid. pp.464-5.
W.H. Barlow's Continuity Experiments - 1858
158. Proc. I.C.E., Volume 26, 19 February 1867, pp. 243-257: 'Description of Clifton Suspension Bridge', William Henry Barlow. The paper includes Barlow's digression into continuous beams (pp.252-5).
159. Ibid. p.253.
160. Ibid.
161. Ibid. p.252.
Stoney's Analytical Textbook:
162. Theory of Strains in Girders and Similar Structures, Bindon S. Stoney, London, Longmans, 1873.
163. Ibid. Chapter 1X, p. 183.
164. Ibid.
Polarised Light and Model Structures
165. Phil. Trans., 1816, Part 1, pp.156-178: 'On the Communication of the Structure of doubly refracting crystals to glass, muriate of soda, flour spar, and other substances, by mechanical compression and dilation', David Brewster in a letter addressed to the Right Hon. Sir Joseph Banks. Read, 29 February 1816.
166. Ibid. pp. 156-7
167. Ibid. p.160.
168. Ferguson's Lectures, David Brewster, (2nd Ed.), 1806, pp.v-x.
169. Proc. I.Mech.E., 1911, p.403: 'Optical determination of Stress', lecture at Conversaxione by E.G. Coker. He followed this by a lecture in 1913, p.83) in which he justified the use of small-scale experiments by referring to the difficulty of calculation of stresses, and dealt with the effect of a notch in a beam, chain links, and crane hook.
170. Phil. Trans., 1816, op. cit., p.159.
171. Ibid. p.163.
172. Ibid.
173. Ibid. p.164
174. Ibid. 171 175. Proc. I.C.E., Volume 111, 1844, 7 March, pp. 218-9: 'Remarks on the Position of the neutral Axis of Beams', by Dr. Charles Schafhaeutl.
176. Ibid.
177. Encyclopaedia Metropolitana, London, 1845, Volume 4, pp.341-586: Article: 'Light' (The article was apparantly written considerably earlier as it is dated: 'Slough, December 12, 1827').
178. Ibid. p.564
179. See, in particular, Professor G.C.Stokes' extensive paper 'On the Dynamical Theory of Diffraction' in Trans. of the Camb. Phil. Soc., 26 November 1849. Also published in; Mathematical and Physical Papers Cambridge, 1883, Volume 11, pp. 243-328.
180. Transactions of the Royal Society of Edinburgh, Volume XX, 1853 Part 1. pp.87-120. Reprinted in the Scientific Papers of James Clerk Maxwell, Cambridge, 1890, Volume 1, pp.30-73.
181. Ibid.p.68.
182. Ibid. p.68.
183. Ibid. p.69.
184. The Philosophical Magazine, fifth series, Volume XXV1, October 1888, pp. 321-342: 'Experiments on the Birefringent Action of Strained Glass', by John Kerr, LL.D., Free Church Training College, Glasgow.
185. The Philosophical Magazine, fifth series, Volume XXX11, December 1891, pp. 481-503: 'The 7nfluence of Surface-Loading on the Flexure of Beams', by Prof. C.A. Carus Wilson, M'Gill University, Montreal, October 12, 1891.
186. Ibid. pp.481-2.
187. Ibid. pp.486-7.
188. Ibid. p. 500.
189. Proc. I.C.E., Vol. CX1V, Part II, 4 May 1893.
190. A Treatise on Photo-elasticity, E.G. Coker and L.N.G. Filon, Cambridge, 1931.
172 Chapter 5
INSTRUMENTATION INSTRUMENTATION
To what extent was the scope and development of model testing limited by the lack of suitable measuring instruments? Or, conversely, to what extent did the demands of model experimenters lead to the development of improved instruments? These are interesting questions but, from the available sources, extremely difficult to answer. The use of instruments at all implies experiments with quantitative objectives whereas many of the early model tests were merely of a qualitative nature.
Even where measurements were taken and in otherwise carefully documented experiments there is a dearth of information relating to measuring instruments. Most of the available space in published accounts was devoted to saying what was done rather than in saying how, or indeed, in many cases, even why it was done. In addition there are no surviving test rigs. Whereas the visual type of model was often preserved as a work of art in its own right, the structural test-model was invariably destroyed when it had served its useful purpose (if not by the test itself), or its parts re-used, and the measuring instruments dispersed.
Nevertheless, certain trends in measurement can be detected in the period under discussion. The quantities measured in structural model tests between 1800 and 1870 were:
(a) Applied Load
(b) Force
(c) Deflection and (d) Strain (in its modern sense).
The detailed description of the measuring technique will, in most cases, be found in the appropriate chapters of this thesis, and here mainly general trends will be discussed.
173 -----__Measurement of-_-_-__ Applied Load - The loading of structural models in the nineteenth century was, on the whole, extremely unsophisticated and its measurement did not present problems of instrumentation. Most early model tests were made principally to determine the ultimate load of the model and hence, hopefully, that of the full-sized structure. This merely required the application of a dead load progressively increased and recording the load at failure. Unless the corresponding deflection was to be noted it was not even necessary to record increments of load, although this was usually done. Loading materials included lead shot, pig iron, cast iron plates, rails, sacks of malt and horse beans, and people. This bizarre collection did not require instrumentation on the model itself as they could easily be weighed adjacent to the test rig before being applied, or even afterwards. There were very few deviations from this
pattern of dead load application. One was the use of a falling weight onto a suspension bridge model by Drewry in 1832 (see chapter 3). This is the first reference to dynamic loading of a model but it was not used in a precise manner. Almost the only other variation was Hodgkinson's use of a lever system to apply load which he adopted for his Manchester tests on wrought iron tubes in 1846 (see chapter 4). This merely had a multiplying effect and was easily calibrated. It is clear, therefore, that the application of load to structural models was not inhibited by the absence of refined instruments neither did it give rise to any development in instrumentation.
Measurement of Force
In this context force refers to the intensity of a tensile or compressive reaction to applied load in some part of a model. Compared with weighing the applied load measurement of these forces required a higher degree of sophistication in model technique and demanded skill and 174 ingenuity in the design and use of special measuring instruments. The
first recorded example of model force measurement was that of Atwood in
1804 in his brass voussoir arch models (see chapter 2). Atwood wished
to compare the voussoir interface thrust with that determined by
calculation. This he did by removing that part of the arch on one side
of the junction and replacing it with a shackle, cord, pulley, and
weight-can (see figures 2.2 and 2.3). By adjusting the weight in the
can he could maintain equilibrium of the semi-arch and hence determine
the interface thrust. His technique only required weighing the lead
shot in the can and did not, therefore, require special instrumentation.
It is, nevertheless, an early example of model force measurement - the
next instance does not occur for nearly half a century. This was in
the late 40's when I.K. Brunel was designing his Chepstow bridge. He
built a simple continuity model (see chapter 4) and measured support
reactions with a steel-yard device (see figure 4.17). Unlike James
Dredge, who had used a steel-yard on his model suspension bridge in
1840 Brunel produced results which could be compared favourably with
theory (see figure 4.18). Brunel's support reactions were measured in
pounds to three decimal places and this degree of accuracy would only
have been possible with a steel-yard. This was presumably the motive
for its adoption rather than a spring-balance. In 1851 Doyne and Blood
compared the forces in the diagonal members of an analytical model
Warren girder with those predicted by calculation (see chapter 4). This
was done by substituting a dynamometer in place of the member under
investigation. Their paper to the Institution of Civil Engineers is a
good example of the dearth of information on measuring instruments
referred to above. Although the model itself is adequately described,
the authors dismiss the force-measuring device in one word - referring
to it merely as a dynamometer. This must, however, have been a spring-balance device, or devices, capable of measuring tensile and 175 compressive forces. The forces, or strains as they called them, were recorded to one decimal place. The use of the graduated cylindrical spring-balance was quite common at this time, having originated in the seventeenth century. Undoubtedly the most unusual dynamometer was that devised in 1868 by Wilfred Airy to analyse forces in the members of a model bowstring girder. This was a measuring instrument in more than one sense in that it functioned by relating the tension in a wire and the note emitted when plucked. Airy adopted the device known as a monochord frame (see figure 4.14), which would have been readily available in physics laboratories. The method involved placing weights in a scale-pan to tension the wire in the monochord frame until it matched the pitch of a similar wire member in the loaded model. With a reasonably good musical 'ear' a high degree of accuracy could be achieved.
This was the last model test to be brought before the Institution of
Civil Engineers in the nineteenth century and it is unlikely that the method was used elsewhere.
Measurement of Deflection
Measurement of the displacement of a loaded structure implies a nascent interest in the concept of stiffness. The awareness of the value of a knowledge of stiffness, or its converse, flexibility came only after an almost exclusive pre-occupation with ultimate load
(strength) tests on the part of nineteenth-century model experimenters.
This was due to the relative importance of masonry bridge structures in the early part of the century. Deflection measurements were never made on voussoir arch models. The masonry was regarded as inelastic and the objective of model tests was to establish stability. With the growth of railways and the introduction of metal girder bridges this situation was to change.
176 The first example of the use of model deflection measurements was in connection with the wrought iron tube research undertaken for the
Britannia bridge design in 1845-6. These tests are of additional interest in the context of this chapter in that they refer to the development of instrumentation during the progress of the tests. In the experiments on the large tube (75 foot span) begun in July 1846 at
Millwall the mid-span deflection was recorded with increments of load.
Difficulty was experienced at first and;
the deflections can be but little relied on in the first experiments, for the tube rested at each end on a timber pier which compressed considerably under the weight, and was materially affected by rain or sunshine, while the deflections were read at the centre from an independent straight edge supported on uprights on either side of the tube, which was subject to similar variations. The ground, moreover, under the timber piers, was swampy and bad. 1
It is not surprising therefore that the deflections were only given to two decimal places. Further difficulties arose during October and
Fairbairn said;
some doubts were entertained as to the accuracy of the deflections taken ... and in order more effectually to determine the error, if any, two different methods were resorted to; one by weights attached to a fine line at each end of the tube, and the other by a fine wire, which moving over a pulley at one end kept them in the same uniform state of tension. These two methods were subsequently adopted, and when any difference existed, which was seldom the case, I generally took the mean of the two observations. 2
Although Fairbairn typically minimised the discrepancies, Clark said
'A comparison of the improved method with that before used shewed 3 errors of more than an inch in the latter'. He added that the stretched wire method was 'found to be imperfect, as the wire was much 4 disturbed by wind'. The stretched wire technique, with measurement on a central vertical scale, was at least independent of ground or support settlement. This advantage was shared by the final optical method adopted in December 1846. Figure 5.1 shows the system: - 177-
N.D
Method of deflection measurement
finally adopted for the experiments
on the large tube — Millwall 1846.
