The D. Van NoSlrand Company 
 
 intend this book to be sold to the Public 
 at the advertised price, and supply it to 
 the Trade on terms which will not allow 
 of reduction. 
 
THE PROPERTIES AND DESIGN 
 
 OF 
 
 REINFORCED CONCRETE 
 
'aw- 
 
 THE PROPERTIES AND DESIGN 
 
 OF 
 
 REINFORCED CONCRETE 
 
 INSTRUCTIONS, AUTHORISED METHODS OF 
 CALCULATION, EXPERIMENTAL RESULTS 
 AND REPORTS BY THE FRENCH GOVERN- 
 MENT COMMISSIONS ON REINFORCED 
 CONCRETE 
 
 TRANSLATED AND ABRIDGED 
 
 BY 
 
 NATHANIEL MARTIN 
 
 Civil 'Engineer, 
 
 A.G.T.C., B.Sc., A.M.Inst.C.E. ; 
 Lecturer on Reinforced Concrete, Royal Technical 
 College, Glasgow 
 
 NEW YORK 
 
 D. VAN NOSTRAND COMPANY 
 
 TWENTY-FIVE PARK PLACE 
 
 1912 
 
AUTHOR'S PEEFACE 
 
 IN setting out to study the properties and the applications of such a com- 
 paratively new material as Reinforced Concrete, one is led to consider the possible 
 sources of information and their nature. The fact should be kept in mind that, 
 from certain points of view, the study of much successful practice is frequently not 
 so fruitful as the study of some examples where failure took place or of full-sized 
 structures tested to destruction. 
 
 A considerable amount of experimental work has been done and a vast number 
 of reinforced concrete structures successfully carried out in America, of which the 
 records are in English. In Germany, Italy, and Austria a considerable amount of 
 both experimental and practical work has been done. In Great Britain the volume 
 of reinforced concrete construction is steadily growing, but very little experimental 
 research on the properties of the material has been made in this country. It is 
 undoubtedly to France and to French literature that a student must turn for the 
 most concise and authoritative information on the subject. 
 
 Reinforced Concrete had its origin in France. French constructors were 
 accumulating experience of its properties, and research was being carried on by 
 French engineers very many years before the material came to be regarded as a 
 practical proposition in other countries. Consequently, the Commission appointed 
 in December, 1900, by the French Minister of Public Works embraced a group of 
 engineers whose experience in this material was unrivalled. The work of this 
 Commission, extending over the succeeding six years, included a series of experiments, 
 simple in detail and comprehensive in range, and directed not to the solution of 
 academical minutiae, but to the obtaining of results immediately applicable to practice. 
 The report of the Commission contains the results of the tests on experimental 
 structures and of the tests to destruction of several of the structures of the Paris 
 Exhibition of 1 900. It is unique in the literature of Reinforced Concrete, containing 
 as it does all the necessary scientific data, based on first-hand observations, for the 
 design of reinforced concrete structures, with the observations thereon of a group 
 of engineers of the widest and most mature experience obtainable. The instructions 
 are characteristically French in their clearness and boldness a boldness derived 
 from intimate knowledge, and entirely justified by results. 
 
 The report has been much quoted and extracts have appeared from time to 
 time in various English books and periodicals, but a complete survey of the work 
 of the Commission was to be obtained only from the French edition. The translator 
 has thought that a useful purpose might be served by an abridged English edition 
 which would enable professional men with limited time to acquaint themselves with 
 the scope of the work of the Commission and to have the results at hand in readily 
 accessible form. It will also guide the research student to the detailed records 
 of methods and results to be found in the French edition, and at the same time form 
 one of the easiest avenues of approach for those who wish to make a systematic 
 study of the properties and applications of Reinforced Concrete. 
 
 NATHANIEL MARTIN. 
 
 GLASGOW, 
 
 December, 1911. 
 
PKEFACE 
 
 THE rapidity of the development of reinforced concrete structures, the 
 principle of which was indicated by Monier in 1877, is well known. Thanks to 
 the initiative of some bold and skilful constructors, a considerable number of 
 applications of Reinforced Concrete had already been made when on December 19, 
 1900, the French Minister of Public Works instituted a Commission to study the 
 question from the point of view of his Administration. 
 
 Notwithstanding the already numerous experiments, the properties of the 
 new material were still imperfectly known, and the methods of calculation 
 followed by different constructors presented essential differences and even absolute 
 contradictions. 
 
 The elementary properties of Reinforced Concrete were incompletely investi- 
 gated, and it was unknown in what measure these properties permitted application 
 to the new material of the principles and the results which had been laboriously 
 acquired for metallic structures, and which constituted the classic science of the 
 Resistance of Materials. 
 
