- 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.