Reference: The Britannia and Conway Tubular Bridges Edwin Clark, London 1850, Volume 1., p.173. S.1 A board with the upper half white and the lower black was secured to the tube at C. A bracket with a
ho Arzbntal top was fixed at about the same level at A; and a similar white bracket moved vertically in a groove, with a scale, at the centre B. Observations were taken by looking from A to C. As the tube deflected, the centre bracket descended, exposing the black part of C. The space through which the centre bracket had to be raised, to just hide the black portion, was the required deflection. 5
Neither Fairbairn or Clark gave details of the central measuring scale
and all deflections were given to two decimal places.
In 1850 several references appeared relating to tests on
models of continuous beams. These involved a simple form of modelling
to determine the deflected profile under load and hence the points of
contraflexure. I.K. Brunel's continuity model of Chepstow bridge
comprised a deal rod, 38 feet long, supported over five unequal spans.
It was loaded with a chain such that 'it was thus bent into an elastic
curve, the ordinates of which were carefully measured, at every foot 6 along the length, by a finely divided scale and magnifier'. This is
the only reference to the instrumentation. The smallest deflection
recorded was 0.01 inches and other ordinates were given to three decimal
places. In the same year (1850) two further experiments on comparable
wooden models were described; the Torksey bridge model and Edwin Clark's
continuity model of Britannia. Bridge (see chapter 4). No details of the
deflection measuring instrument were given but they must have been
similar to.Brunel's - the degree of accuracy was comparable. In 1858
W.H. Barlow also made continuity models, this time in,metal, and his
deflection ordinates were consistantly measured to four decimal places,
although yet again the instruments are not described.
Although the stiffness of suspension bridges was considered
in a qualitative manner by the early experimenters, measurements of deflection were only made in the later tests where the effect of 178 combining a girder with a suspension chain was under investigation.
The first example was that of P.W. Barlow on his Londonderry bridge model of 1857 (see chapter 3). In the first experiment he connected a wooden box girder to the chain and measured the deflected profile under load to three decimal places, the smallest deflection recorded being
0.005 inches. The measuring instrument was not described but it must have been a vernier or, more likely, a micrometer. The box girder was too flexible and he substituted first an angle iron and then two stiffer planks, in which cases he measured the deflection to two decimal places.
Ten years later G.B. Air0y undertook very similar experiments recording the deflection ordinates in whole numbers, the units of which were
1/32 nds. of an inch (see figure 3.13). This less-discriminating instrument was again not considered worthy of description. This was surely because there was nothing special about it and would presumably have been available in any scientific laboratory as standard equipment.
We may assume therefore that model deflection measurement was not inhibited by the lack of suitable instruments and neither did it raise problems leading to new instruments.
Measurement of Strain
The history of scientific research teems with instances of discoveries which at first seemed to have had no practical value, but which nevertheless have ultimately proved to be of the utmost importance to the engineer. 7
This is particularly true of strain measurement. The ability to measure small changes of length on the surface of models under load is a technique, which although having its origins in the nineteenth century, was only developed in the first quarter of this, and indeed accounts for the renaissance of model testing after its decline around 179 1870. In chapter 4 Brewster's germinal work on polarised light is discussed and the resistance wire strain gauge, which was to extend the scope of model testing enormously after 1930, had its origins in 1856
(but not as a part of model testing of course) in Lord Kelvin's work o on the proprtionality of electrical resistance and strain. Although optical and electrical methods were not exploited by engineers in the nineteenth century, mechanical methods of strain measurement had their origin in the attempts to measure, physically, the position of the neutral axis of loaded beams. Although the question was regarded as settled by mathematicians in the middle of the century it was still a subject of discussion amongst engineers in the 1840's and 50's. Of those who approached the problem from the viewpoint of mechanical measurement two names stand out - Joseph Colthurst and William Henry Barlow.
Joseph Colthurst - 1841
Colthurst made his experiments 'in consequence of the difference of opinion which has long existed respecting the position of 8 the neutral axis of extension and compression of iron and wood'. He made a series of experiments on metal beams, some more successful than others, and they fall into four groups. The first series involved cutting through the centre of a set of eight girders each 6 feet 6 inches long, the first to a depth of inch, the second to 1 inch, and so on, until in the eighth only 1 inch of metal remained:
The spaces cut out were then filled with carefully fitted wrought-iron keys, and the girders were broken by the application of weights, in the expectation that these weights would be some indication of the neutral point of each girder. The results were, however, so irregular, that no satisfactory deductions could be drawn from them. 9
It is not clear what he intended here but his willingness to discuss his failures in this way is rather disarming. His second attempt was no more successful and the failure relates to instrumentation. On the 180 polished side of the beam fine vertical lines were scribed, 2 inches apart, in the centre of the span (see figure 5.2). When the beam was loaded he intended to measure the convergence and divergence of these lines, 'but the differences were too small to be susceptible of accurate determination, otherwise than by a fine micrometrical operation 10 which at that time he had not an opportunity of applying'. The third series was more interesting:
In the side of a cast-iron girder, 6 feet 6 inches long, 7 inches deep, and 1 inch thick, a recess was planed at the centre, 3 inches wide by i inch deep. This was filed up very true, and fourteen small bars of wrought-iron, with conical ends, were placed in at regular distances of an inch apart. These bars were of such lengths as to hold sufficiently tight to carry their own weight, and yet the slightest touch should detach them. 11
Figure 5.2 is based on this description. The beam was loaded, over a span of 6 feet, and when the 'strain' (load) reached 100 lbs. 'the lower bar fell out; as it was increased, they continued to drop, and 12 with 1500 lbs. all those below the centre had fallen'. The load was increased to 7000 lbs. but no more bars fell and 'The centre bar remained exactly as when put in; all those above the centre became 13 firmly fixed'. On gradual removal of the load all bars above the centre fell having been compressed. These experiments were repeated 13 'with pieces of fine wire and dry lance-wood at the ends'. The results showed the neutral axis to be within 0.2 inches of the centre.
The fourth experiment was more sophisticated, came close to using a strain measuring instrument, and according to Colthurst 'more decisive';
A girder 9 feet 6 inches long, 8 inches deep, 1 inch thick, was cast with two brackets or projections on the side, each 9 inches on either side of the centre. A brass tube bar, with circular ends and a sliding adjustment, was fixed between the brackets, which had been filed true. The clear bearing was 7 feet 6 inches; a strain of 50 lbs. was sufficient to cause this bar to drop out; and with 250 lbs. the whole effect of the previous experiment was produced. The tube, when placed loosely, 1 inch above the centre, was held fast by a strain of 1000 lbs. 14 181
cast iron sawcut of varying depth beam 5" X i"
EXPERIMENT 0
polished surface 1
'-'"*■■ IA 22„ I fine lines A
EXPERIMENT 0
711 I I r F 311
_,_,_,__4_ 4 Jltt 4 EXPERIMENT 0
measuring bar placed at various depths f1" 'filed true'
8" 7'-6"
centre of span
EXPERI1 ENT.-0
Reference: Proc.I.C.E., Volume 1, 20 April 1841, pp. 118-121.
(Author's drawings based on Colthurst's description) 5.2 Colthurst concluded that 'the neutral axis . in rectangular beams of
cast and wrought iron and wood, is situated at the centre of their 15 depth'. It is interesting to compare this rather crude technique,
essentially a strain measuring technique, with the experiments of
W.H. Barlow with identical objectives, but superior instrumentation,
made fourteen years later.
W.H. Barlow's Experiments - 1855
Barlow must surely have read Colthurst's paper to the
Institution of Civil Engineers and adopted an improved version of his
fourth experimental technique. Barlow's experiments involved more than
3,000 readings and were made 'on such a scale and in such a manner as to 16 place this question beyond doubt', and to achieve this;
Two beams were cast, 7 feet long, 6 inches deep, and 2 inches in thickness; on each of which were cast small vertical ribs at intervals of 12 inches: these ribs were one-fourth of an inch wide, and projected one- fourth of an inch from the beam. In each rib nine small holes were drilled to the depth of the surface of the beam, for the purpose of inserting pins attached to a delicate measuring instrument. 17
The superiority of Barlow's method over that of Colthurst lay entirely
in the design of this instrument for measuring the distances between the
holes with the beam under load.
The measuring instrument consisted of a bar of box- wood, in which was firmly inserted, at one end, a piece of brass, carrying a steel pin; and at the other end a similar piece of brass carrying the socket of an adjusting screw. The adjusting screw moved a brass slide ... which carried another pin similar to that inserted in the box-wood bar, at the other end of the instrument. The instrument was first made entirely of brass; but the effects of expansion from the heat of the hand were so sensible, that the wooden bar was substitued. 18
The instrument is shown in figure 5.3. It was indeed a sensitive
instrument, and needed to be; 'The head of the adjusting screw was
graduated to 100 divisions, and the screw had 43.9 threads to the inch, so that one division was equal to 1/4390 th, of an inch'.19 Barlow was 182
I
; , •
Reference: Phil. Trans., Volume 145, Part 2, 1855, Plate X11. 5.3 a meticulous experimenter and;
The measurements were, in all cases, taken by the outsides of the pins of the measuring instrument; and when the instrument read zero, the actual distance of the outer sides of the two pins was 51661/4390 inches, so that the constant number 51661 being added to the micrometer readings gives, in each case, the total distance in terms of 1/4390 th. of an inch. 20
The first beam was merely used to calibrate the measuring instrument
(see figure 5.4). He then tested a series of somewhat smaller beams with both solid and open webs (see figure 5.6). The results of the experiment on the second beam are shown in figure 5.5. Barlow's were, not surprisingly, the last experiments of this type and what is surprising is that as late as 1855 the need to find the neutral axis experimentally should still be felt. Barlow concluded from the experiments on the solid web beams that they 'point out the position of the neutral axis, as the centre of the beam, in a manner so decided, as 21 to remove all further doubt upon this subject'. It is worth noting that although Barlow was an engineer he offered this paper to the Royal
Society - certainly no such detailed small-scale experimental results, with adequate description of the strain - measuring instrument, were presented to the Institution of Civil Engineers in the nineteenth century.