 The Commission decided that they ought first to study the elementary 
 properties of Reinforced Concrete, reserving for later research, in the light 
 of these properties, the interpretation of the complex phenomena arising in 
 structures. 
 
 The following are some of the facts established and results obtained by the 
 Commission : 
 
 Experiments of several months' duration have shown the importance of the 
 contraction, denied by certain constructors, which occurs in concrete, not only at 
 the end of the period of setting but also during a long period of hardening, and 
 which influences the distribution of the stresses between the concrete and the 
 metal. The constructor ought to make the necessary arrangements to avoid the 
 undesirable consequences this contraction may produce. 
 
 The study of elasticity is the basis of that of stress. The Commission made 
 an important contribution to the former, and verified for the first time the exacti- 
 tude of the law announced by one of its members concerning concrete under 
 tension. The modulus of elasticity of concrete under tension varies according to 
 a straight line law up to a certain limit, and afterwards becomes almost rigorously 
 constant till rupture. The stronger the reinforcement with bars well distributed 
 in the tension areas, the longer is rupture postponed. 
 
 The laws of elasticity of concrete in compression had already been the object 
 of numerous experiments. The Commission made additional experiments without 
 revealing any new facts. 
 
 Attention has been drawn to the fact that in compression members, the longi- 
 tudinal bars necessarily produce resistances proportional to the shortenings which 
 the concrete with which they are associated supports without crushing. Thus 
 arises the idea of the importance of the ductility of the concrete. 
 
viii PREFACE. 
 
 By varied experiments, which have confirmed the results announced by one of 
 its members, the Commission has definitely proved that for equal weights trans- 
 verse reinforcements and especially spirals increase the resistance to compression of 
 the concrete much more than longitudinal bars of the same weight. In preparing 
 the regulations for the employment of transverse reinforcements the French 
 Minister of Public Works may, at first sight, have appeared rather daring, but the 
 expediency of his initiative is now demonstrated by the almost identical regulations 
 on this matter which have been issued in Germany, and particularly in Austria, 
 after the repetition of the experiments inaugurated in France. 
 
 The tests by the Commission have given useful but too scanty information on 
 the resistance of Reinforced Concrete to shear and to torsion. 
 
 The study of flexion is of prime importance. The Commission has given to it 
 a rational basis by proving by numerous experiments that the conservation of 
 plane sections, which is the foundation of the classic theory of bending, is realised 
 almost as exactly in Reinforced Concrete as in metallic members, 
 
 The application to Reinforced Concrete of the exact ideas of the science of 
 flexure, and particularly of those of the neutral axis and of the moment of inertia, 
 has thus been sanctioned. Together with the laws of elasticity, they permit of the 
 determination of the stresses which are developed in statically indeterminate 
 structures. These stresses depend not only on the laws of statics, as in members 
 statically determinate, but also on the deformations. 
 
 Light has been thrown by some interesting experiments on the question of the 
 extent to which, from the point of view of resistance to compression, slabs assist 
 the ribs with which they are continuous and form part. 
 
 Structures in Reinforced Concrete slab, floor, footbridge and retaining wall 
 which were erected for the Exhibition of 1900, were tested to destruction. Made 
 with care and method these tests have given useful information. 
 
 Finally, the theoretical studies of the Commission following on its experiments 
 cleared up several questions until then obscure, and have thus given a new 
 impulse to the researches of engineers. 
 
 A. CONSIDERE. 
 
 PARIS, 
 June 11, 1912. 
 