In 1871, just after the close of our period, an interesting pointer to the future of structural model testing was given by William 22 Bell in a paper to the Institution of Civil Engineers. Although his remarks were headed'Direct measurement of Stress' it was with strain that he was concerned:
It would be somewhat difficult, by ordinary methods, to test satisfactorily the stresses on an arch rib, so as to compare them with calculation. Observations on deflection would give some information, but a model would necessarily be on a comparatively small scale when it is desirable to know the stress which any part of a structure or model is sustaining, it is possible to ascertain this by direct observation. 23 183 Uul
:03U8.18j98 Micrometer strained. readings. in evious to being At lest No. 1. 2208 2186 2095 2110 2127 2052 2052 2095 2101 Difference. +70 +55 +36 — 5 —21 +14. —39 —7 —58 3
on thecentre. . the end,equal to 11,716lbs. Strained with
Micrometer 7373 lbs.on readings. Beam erect. No. 2. 2278 2241 21:11 2141 2105 2031 2056 2028 1994
I
Di ff —67 —53 —33 ± —13 +68 +42 +76 + erence. 13 5 Weight tato' o Note.—The Micrometer the sameas ff readings. , No. 3. 2211 No. I. condition 2188 2098 2110 2128 2098 2054 2052 2104 : . onthecentre., Beam reversed. Determination ofthe.,VeutralAnis. extensions are marked +;thecompressions aremarked—. ossa sscight 1,,...„i Micrometer Measurements oftheFirstBeam. readings. No. 4. 2210 2187 2129 2103 2117 2056 2060 2101 2111 nf .. its
1 i
Difference. —33 —25 + 5 +28 +15 — 2 —20 +21 —10 to 57S6Ihs.olt the end.equal', 2s9311 Micrometer the centre. Strain of readings. No. 5. 2177 2162 2115 2119 2083 2077 2065 2139 2116 ) ,.,,„
1 ! Difference. —25 +26 —16 +21 + 6 — 1 —12 +14 — 8 Beam inseitell. the end,equal on thecentre. to 10,066lbs. 5133 lb.,.on Micrometer Strain of readings. No 6 2152 2071 2146 2071 2114 2111 2165 2130 2098 .
. Difference. —26 + 2 —21 +29 +12 —13 +34 +19 — 5 on thecentre. the end,Iqua! to 14,7061ln. 7;i Micrometer Strain of readings, 7 No. 7. 2126 2125 2106 :t lbs.on 2116 2058 2083 2127 2149 2199 Difference. +71 +21 +36 -1.53 —20 —37 —73 —GO • 2178 Weida taken mr, the •atneas Micrometer readings. No. S. * condition No. 2197 2063 2116 2094 2126 2067 2127 2112 I. Determination qf the .:Veutral Avis. Measurements of the Second Beam.
Beam erect. Beam inverted. _...... No. 1. No...f. c7 No. 3. No. 5. 17 No. G. } Z No.4. clI". c.. t; 1 No.:. AL rest '..' tlitin of 1.:- Strain of P . . .2 Strain of :r. Strain of rf 1— : 7— prnions to - tionn lb.. '... 16,0001bs. NN eight ,:...! 8000 lbs. 16,000 lbs. ;...= %I riglit ..-r. removed. ' strained.being ...,. on velar,. 4 on centre. -4 4 on centre. ..:.,.-- on centre. —= 1i remold-II. i--- Micromoed Micrometer Micrometer Micrometer Micrometer Micrometer .Micrometer readings. readings. readings. readings. readings. readings.. I readings. 1633 +37 1670 +65 1735 —89 1646 —44 1602 —56 1546 +97 . 1633 1525 +28 1553 +47 1600 —63 1537 —24 1513 —46 1467 2-67 i 1534 1481 +21 1502 +34 1536 —44 1492 —19 1473 —28 1445 j +421 1487 1442 +11 1453 +21 1474 —23 1451 —10 1441 —12 1429 1 +22 1451 1392 1 + 2 1394 + 7 1401 — 1 1400 + 1 1401 — 1401 ! + 4 1405 1375 —10 1365 — 9 1356 +18 1374 +17 1391 +11 1402 —17 1385 1338 —18 1320 —24 1296 +44 1340 +20 1360 +27 1387 1 —35 ! 1352 1257 —27 1230 —37 1193 +64 1257 +31 1288 +43 1331 ; —571 1274 1248 —42 1206 —46 1160 +85 1245 +44 1289 +57 1346 I —761 1268
Note.—The extensions are marked +; the compressions are marked —.
compression — -r I 1:111J.U11
N
W = 8000 lb 2
3
4 NNI.46
5
6
W = 16000 lb 7
9 0
hi
9 equi—distant SECOND BEAM El I measuring paints
Reference: Phil. Trans., Volume 145, Part 2, 1855. 5.5 :83U8.181BU 'ITUel eTd 'SSBI - 'Z 4Jed 'Sh6 awnToA '•sued •TTyd I L__1 1
J
PrP I L L_ fl P 1
EI 1 r [ 11 L
4
|^ ...11rr Jr
.A N.° [1 II1HEMI r J .° 6. I • J.
L- I 4.
• . 1 __J
[ IL IL_I
• ......
•
F U •
l [1 • He was aware of the Stress/strain/elastic modulus relationships and
confined his comments to the practical problems of measurement:
In wrought iron, the extension on a length of 50 inches, with a strain of 1/5 th ton per square inch, would be 1/1000 th of an inch. This length is quite within the reach of exact measurement by means of magnifying glasses ... If two microscopes, magnifying even less for iron, and considerably less than this for timber, were attached to a bar of the same material as the structure to be tested ... and were each capable of being moved a short distance along the bar by a micrometer screw it is believed that stresses of 1/5 th ton per square inch could be read off with certainty. For this purpose, it would only be necessary to furnish the eye-pieces of the microscopes with finely- divided scales. 24
Even in 1871 he is still inconsistent in his use of the terms stress
and strain. But he certainly indicated the direction of future methods
of mechanical strain measurement. Later strain measuring instruments were to magnify the small changes in length by means of optical and
mechanical lever systems. An alternative technique is to make the
model of a material with reduced elastic modulus to increase model strains. But this was not done until the turn of the century in the 25 analysis of model dams. However, measuring techniques were developed
in the 1880's and 90's in the emerging engineering teaching laboratories and in those devoted to materials testing on a routine basis of the
type founded by David Kirkaldy. So strain measurement really only began
to make progress when model testing was out of favour in the latter part of the nineteenth century.
184 INSTRUMENTATION
REFERENCES and NOTES
1. The Britannia and Conway Tubular Bridges, Edwin Clark, London, 1850, Volume 1, pp. 161-2.
2. The Britannia and Conway Tubular Bridges, William Fairbairn, London, 1849, p. 257.
3. Clark, op. cit., p.170.
4. Ibid. p.173.
5. Ibid. p.173,
6. The Life of Isambard Kingdom Brunel, Civil Engineer, Isambard Brunel, London, Longmans, 1870, p.229,
7. Proc. I.C.E., Volume CX1V, 4 May 1893, pp.255-283: 'The Interdependence of Abstract Science and Engineering', by William Anderson (p.267).
8. Proc. I.C.E., Volume 1, 20 April 1841, pp. 118-121: 'Experiments for determining the position of the neutral axis of rectangular beams ... when subjected to transverse strain', by Joseph Colthurst. (p.118).
9. Ibid.
10. Ibid.
11. Ibid.
12. Ibid. p.119.
13. Ibid.
14. Ibid.
15. Ibid.
16. Phil. Trans., Volume 145, Part 2, 1855, pp.225-242: 'On the existence of an element of Strength in Beams subjected to Transverse Strain by William Henry Barlow. (p.225).
17. Ibid.
18. Ibid.
19. Ibid.p.226.
20. Ibid.
21. . Ibid. p.228. 185 22. Proc. T.C.E., Volume X11111, 5 December 1871, pp. 5S-165: 'On the Stresses of Rigid Arches, Continuous Beams, and Curved Structures', by William Bell.
23. Ibid. p.123.
24. Ibid. p.124.
25. See: "On some Disregarded Points in the stability of Masonry Dams", by L.W. Atcherley, with some assistance from Karl Pearson. Drapers Company Research Memoir, London, 1904. (Model dam in Jelly). and Proc. I.C.E., Volume CLXX11, 1907-8, Part 2, pp.107-133: 'Stresses in Dams: An Investigation by means of India-Rubber Models', by John Sigismund Wilson and William Gore.
186 Chapter 6
SIMILARITY SIMILARITY
Scaling Laws in the first half of the Nineteenth Century
The first section of this chapter will consider the engineering literature of the period and examine the evidence which it
provides for a knowledge, and use, of scaling laws relating the performance of similar structures or elements of structures. It deals therefore with the philosophy of the subject rather than with specific model experiments - these will be considered later. A fundamental
problem, that of the effect of scale on self-weight, had been identified by Galileo;
You can plainly see the impossibility of increasing the size of structures to vast dimensions either in art or nature; likewise the impossibility of building ships, palaces, or temples of enormous size in such a way that their oars, yards, beams, iron-bolts, and, in short, all their other parts will hold together; nor can nature produce trees of extraordinary size because the branches would break down under their own weight ... If the size of a body be diminished, the strength of that body is not diminished in the same proportion; indeed the smaller the body the greater its relative strength. 1
It is interesting to compare Galileo's statement with that published in a textbook of 1830;
it is obvious, that although the strength of a body of small dimensions may greatly exceed its weight, and, therefore, it may be able to support a load many times its own weight; yet by a great increase in the dimensions the weight increasing in a much greater degree the available strength may be much diminished, and such a magnitude may be assigned, that the weight of the body must exceed its strength, and it not only would be unable to support any load, but would actually fall to pieces by its own weight. 2
The two statements, separated by almost three hundred years, are remarkably alike. Thus from a purely qualitative viewpoint the problem was already of respectable antiquity by the beginning of our period. But in order to develop a rational system of quantitative structural model testing a pre-requisite was the need to develop laws of similitude for 181 strength and other parameters - until one can relate quantitatively the performances of models and full-size structures then model testing is obviously of limited value. However, the nineteenth-century authors quoted above merely said 'The strength of a structure of any kind is not, therefore, to be determined by that of its model, which will 3 always be much stronger in proportion to its size'. Nevertheless, this proportional relationship connecting the strength of small and large similar structures is exactly what the practical handbooks, or pocket- books, of the 1820's and 30's were concerned with in their rule-of-thumb design methods.
Beam Design and the Mechanic's Pocket-books
The day-to-day design of solid beams in timber and metal was commonly undertaken by making use of rules published in handbooks. These convenient, portable, pocket-books were produced in increasing numbers from the 1820's and a study of them reveals a great deal about routine design techniques for machines and structures. They contain a unique blend of the experimental work of men like Smeaton, Tredgold, and
Barlow, some codified experience, and a distillation of the mathematical work of the theoretical elasticians. For research into nineteenth century design methods they represent an important, but as yet little studied, source for the historian of technology. They tell us little, however, about structural analysis. There are occasional specific references to models, but they are principally of interest in that the design rules essentially involve scaling laws - an important adjunct to model testing techniques. There was no attempt to derive these rules from first principles and one writer justified this by saying;
It is not intended to disparage Mathematics, or Mathematicians, none values that science and its followers more than the writer: but everybody knows, that the majority of mankind are not Mathematicians; and among Mechanics, where there is one Mathematician, 188 there arc one hundred who know nothing about it. Books intended to instruct them should, therefore, be written in a language they understand. 4
The pocket-books were used, rather like our contemporary Codes of
Practice, to provide design methods for straightforward cases and the habitual use of the rules would not have equipped a designer to tackle an unusual case. In the early part of the nineteenth century provincial cities often provided a forum, independent of London, for the discussion of engineering problems. Glasgow was such a city and was an important source of the early engineer's, or mechanic's, pocket- books. As it is not possible here to deal at length with the role of pocket-books in engineering design, only two principal authors from
Glasgow - Robert Brunton and William Grier - will be considered in detail.
Robert Brunton's 'Compendium of Mechanics'
This book was first published in 1824 and like most of the pocket-books, ran to many editions. Introducing the first edition
Brunton claimed that 'The want of a Text Book for Operative Mechanics has long been felt - The great inconvenience arising from this, was the cause of the compiler collecting the following rules for his own 5 personal use'. The only section that need concern us is that dealing with the transverse strength of beams where he stated laws relating the performance of rectangular beams:
If a beam be supported at both ends, and loaded in the middle, it will bend; (which is called, deflection) and if the load be increased, it will break, (which is called fracture.) - If a beam 2 inches deep and 1 inch broad, support a given weight, another beam of the same depth, and double the breadth, will support double the weight: hence, beams of the same depth are to each other as their breadths:- again, if a beam 2 inches deep, and 1 inch broad, support a given weight, another beam 4 inches deep, and 1 inch broad, will support four times the weight:- hence, beams of equal breadths are to each other as the squares of their depths:- again, If a beam of a given cross section 1 foot long, support a known weight, another beam of the same cross section 189 but 2 feet long, will support only half the known weight:- hence, beams of equal dimensions are to each other inversely as their lengths; therefore, the strengths of beams is directly as their breadths and square of their depths, and inversely as their lengths; and if cylindqVcal, as the cubes of their diameters. 6
This statement is true if rectangular beams of the same material are compared and stress induced by self-weight is ignored. He is effectively saying that the maximum bending stress, due to a centrally-applied concentrated load, is the same in each case. This follows from the simple bending formulae: applied bending moment(M) bending stress (6) = section modulus (Z) 2 .L b d where M = ---W4 and Z = 6
The remaining section on beams in Brunton's Compendium is devoted to design rules which are absolute (rather than relative) for simply- supported and cantilevered beams. These involve multiplicands for various 7 structural materials. If 'K' is the multiplying factor then for rectangular simply supported beams the breaking.load in lbs. is: 2 W - K.4b.d where W = breaking load (lbs.) L b = breadth (ins.) d = depth (ins.) L = span (ins.) and, similarly, he gives the formula for cantilevers as: W = K.b.d2 L From which it follows that Brunton's experimentally-determined multiplicand (K) is numerically equal to one-sixth of the breaking 2 stress of the material having units of lbs/in . This grouping of non- dimensional and dimensional terms in one constant was a common, though variable practice in the nineteenth-century handbooks. Having determined the breaking weight Brunton employed a load factor and' • • considered that 'two-thirds of the result is sufficient to lay upon a 8 beam for a permanent load'. Although his comparison of similar beams essentially involves scaling laws Brunton never used the term neither did he refer to models. When Brunton's Compendium was published in 1824
190 he said 'it had few companions in the department of science to which it
belongs' but within a decade several others had been published 'written
in a style that the Operative Mechanic, possessing but a scanty stock of 9 information, can understand'. Amongst these two further pocket-books
of particular interest emerged from Glasgow written by William Grier, a civil engineer.
William Grier's Pocket-Books
Grier produced two pocket-books both of which ran to several
editions. The first was The Mechanic's Calculator of 1832 in which
he referred to models and the importance of scaling laws; 'A model may
be perfectly proportioned in all its parts as a model' and yet the
structure, 'if constructed in the same proportion, will not be
sufficiently strong in every part; hence particular attention should be 10 paid to the kind of strain the different parts are exposed to'. His
use of the words stress and strain is not at all consistent as may be
gathered from the following:
If the strain to draw asunder in the model be 1, and if the structure is 8 times larger than the model, then the stress in the structure will be 83 = 512. If the structure is 6 times as large as the model, then the stress on the structure will be 63 = 216, and so on; therefore, the structure will be much less firm than the model; and this the more, as the structure is cube times greater than the model. 11
This is not very clear and only makes sense if 'strain to draw asunder'
and 'stress in the structure' both merely mean self-weight. If the
structural element considered was a beam and a geometric scale-factor
'n' related the 'model' and 'structure' then the bending stress, due to
self-weight only, would be proportional to n, so his statement is far
from clear. He is little more explicit when speaking specifically of
model beams;
191 The greatest weight which the beam of the model can bear, divided by the weight that it actually sustains = a quotient which, when multiplied by the size of the beam in the model, will give the greatest possible size of the same beam in the structure. Ex. - If a beam in the model be 7 inches long, and bear a weight of 4lbs., but is capable of bearing a weight 26 lbs.; what is the greatest length which we can make the corresponding beam in the structure? Here 26 = 6.5 therefore, 6.5 X 7 = 45.5 inches. 12 4 This is rather confusing. If Grier meant that the 26 lb. weight would 6 break the model beam then his quotient 2 = 6.5 is a type of load factor 4 which he used as the geometric scale-factor for the span only, i.e. 45.5 = 6.5. What he apparantly meant was that 46.5 inches was the 7 greatest span over which a beam of the same cross section as the model
could carry a central load of 4 lb. In other words, a central load of
4 lb. would just break the beam of 46.5 inch span. This is true as, other
things being equal, the breaking stress'is proportional to W X L. Grier did not apply a geometric scale-factor to all the linear dimensions so it is difficult to see that his statement added much to the understanding of the similarity between a model and its prototype.
Another of Grier's handbooks, The Mechanic's Pocket Dictionary, first published in 1837, included a number of proportionality rules for rectangular beams;
In rectangular beams, the lateral strength4 are as the breadths into the squares of their depths. The lateral strength of a beam with its narrow side upwards, is to its strength with its broader face upwards, as the breadth of the2broader side to the breadth of the narrower. That
is, bd :db2 d:b. Thus, the area of the end of a joist which is 3 inches by 4 inches, is 12 inches; and its strength, with its narrow side upwards, is as 42X 3 = 48. A joist 6 inches by 2, contains the same quantity of timber, but with its narrow side upwards, its strength is as 62X 2 = 72. A joist 8 inches by still contains the same quantity of timber, and with its narrow side upwards, its strength is as 82X1 = 96; so that a joist 8 inches by which contains exactly the same quantity of wood as a joist that is 3 inches by 4, however, exactly twice as strong; for 96 = 2 X 48. 13
192 What Grier says here is correct, and in saying that the 13 inch by 8
inch beam is 'exactly twice as strong' as the 3 inch by 4 inch beam he
means that, for a given span and load, the maximum bending stress in the
former would only be half that in the latter. The sense of Grier's
statement was echoed by an architect writing to the Institute of
British Architects in January 1838 saying that his own experiments on
small cast beams proved 'that the mere sectional area of a beam is not
to be the basis of calculating its strength'. 14 Another section of
Grier's Dictionary deals with floor joists and he extrapolates from a
joist of sufficient strength to another, equally strong, but of
different dimensions:
Suppose it to be known what size of the section of a joist is sufficient for a given length in a certain case, let it be required to find the section of a similar joist of a different given length in a similar case. Multiply the cube of the depth of the joist whose section is known, by the square of the length of the joist whose section is required, and divide the product by the square of the length of the known joist; the cube root of the quotient is the depth of the section required. Thus if in a certain case a joist whose depth is 1 foot, and thickness 3 inches, be sufficient for a length of 30 feet; what must the section of a similar joist be in a similar case whose length is 15 feet? By the rule the 3 2 X 15 225 depth =21 = 3 = = .6298 feet 2 900 1 30 and 1 foot: 3 inches :: . 6298 feet: 1.8894 inches = thickness of similar beam. 15
This again can be shown to be true by equating stresses in two geometrically similar beams (i.e. b = 4) subjected to equal uniformly distributed loads. A distributed load was the necessary condition as
Grier was discussing a floor joist subjected to a floor loading in lbs/f t2 In summarising his work on proportionality rules, or scaling laws, Grier again brought the subject back to models;
it is plain, that in similar beams of the same materials, the force which tends to break them in the larger beams increases in a greater proportion than the force which tends to keep them whole, or to secure them against 193 accidents; their tendency also to break by their own weight increases as their length increases, so that although a small beam may be firm and secure, yet a large, though similar one may be so long, as to break with its own weight. Hence we find, that what often appears firm and successful in a model, is weak, or infirm, or often falls to pieces by its own weight, and will by no means answer in a large machine. 16
No evidence has been found to show that Grier made use of experimental
models in his structural analysis and design. But we might infer his evaluation of their importance from the fact that he considered the subject worthy of mention in his published pocket-books where pressure on space must have made strict editing essential.
The Engineer's and Contractor's Pocket Book - 1847
Although many other pocket-books were published (see the appended select bibliography), *he above is typical of the mid-century type and in the direct tradition of Brunton and Grier. Only brief mention need be made to its section on beams where the design rule for lateral resistance was re-stated:
The strength of beams to resist fracture in this direction is as the breadth and square of the depth, and inversely as the length. The general formula being:- 2 S a d = 1 w where a the breadth, d the depth, 1 the length, w the weight, and S a number determined by experiment on different materials. When the beam is supported at each end and loaded in the middle, the values of S for different materials have been determined by Mr. Barlow, as in the following table - the breadth and depth being taken in inches, the length in feet, and the weight in pounds. 17
There followed a table giving the 'Elastic Strength' of various timbers, cast iron, and 'Good English Malleable Iron'. With the units given for a, d, w, and 1, the multiplying constant (S) is numerically equal to
1/18th. of the breaking stress with units of lbs/int, providing yet another version of the constant.
194 There were many other examples of pocket-books, handbooks, Aromd6 and dictionaries quoting this f.eaamffle right through the nineteenth
century and indeed into this. We may be sure, therefore, that this
design method for floor joists, and solid bridge girders of modest span
was widespread. It was indeed what Stephenson, Fairbairn, Hodgkinson,
and Clark regarded as 'received opinion' when tackling the design of the
Conway and Britannia Bridges. The model tests in connection with these
bridges led to a modest outpouring of general articles concerning the
issue of similarity between a model and its prototype. The subject had
an intellectual fascination which undoubtedly prompted the two articles
about to be considered.
The Technical Journals
Typical of several anonymous articles in the technical press
which were stimulated by the Britannia Bridge experiments was that 18 published in The Builder in 1846 entitled:
EXPERIMENTAL MODELS
"Parvis componere magna" 19
The piece begins with the common justification for model testing
observing that although bridge proportions 'may be calculated, sometimes with mathematical nicety' there are occasions when;
If the design be unusual and complicated, and change of form or motion is likely to take place from causes extraneous of the structures, as in a suspension- bridge from the action of a load passing over it, or of the wind, it is well to use a model, as by its means the changes and vibrations of the proposed structure may be more satisfactorily inferred than from the most laborious calculations. 20
This is a classic statement of motive. The article is interesting as it considered not only scaling laws relating self-weight and strength, but also live load relationships. It also dealt with the effect of making the model of a material different from that of the full-scale structure.
It began by saying: 195 In masses of similar forms and materials, but of dissimisilar dimensions, the strengths are as the squares,but the weights (and of course the strains depending upon the weights) are as the cubes of the respective dimensions. For instance, with respect to two rectangular beams laid horizontally, the first 1 foot deep, 1 foot wide, and 20 feet long between the supports, the other 2 feet deep, 2 feet broad, and 40 feet long, the dimensions are as 1 to 2; the strengths are as the number of parts in the cross section which oppose extension, that is, as the areas which are as the squares of 1 and 2 or 1 to 4; the cubical contents, and, therefore, the weights are to each other as the cubes of 1 and 2 or 1 to 8. 21
This makes rather difficult reading,and,as it stands,is not correct. A geometric scale-factor of 2 is applied to two prismatic beams, and, therefore, their self-weights would act as uniformly distributed loads.
The stresses due to these would be directly proportional to the scale 22 factor and not to its square. The statement would be true only if the self-weight were regarded as a single concentrated load acting at mid- span. The writer did not state that this was his assumption - later writers did, as we shall see, and in fact when speaking of achieving equal strength/weight ratios he categorically stated;
while the resisting power and weight (or straining force) of the smaller beam,• are to each other as 1 to 1, the resisting force and weight of the greater beam are to each other as 4 to 8, or as 1 to 2. If we suppose that the latter is just so strong as not to bend with its own weight alone acting upon it, the former would bear a load equal to its own weight, uniformly distributed over it, without bending; for then the resisting power and straining force of each would have the same proportion, viz. 1 to 2. In experimenting with a model, care must be taken that this condition is fulfilled. 23
This, of course, follows from his previous statements. The expression
'just so strong as not to bend' is particularly imprecise, but presumably meant without perceptible deflection.
In choosing an example to illustrate the principle the writer surely revealed the stimulus for his article:
196 If we proposed to construct a suspension bridge, or say for the novelty, a tubular bridge, of 450 feet span, with 500 tons iron, and an experimental model of 45 feet span, the dimensions being as 1 to 10, the cross sections of the great tube would be 100 times greater than those of the model; its weight would be 1,000 times greater, which numbers also are as 1 to 10. To put the model, therefore, upon equal terms with the projected bridge, it would have to be loaded with 9 times its own weight, or with 500/1000 X 9 = 4i tons; and the same allowance would have to be made for all external disturbing causes, as the weight of carriages, &c. 24
The model would weigh 0.5 tons (500/1000) and adding the surcharge of
4i tons made the model's strength/weight ratio the same as that of the
large tube.
In 1801 witnesses giving evidence to the Select Committee discussing Telford's London Bridge were asked to state a preference for
the material of a model (see chapter on arches) but this article appears hie to beAfirst to attempt to quantify, however simply, the effects consequent on using different materials for model and bridge.
The model may be made of materials the same as - or different from, if more convenient - those intended to be used on the larger scale; but in either case regard must be had to the relative strengths and weights of the materials when put together in the proposed manner, if we wish to make a just comparison of the little with the great structure. 25
If the model were made of tin, 'as being more manageable on a small scale
... we must proceed in the same way to reduce the strengths and strains to the same ratio'. Here again for 'strength' read stress and for
'strain' read self-weight.
The relative strengths of tin and iron to resist extension, are nearly as 1 to 4, and their specific gravities nearly equal. Making the respective dimensions as 1 to xlthe strengths are as 12 to 4x2, and the strains as 1 to x3. 2 3 2 3 1 : 1 :: 4x : x 3 2 x = 4x
x = 4. 197 Whence it appears that if the dimensions were as 1 to 4, a bridge of tin of, 450/4, or 112.5 feet span, would be nearly upon the same terms with regard to strength and strain as an iron one of 450 feet span. If we were to make our model of 112.5/3, or 37.5 feet span, we should have to add in our trials only twice its own weight, &c. If we were to construct the model of lead, the strengths of lead and iron to resist extension being nearly as 1 to 10, and their specific gravities as 11 to 7. 2 3 2 2 1 : 11 X 1 :: 10x : 7x . 3 2 7x = 11 X 10x .
x = 110 15.7
The dimensions in this case are as 1 to 15.7. The span of the model being made 450/15.7, or 29 feet nearly, no extra loading would be required. 26
The use of lead to model the elastic behaviour of iron is obviously of doubtful value - but that apart, the mathematics is otherwise sound.
The anonymous author concluded by saying that although tensile properties only had been mentioned, 'the same reasoning, however, applies to the resistance which they offer to compression. A bridge built of chalk might be made to indicate the strength of one built of granite, if 27 the qualities of the two materials were taken into account'. The latter is true, but not for the reasons he gives (see chapter on arches) and it would appear that our anonymous author had not heard of the difficulties that his contemporary Fairbairn was facing at Millwall with the buckling of wrought iron plates.
The article, with all its imperfections, is nevertheless an interesting early attempt to relate many of the factors of importance in model testing. The author is unnamed - the piece merely being signed
'W'.- it might possibly have been C.H. Wild whose mathematical attainments were more than adequate and we know from his subsequent work in connection with the Torksey Bridge (see chapter 4) that he was to become interested in structural models. But speculation of this
198 type is not particularly rewarding.
Just a year after the previous article, The Civil Engineer
and Architect's Journal produced an anonymous piece - 'On Model 28 Experiments', which began philosophically:
Until the present era ... the studies of the engineer, like those of the lawyer, were confined to the acquiring of details of precedent, while the knowledge of the scientific principles of his profession was neglected as of comparatively little importance ... But with the railway arose a new epoch in the history of engineering: works were required to be constructed of unprecedented magnitude and solidity, and for the execution of which a higher amount of mechanical science and a wider range of experience were required. To supply the latter of these two desiderata, numerous experiments have been conducted of late years on the strength of materials, and on models of the whole or most important component parts of proposed structures. 29
The author dealt with the latter, 'particularly with reference to the
difference of amount of thrusts and strains in the model and its
original'. The case considered was that of a horizontal girder of 'I'
section loaded with a given weight - 'to this case may be referred almost,
all the cast iron railway bridges now completed, as well as the proposed
tubular Menai Bridge'. Figure 6.2 shows his only illustration together
with a drawing made to assist in following his reasoning. See Figure
6.1 for the published mathematical development together with analytical
comments added on the right.
It is interesting to note that he applied the geometric 3 scale-factor to the applied load (ie. 'weight at w = w.0 ') which, as
we have seen, makes the strength/weight ratio of model and prototype
('original') different - and in favour of the model. Admitting that,
equation 6 shows that 'Te, the moment of resistance of the full-scale section, is proportional to the fourth power of the scale-factor (u);
'u' being a whole number. This is correct for the condition stated but
199 PUGLISHED EQUATIONS ANALYTICAL CCIVENT
3 Let the weight at w = wu (because the weight varies as the cube of the scale u)' the 3' weight of beam and girder = ; CE = lu; R and R' the reactions at A and S.
Then first considering the equilibrium of the whole girder, we shall have
R + R' = (w + w') u3 O taking moments about A: 3 3 u R'.au = (wu hu) + w'u — a2 w ' t.Ta ..] u3 R' au = Idhu + O [ 2 the girder being supposed uniform and symmetrical throughout its mass. —h w' ... R = w(---)a + — taking moments about 13„ a 2 u3 O [I For the equilibrium of the portion CF, if T be the tension and thrust of the lower and upper flanges, Y the vertical force at F, z the distance between the points of application of the thrust and tension, we have
T = T sum of horizontal forces = O.
Y + R = (w + w') u sum of vertical forces = 0.
and 12 u 3 moments about A for portion Y 1 u = Ihu' + u — Tz w ' 2a O AFCE. (u' is obviously a [ misprint).
whence
La——1 a 1 4 'Tz' = the 'moment of T z = h w+ 1 w' u O a 2a resistance' of the section.
Reference: The Civil Engineer and Architect's Journal Volume 10, November 1847, p. 352. 6.1
a
A
Let A 13 be the girder, supported at A and II, and composed of the loser flange X11 ab, the upper flange CD cd, and the web e ab d. Let AD v au; AC t, bu; Aa a cu; Cc= du; Cw = Au.
The published drawing
w.03
hu (a—b)u uk
C c _LUC lu wilu3 e 3 bu 1 u ir 2 I a Y .4,..f 1% a f A r------1 ud F au lu 2 stress au uk' diagram 1
The 'Original' (full—scale) beam
k
The model beam
Reference: The Civil Engineer and Architect's_Journal Volume 10, November 1847, p. 352. 6.2 it is not in a particularly relevant form for the model experimenter.
This is most likely the work of a theoretical man who is enjoying the mathematics. He took the matter a stage further by saying;
If the web of the girder be very thin compared with the breadth of the flanges and their vertical depth, - and if their vertical depth, uc, ud, be small compared with ub, - and if uk, uk' be the width of the upper and lower flanges respectively, - t and t' their thrusts and tensions per square inch respectively - then we shall have 2 2 T =tkcu . t' k'du ; and z = au nearly 3 3 therefore Tz =takcu = t' k'adu nearly
therefore, t and t' both vary as u nearly; that is, approximately, the tension per square inch on the lower flange, and the thrust per square inch on the upper flange, of all similar and similarly loaded girders varies as their scale of linear dimension. 30
It would appear that 'z = au nearly' is a misprint and should read
'z = bu nearly' and b should be read for 'a' in what followed. The
bending stress is only directly proportional to 'u' when, as in this
specific case, the applied load is also scaled by the geometric scale 31 factor. The influence of the Britannia Bridge was again in evidence;
We have been especially induced to call our reader's attention to the subject of model experiments, from the fact that the proposed tubular bridge over the Menai Straits is to be constructed, as to its dimensions, according to laws developed in a series of experiments, conducted by Mr. Hodgkinson at Blackwall. 32
The innaccurate phrase 'Hodgkinson at Blackwall' can presumably be attributed to Journalistic pressures: The article was concluded int the
following issue of December 1847 in a short essay which included the
table of results of rectangular tube experiments published in
Hodgkinson's Report of the previous February. Undoubtedly the tubular girder experiments of Fairbairn and Hodgkinson created wide interest in the technical press as these two examples, which attempted a general theoretical approach to model/prototype similarity, bear witness. Both
Fairbairn and Clark considered the problem in their publications and 200 it is to these that we now turn.
Similarity and the Britannia Bridge Experiments
The tests on 'model' tubes at Millw•all and Manchester provided the greatest spur to the consideration of scaling laws - in fact they were integral and crucial. Many of the experiments from the beginning were designed to compare the performance of similar tubes, but the problem really became central after the decision, in December 1845, to make a 1/6th. scale model of the established dimensions of the
Britannia Bridge. In December Fairbairn felt convinced that the proposed large-scale experiment would put them in a position 'to state with considerable accuracy, what can be done, on the enlarged scale, six 33 times the size of the tube we are now constructing'. Of the'received opinion' respecting tube-scaling laws Fairbairn typically misquoted;
'Professor Airy, the Astronomer Royal, in a letter addressed to Mr.
Stephenson, had given it as his opinion, that the strength of wrought-. iron tubes varies as the square of the length, and the weight as the cube 34 of the length'. Clark added in the margin of his own copy of Fairbairn; 35 'Professor Airy could not of course have made any such vague statement'.
But elsewhere Fairbairn showed that he was aware that it is the square of the geometric scale-factor that relates the strength of two tubes.
One of the problems, as we have seen from the pocket-books, is how the scaling law is affected by taking into account the self-weight of the structure. In uniform tubes this would act as a uniformly distributed load whereas the model tubes were broken with a concentrated load at mid-span. Fairbairn and Clark both overcame this difficulty by assuming that half the self-weight acts at mid-span. This equivalent load would produce the same maximum bending stress at mid-span as the whole load 36 uniformly distributed. The ideas on similarity of Fairbairn, Hodgkinson, and Clark will now be considered separately, although, of course, there 201 is a great deal of agreement.
William Fairbairn
The best source of Fairbairn's ideas is his book and in the
preface, dated June 1849, he stated that he was 'indebted to Mr. Tate, of Battersea, for the mathematical analyses, and for the interesting and valuable deductions and formulae, which will be found at the close of the experiments'. It is difficult therefore to be certain just how much
Fairbairn contributed to the work on similarity contained in his book - it was almost certainly due to Tate. However, in the equations the following terminology was used:
Let W = total breaking weight of the experimental tube. w = half weight of the experimental tube. L = weight of the breaking load W = L + w 1 = span of experimental tube. and W,= total breaking weight of the large tube. w,= half weight of the large tube. L,= weight of the breaking load of large tube. W, = L, + w, 1,= span of large tube.
He then proceeded:
It is desirable that we should have a formula containing, in one expression, the essential data of the problem. adC Assuming W _ L , a,c,C11 W
W, hence by division we have a,d,1 a d 1, but since the solids are supposed to be similar, we have
a ; a, :: 12 : 12
d : d, 1 : 1, •• ad : a, d, 13 : 13 3 . a,d, ...., 1, 3 a d 1 substituting
202 3 W, 1, 1 12 = — X - = 3 2 W 1 1, 1 2 , • W, = 12 . w 1
substituting L = W for W and L, w, for W, we have 2 1, (L w) L, w, = 1 2 1 •. L, (L + w) - w, = 2 1 3 - 1 3 but as w :w, 1 : 13 . w • • ' we have 1 ,3 = (r) w
1 2 1 3 . . L, = (-0 (L + - (I-) w 1 2 L 1, - L, = (11) 1 w
which expresses the breaking load of a tube 1, feet long, and in all respects similar to an experimental tube, whose length is 1 feet, weight w tons, and breaking load L tons. 37
Fairbairn really meant 'half weight w tons' - yet another example of the confusing errors which mar his book. This work of Fairbairn (or gate) on the realtionship of similar tubes is typical of the period in that it is only concerned with the ultimate load in cases where the model was made of the same material as the large structure.
Eaton Hodgkinson
Hodgkinson, as might be expected, was well aware of the square-cube law for strength-weight relationships for solid beams and used it in reducing his experimental data and he also sought to verify it experimentally. His abstract of experiments on 'mathematically similar' tubes is shown in figure 6.3, and from which he concluded that as 'the strength was somewhat lower than as the square of the lineal dimensions, we may perhaps with safety adopt 1.9 instead of 2 to 38 represent that power'. To help understand his similarity technique one of his experiments will be studied in detail using an unpublished 203
130 APPENDIX to REPORT of the COMMISSIONERS appointed to
Fxrtsr.'Surriv.7.ttNT to T.ttr.r: I.- Comparison of Re,oltg from Exwriments on the Transverse Strength of Tubes of Wrought Iron, all the Tubes Mng constructed to Le mathematically similar, or proportional to cn.01 other, in lengtli, breadth, tlep:11, and thiclme,, of Plates. The principal oltject of the Experiments was to afccr_ thin the power of the lineal dimensions on witiLlt the strent4th of similar Tubes, varying in size, dep.-ntls. To judge of the stizmo.11 of the Menai Tube from that of modtic. ItreAlsin: 11:.1•1e., of I Poe-cr N Dislance T.....;h: a th. tVei•Zht.. Derth of Dre:th of • • the• : tItLe 1..'nal Term of t-7.tctiort, I.:weer' the Tubs, b•tween exd.....se of the , the I Dime:1,10os out and Comp,: ,tire MnInitt.tle cf the. • Supports. i the Scports. the Wei,..los Tubes. Piers Tubes' of the Tu'es I wht' s h '''"e Tut cc cur:Tared. of the Tabes. - "Streit1 •th•• tlenerlt. Feet. Tons. Inches. Inches. • Inch. 30 42.62 cwt. 57.5 2.4 nearly 16 nearly •525 1 7.5 72.36 lbs. 4.454 6 „ 4 ,, •1323 5 1.639 • 0
33 • 23.09 cwt. 22.84 24 ,, 16 „ •272 1 1.946 . 7..5 • 35.33 lbs. • 1.409 6 ,, 4 „ •06.3 J CI I •
30 42-62 cwt. 57.5 24 ,, IG .525 1 3.75 }, 1903 5.65 lbs. I.! 3 PP 2 ,, •061 1 1 0
• 30 23.09 cwt. 22.54 24 „ 16 „ •272 1 1.93.5 3.75 4-34 lbs. •3 3 PP 2 ts •(:3 if 0
45 130•35 cwt. 11F76 36 „ 24 ,, .751 1•570 3.75 9.63 Its. 1.1 3 Pt 2 „ •061 J 45 130.35 cwt. 114.76 36 „ 24 „ •751 0 D 7.5 72.36 lbs. 4.451 6 ,, 4 „ •1325 I 1.874 .
45 130.35 cwt. 114.76 36 „ 24 „ .75 1 30 39. nearly 51.3 21 ,, 16 ,, .5D )•846- • . . 45 59.60 cwt. 65•5 ZG „ 24 ,. As 1, 2,3, 2.271 30 20.46 cwt, 25.1 24 „ 16 ,, As 1, 2. 3. . Sianilar Tubes • with difterent • • tluchn of Plates in earls. ' 1.942= clean,c: • • 1.6:5 ii we 7! t••• gh.ct the last result, 2.271.
In several of these e-.perialents the Tubes gave s.r,y by the met$ at the tcp becoming aYrink:ed; and as it :ppenr, that in mo of the cases the strength was somewhat lower than as the square of the lineal d:mensious, we may porhaps with safely a;'.opt 1•9 instead of 2 to represent that power.
Hodgkinson's Abstract of Results
Reference: Parl. Pap. 1849 (1123) XX1X Report of the Commissioners appointed to inquire into the Application of Iron to Railway Structures. Appendix AA, p. 130. 63 letter, written soon after the experiment, and comparing it with the
results published three years later. The experiment was begun on
24 August 1846 and completed on 8 September. The plain rectangular
tube was of 45 feet clear span and its cross sectional area diminished
towards the supports. Writing to Stephenson in September he described
the experiment:
The breaking weight of the tube was 65.5 tons + the pressure from9the weight of the beam; and a;suming this last as 73 the weight of the beam, or 73 (3 tons 1 cwt) = 2 tons nearly, we have 65.5 + 2 = 67.5 tons. Now this tube is of 1/10 the length and depth of the large tube, therefore the strength varying as the sqpre, where the tubes are similar, therefore 10 X 67.5 = 6750 tons = strength of the large tube if it were similarly formed. The weight varying as the cube of the lineal dimensions, gives 103 X 3 = 3000 tons for the weight of the large tube, the small one being taken as weighing 3 tons (its real weight is 3 tons 1 cwt.). If, as is probable, the pressure in the middle of this varying tube, from its own weight, is 3 of that weight, therefore 3 X 3000 = 2000 tons will be the pressure from the weight of the tube; and the strength of the large tube will be reduced by this weight, 6750 - 2000 = 4750 tons the weight, which, in addition to its own weight, the tube would bear. 39
Here he estimated the equivalent concentrated load at mid-span due to
self-weight as 3 the actual weight. If we compare this letter with the
worked-up results published in his Appendix to the Report of the Iron
Commissioners in 1849 (the best source of Hodgkinson's work) an
interesting comparison can be made. In table 11 he gave the bare facts
of the experiment but in table VII the data had been operated on so as
to compare the 45 foot span model, with a bridge tube of 450 foot span and weighing 1,000 tons - the object aimed at in the Britannia Bridge.
(see figure 6.4). The equivalent mid-span concentrated load had now been rationalised to 6/10 rather than 2/3. If we analyse his working we see
that:
204
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Hodpkinson: Manchester Experiments Results
Reference: Parl. Pap. 1849 (1123) XX1X
Appendix AA, P. 157. 6.4 Model Bridge (45 feet span) (450 feet span) 2 Breaking weight 67.293 tons 67.293 X 10 = 6729 tons
Self-weight 3 (between supports)2,988 tons 2.988 x 10 = 2988 tons
and, by proportion, for a 450 foot span tube weighing only 1000 tons
we have:
let the strength of such a tube = S, then
2988 : 1000 :: 6729 : S 6729 X 1000 S = - 2252 tons, 2988 1.9 or, using n the strength of the bridge would be 1789 tons. From
both these figures 6/lOths. of the self-weight would have to be
deducted,
ie. 2252 - 600 = 1652 tons - the additional load required to
break the bridge. For uniform tubes, half the self-weight (ie. 500 tons)
would have to be deducted. Here again the similarity equations are
only concerned with ultimate load conditions, although Hodgkinson did
attempt to take into account variations in cross-sectional dimensions
of the tubes.
Edwin Clark
Clark also considered model similarity and scaling laws and
drew particularly on the experiments of Hodgkinson. He quoted the
usual square law;
The strength of similar beams should be directly proportional to the square of their lineal dimensions; so, that if we find the strength of any given model to be W tons, then any other similar beam, which is n times as long, n times as broad, n times as thick, and n times as deep, should be n2 times as strong, or its strength should be n2W tons. 40
He reproduced Hodgkinson's abstract of experiments on 'mathematically
similar' rectangular tubes which had been published a year earlier
(see figure 6.3). Although this showed that the strength was more 205 1.9 adC nearly proportional to n he added; 'Conversely, the formula W 1 is proved experimentally to hold true for similar tubes. For, in 2 a similar tubes a varies as n , and y is constant, therefore 1— varies as 2 2 n ; but we have seen the strength varies as n , therefore the strength ad adC' 41 varies as -7r, or W = The foregoing was published in Clark's
first volume. In the second he repeated the square-cube law and added
an interesting piece on the strength/weight relationship of similar
tubes:
as regards the limit at which any tube would just break with its own weight: as we increase any tube n times in lineal dimension, the ratio of the breaking-weight to the weight of the tube itself varies as n2/n3, or as 1/n, or inversely as the lineal dimensions. Hence this important practical result. If the weight of any tube is 1/2, or 1/3, or 1/nth. of its breaking-weight, a similar tube made twice or three times, or n times the same size respectively, will just break with its own weight. Thus, if the breaking-weight of any tube be three times its own weight equally distributed, a similar tube of three times the same dimensions would just support itself. Again, if we take any given model and enlarge it to twice, three times, four times, n times the same lineal dimensions, n being of such a magnitude that the tube will just fail from its own weight, the tube in this series which will bear the greatest weight per foot run will be the tube corresponding to the number n/2. The strain on the bottom of such a tube will be also equal to one-half the ultimate tensile strength of the material. 42
To discuss this rather complex statement (which does not appear in
Fairbairn or Hodgkinson's work as such) it will be advisable to consider each of the three paragraphs separately.
In the first paragraph Clark discusses, and correctly demonstrates, the limits of self-weight induced failure. This can be seen to be true by considering the breaking stress in two similar beams, one being twice the size of the other. In the smaller beam the self-weight (w/unit length) is deemed to be half the load required to break it. Therefore, the breaking stress in the smaller beam would be:
206
9 M (2WL). = L. 6 w. L . 3 Where M = bending moment due Z 8. 9 to self-weight b. d- b. d 2 + equal weight. Z = section modulus. L = span b = breadth d = depth.
Whilst the breaking stress in the larger beam (where n = 2) would be: 3 2 M (2 wL). 2L. 6 w. L . 3 Z 2 2 2 8. 2b. 2 d b. d . 2
ie. the same stress as in the smaller beam and therefore the larger
beam would 'just break with its own weight'. In the second paragraph
Clark's statement that the breaking weight of the small tube'be three
times its own weight equally distributed' must be taken to include its
welf-weight, ie. a surcharge of 2w is required to break it. Given this,
a similar calculation shows the maximum bending stress to be the same
in both the smaller and larger beam (where n = 3). It is interesting
to note however that whereas in the first paragraph when both tubes were
at the limiting stress he said that the larger would 'just break with
its own weight' whilst in the second example when both tubes were at
the stress limit he describes the larger tube as being able to 'just
support itself'. The third paragraph contains an interesting, but not
at first sight obvious, statement on the relationship between the
geometric scale factor and the limiting superimposed load on a series
of similar beams. The self-weight of a series of geometrically similar
beams is obviously proportional to the cube of the scale factor (n) and
the maximum bending stress induced by this self-weight is directly
proportional to n. It is not so obvious however that the maximum capacity
for superimposed load occurs on the beam whose size is determined by half
the scale factor which produces self-weight failure. Nevertheless, this
is the case and a specimen set of calculations is given (figure 6.5)
for a particular beam which if scaled up six times (n = 6) the self-
weight would produce the ultimate stress. A similar set of calculations
207 may be made for a series of values of n and I have expressed these max graphically and give curves for n = 5, n = 4, n = 3, and n = 2 in
figure 6.6. The curves show that the superimposed load per unit length
to produce failure is always a maximum at half the limiting scale factor.
It follows also that the maximum stress due to self-weight only in these
cases is half the ultimate stress (or 'strain' as Clark says). Although
this was an interesting exercise it is difficult to see any practical
use for the result. It nevertheless demonstrates the inherent fascination
that scaling laws of this type had for such men as Edwin Clark.
However, the interest in similarity, and indeed in model
testing itself, was soon to wane after the initial interest engendered
by the design and construction of the Britannia and Conway Bridges. The
last important experimental model tests to involve similarity
considerations were those made by P.W. Barlow in 1857 for his design of
a suspension bridge with stiffening girder at Londonderry (see chapter 3).
It is interesting to note that when G.B. Airy made similar experiments
ten years later (1867) his model was of the analytical type and
similarity with a particular bridge was not involved (see chapter 3).
More complex issues of similarity did not arise in structural analysis
until model strains could be measured accurately, making it necessary
to consider the elastic properties of the model material, such as
Poisson's ratio. The possibility of studying the distribution of stress
in structural models shifted the sphere of interest away from ultimate
load behaviour and made the refinement of similarity techniques essential.
This did not occur until the early part of this century after a break in
structural model testing during which the focus of interest in
similarity relationships, and in model testing generally, had shifted to
the hydraulic model and ship towing-tank experiments of Reynolds and
Froude.
208 • •
O 0 W Self—weight Stress due Self—weight stress Superimposed Superimposed P. Span o -4 Scale W = w.L to as a fraction of load to break load per unit • W • n factor 3 Self—weight ultimate stress beam length m3- cr (oc n ) (ocn) lo P.0 (n) COD (cc n) O W a m m 0- a • W rt- n n = 1 12 (say) 1 1 1/6 72 — 12 CL a 60/1 = 60 cr' cr = 60 c 1-4 P. 3 m rt- E• Ca n = 2 96 2 2 1/3 288 — 96 o P• C 192/2 = 96 3 -0 SO CD = 192 • C-) I-1 P- CD 3 X" 0 n = 3 324 3 3 1/2 648 — 324 ,--... cr) 324/3 = 108 0. = 324 Cll 0 0 a n = 4 768 4 4 2/3 1152-768 384/4 = 96 = 384
n = 5 1500 . 5 5 5/6 1800-1500 300/5 = 60 = 300
n = 6 2592 6 6 1 0 0 ■ . UJ n ....Ol co CD -t) ~ Dl ::J n roi rt" ..... a co ..., c.- Dl CD :J U 0. ::J "'0 .... a .... ~ ....3 0. ....("f ...,o j a .c..., en 01 c c: o ID ...,C1l roi 1"· ..., 3 .,..j a a C en CO <-"'0 0. CO .... o a ...J ru "'0 0. CD Ul n o ...,C 0. c::: .....E CO ~ 01 CD 0. ::J Ul
Geometrie Scale Factor (n) Similarity
Scaling Laws
1. Dialogues Concerning Two New Sciences, Gallileo, Leiden 1638. English translation by Henry Crew and Alfonso de Salvio, Macmillan, New York, 1933, p.130. Reprinted New York, 1952.
2. A treatise on Mechanics, Capt. Henry Kater and Rev. Dionysus Lardner, London, 1830, p.277,
3. ' Ibid.
4. A Compendium of Mechanics, Robert Brunton, Glasgow, p. x Preface to the 6th. edition.
5. Ibid. Preface to first edition, 1824.
6. Ibid. p.82.
7. Ibid. pp. 83-4: Brunton's table of Multiplicands acknowledges Barlow's Essay on the Strength and Stress of Timber, Art.149.
8. Ibid. p.87.
9. Ibid. Preface to the 6th. edition.
10. The Mechanic's Calculator, William Grier, Glasgow, 1832, P. 171.
11. Ibid.
12. Ibid.
13. The Mechanic's Pocket Dictionary, William Grier, 1837, p. 321.
14. R.I.B.A. Library. mss. letter SP 5, from Charles Parker, dated 29 January 1838. This letter is attached to 22 foolscap sheets of results of experiments on cast iron beams of 22 inches span; load, deflection, and cross sections are given.
15. The Mechanic's Pocket Dictionary, William Grier, Glasgow, 1837, p.284,
16. Ibid. p. 323.
17. The Engineer's and Contractors' Pocket Book for the years 1847 and 1848, remodelled and improved on Templeton's Engineer's Pocket-book, John Weale, London, 1847, p.285.
18. The Builder, 17 October, 1846, p.500.
19. The sub-title appears to be a paraphrase of Vergil, Georgics, book 1V, where the activities of bees are compared to those of humans.
20. The Builder, op. cit. 209 21. Ibid. WL 6 22. The bending stress f = M = a7:1 If the scale factor is z 2* 3 'n', then f is proportional to: n n = n, n n2 23. The Builder, op. cit.
24. Ibid.
25. Ibid.
26. Ibid.
27. Ibid.
28. The Civil Engineer and Architect's Journal, Volume 10, November 1847, pp. 352-3 (Concluded in the December issue, p. 398).
29. Ibid. p. 352.
30.- Ibid.
31. Ibid. p. 353.
32. Ibid.
Similarity and the Britannia Bridge Experiments
33. An Account ... of the Britannia and Conway Tubular Bridges, William Fairbairn, London, 1849, pp. 24-5: Letter from Fairbairn to Stephenson, 3 December 1845.
34. Ibid. p. 134.
35. Ibid. in Clark's copy of Fairbairn op. cit. (See reference 37 in chapter 4 of this thesis).
36. This is because the equivalent concentrated load would produce the same mid-span bending moment as the u.d.l. viz: 2 (wL). L (wL). L w. L M - 8 2. 4 8
37. Fairbairn, op. cit. p.
38. Parl, Pap. 1849 (1123) XX1X, Appendix AA, p. 130.
39. Autograph Letters, I.C.E. library, Hodgkinson to Stephenson, 28 September 1846.
40. The Britannia and Conway Tubular Bridges, Edwin Clark, 2 Volumes, London, 1850, volume 1, p. 419.
41, Ibid. p. 422.
42. Ibid., volume 2, p. 788
210 Appendix:
ENGINEER'S POCKET-BOOKS
A Select Bibliography
A Compendium of Mechanics, Robert Brunton, Glasgow, first edition 1824, 2nd. edition 1825, 5th. edition 1831, 7th edition
The Mechanic's Calculator, William Grier, Glasgow, 1st. edition 1832, 2nd edition 1835 ... 7th. edition 1839.
The Mechanic's Pocket Dictionary, William Grier, Glasgow, 1st. and 2nd. editions 1837.
Adcock's Engineerb Pocket Book, for the year 1838, Henry Adcock, London, 1st. edition 1838.
The Engineer's Architect's, and Contractor's Pocket-Book for the Years 1847 and 1848, London, John Weale, 1847, 3 vols. in wallet with clasp includes monthly almanac, rules cash book, and memoranda. Other editions 1863 and 1865.
The Engineer's Hand-Book, C.S. Lowndes, London, Longmans, 1st. editions 18 , 2nd. edition 1863.
Engineer's Manufacturer's and Miner's Vademecum, in five languages, K.P. Reehorst, London, 1863.
Useful Rules and Tables, relating to Mensuration, Engineering, Structures, and Machines, W.J.M. Rankine, London, 1866, 2nd. edition 1867 ... 7th. edition, 1899.
Pocket-book of useful formulae & memoranda for civil and mechanical engineers, Sir G.L. Molesworth, London, , ...17th. edition 1871,... 22nd. edition 1888.
A hand-book of formulae, tables, and memoranda for architectural surveyors and others engaged in building, John Thomas Hurst, London , 5th. edition 1871.
211 Chapter 7
CONCLUDING REMARKS CONCLUDING REMARKS
The foregoing chapters reveal the nature and scale of the stimulus which led to unavoidable developments in the analysis, design and construction of British Bridges between 1800 and 1870. Before this
the greatest period of structural innovation was that of twelfth-
century France during which the distinctive load-bearing and spatial- enclosing aspects of Gothic structure replaced earlier systems. But no
comparable development in bridge construction occurred until after 1800.
At the beginning of the nineteenth century horse-drawn road traffic only demanded structures of modest span where live load was insignificant compared with dead load. Where long bridges were required designers merely resorted to multiple-span systems within the modest limits of the traditional structural materials of timber, stone, and brick.
Although cast iron had been introduced, and used spasmodically, during the last decades of the eighteenth century the era of the wide-span, heavily-loaded, metal bridge was yet to come. Moreover, structural design was only at an embryonic stage of organisation. Civil engineering and the construction industry had evolved with the development of inland navigation and roads where traditional techniques of design and site organisation based on accumulated experience were adequate. As we have seen, this changed dramatically after about 1830 when the unprecedented demands of the railways required drastic changes not only in methods of structural analysis and design, but also in professional organisation, education, and recruitment of engineers to match the scale of bridge- building activity. British engineers were suddenly confronted with the urgent need for a large number of bridges to carry enormous loads over large spans for which there were no precedents. Moreover, they were ill-equipped to cope with the ensuing analytical problems. In addition,
212 Larcm494 c•uth and in response to this challenge, ~IA iron largely replaced Irlm'im■44
iron, between 1840 and 1850, as the principal spanning material for
railway bridges, and to exploit its distinctive properties innovations
in structural form were necessary. This thesis shows how the
combination of unprecedented load,a new structural material, and novel
form, together with a limited grasp, indeed a mistrust, of mathematical
structural mechanics explains the extent to which British engineer's
enlisted the help of structural models. The frenzied decades from 1835
to 1855 were a period of disturbed equilibrium in structural design
circles where the most significant contributory factor was the change in
the magnitude of live loads following the development of the steam
locomotive. The growth of tractive power also explains the pre-occupation
with model bridge experiments in nineteenth-century Britain; no other
aspect of structural engineering provided such a challenge. The only
comparable metal spans were to be found in the roofs enclosing the train
sheds at main-line termini, but these had merely to carry their own weight.
It is relatively easy to identify and describe those bridges
which are significant in the evolution of innovation in structural form
and materials to meet new demands. It is equally easy to chart the
major publication dates of papers from the theoretical elasticians,
notably on the Continent, but to argue that there was a rapid transition
into the design offices of British engineers would be naive. Apart from
the structures themselves (where they survive), and engineering drawings,
nineteenth-century engineers have left us less in the way of evidence
indicating their analytical and design philosophy. We know that
structural materials experiments by Barlow, Tredgold, and others had wide
currency and provided data on ultimate stresses which were used in
arriving at a safe structure. Further research needs to be done in this area which will undoubtedly provide additional insights into design 213 methods. The sources studied for this thesis reveal much about the attitudes of nineteenth-century engineers to the problems confronting them, and the research indicates that the use of structural models should be seen as important not only in bridge design problems but also as an aspect of the developing civil engineering profession. The need for engineers to develop a surer grasp of structural analysis and design was inescapable, and in Britain model experiments played a distinctive role in this respect. Although there was some scepticism about the value of model experiments on the small scale generally adopted (the Britannia
Bridge experiments were a notable exception), there was also an overriding feeling that anything which might shed light on the pressing
problems would be worth trying. There was in addition, as there is today, an instinctive feeling that a model would demonstrate the response to load of a structure with a degree of reality not to be found in mathematical abstractions. Reasons for the decline in British structural model testing in the last three decades of the century have been discussed, and further research might well reveal significantly different patterns of activity in other parts of Europe and America.
In Britain, the renaissance of structural model experiments in the early part of this century was made possible by the ability to measure model strains with a high degree of accuracy by electrical means.
This development freed the experimenter from the nineteenth-century
pre-occupation with ultimate load considerations. It also coincided with the increased exploitation of reinforced concrete; a complex composite material presenting analytical and design problems. Reinforced concrete provided a stimulus for the use of models in this century very similar to the role played by the introduction of wrought iron in the middle of last century. This thesis deals with what might be called the pre-history of structural model experimentation as we know it today. 214 Nevertheless, without such a discussion of the objectives and scope of model testing, our understanding of the development of structural analysis and design techniques in nineteenth-century Britain would be incomplete in this important respect.
215