CONTENTS 
 
 INTRODUCTION 
 
 CHAPTER I 
 
 INSTRUCTIONS RELATIVE TO THE USE OF REINFORCED CONCRETE 
 
 PAGE 
 
 Imposed Loads . . . ... 1 
 
 Limits of Stress 1 
 
 Calculations of Resistance . . 2 
 
 Execution of Works 2 
 
 Tests of Works 3 
 
 CHAPTER II 
 
 A CIRCULAR ISSUED BY THE FRENCH MINISTRY OF PUBLIC WORKS IN EXPLANATION 
 
 OF THE INSTRUCTIONS 
 
 List of Symbols used in Chapters II and III 5 
 
 On Imposed Loads and Working Stresses 6 
 
 On Calculations of Resistance 8 
 
 On Simple Compression 9 
 
 On Compression with Bending 9 
 
 On Simple Bending ............. 13 
 
 On Bending with Thrust 14 
 
 On the Design of Slabs . . . . . . . . . . .15 
 
 On Slipping of Reinforcements . . . . 16 
 
 On Shear Resistance ............. 16 
 
 On the Strength of Long Columns 17 
 
 CHAPTER III 
 
 REPORT ON THE DRAFT REGULATIONS BY THE COMMISSION NOMINATED BY THE 
 GENERAL COUNCIL OF BRIDGES AND ROADS 
 
 A Discussion as to the Advisability of Sanctioning the High Working Stresses 
 
 proposed, with Observations on the Values of " ra " and " m'" . . . 19 
 
 CHAPTER IV 
 THE EXPERIMENTAL WORK OF THE COMMISSION 
 
 1. Measurement of Contraction during Setting of Concrete ..... 22 
 
 2. Measurement of Elasticity of Concrete without Reinforcement . . . .22 
 
 3. Determination of Resistance to Crushing of Concrete prepared in different 
 
 Degrees of Plasticity 22 
 
 4. Influence of Percentage of Reinforcement on Stresses developed during Setting 23 
 
 5. Tension Tests 23 
 
x CONTENTS 
 
 CHAPTEE IV. continued PAGE 
 
 6. Shearing Tests . , . , . .' ~'. . . . . . 25 
 
 7. Torsion Tests . .27 
 
 8. Measurement of Eesistance to Slipping of Reinforcements . . . . .27 
 
 9. Bending of Beams .... . .30 
 
 10. Bending of Flat Slabs < . . . . . .42 
 
 11. Bending of Eibbed Slabs . . . . . ... . .46 
 
 12. Compression Tests of Columns and Prisms . . . . . . . 48 
 
 13. Compression Tests of Spiralled Mortar and Concrete . . . . . .59 
 
 14. Tension Tests on Eeinforced Concrete Members 66 
 
 CHAPTEE V 
 
 THE REPORT AND DRAFT REGULATIONS PRESENTED BY THE COMMISSION, BEING A 
 REVIEW OF THE PRINCIPAL RESULTS OF THE EXPERIMENTAL WORK OF THE 
 COMMISSION 
 
 Variations in Volume resulting from the Setting of the Cement . . .68 
 
 Thermal Variations in Volume 68 
 
 Resistance and Deformation of Concrete submitted to Tension ..... 69 
 
 Resistance to Crushing 69 
 
 Pitch of Spirals 76 
 
 Elasticity of Concrete Reinforced and without Reinforcement . . .77 
 
 Deformation of Plane Sections in Bending 78 
 
 Application of the Laws of Simple Deformations to Bent Pieces . . . .79 
 
 Adhesion of the Concrete to the Metal 79 
 
 Resistance to Shear 80 
 
 Note on the Results of the Tests on the Works constructed for the Exhibition of 1900 80 
 
 CHAPTER VI 
 
 SOME CONCLUSIONS OF THE COMMISSION FROM THE STUDY OF THE ELEMENTARY 
 PROPERTIES OF THE MATERIALS CONSTITUTING REINFORCED CONCRETE 
 
 Calculations of Stresses and Deformations 81 
 
 Coefficients of Security 81 
 
 Simplification of the Calculations 81 
 
 Members Compressed and Bent 85 
 
 Adhesion of the Metal to the Concrete 87 
 
 Transverse Reinforcement of Members subject to Bending 88 
 
 Empirical Formulae 89 
 
 Tests 90 
 
 CHAPTER VII 
 
 NOTES PRESENTED BY M. CONSIDERE 
 
 A. Tension Tests on Reinforced Concrete : 
 
 Initial State 93 
 
 Elongation without Cracking of the Concrete 93 
 
 Law of Deformation of Reinforced Concrete 93 
 
 Curves of Loading and Unloading v ... 94 
 
 Effects of Tension on the Resistance and Elasticity of Concrete to Compression 94 
 
 Effects of Repetition of Stress 94 
 
 The Final State after Unloading 95 
 
CONTENTS xi 
 
 CHAPTER VII. continued PAGE 
 
 B. Bending Experiments on Large Reinforced Concrete Beams : 
 
 Initial State 96 
 
 Deformation of Plane Sections during Bending ...... 96 
 
 Position of the Neutrql Axis 96 
 
 Law of Deformations of Reinforced Concrete 98 
 
 Adhesion and Slipping of the Reinforcements 99 
 
 Influence of Fissures on the Resistance of Compression Areas . . .100 
 
 C. Effects of Transverse Reinforcements : 
 
 Bending Experiments 101 
 
 Tension Experiments 102 
 
 D. Resistance of Reinforcements to Shear ........ 102 
 
 E. Experiments on Ribbed Slabs 103 
 
 Participation of Slabs in the Resistance of the Ribs 104 
 
 F. Variations in Length of Bars of Metal buried in Concrete during Setting . . 105 
 
 G. The Influence of the Proportion of Gauging Water on the Strength and 
 
 Elasticity of Concrete . . . . . . . . . . .106 
 
 H. The Effects of Direct and Repeated Shocks on the Adhesion and Resistance of 
 
 Concrete . . 107 
 
 APPENDIX 
 
 PART I 
 
 Vertically Imposed Loads and Wind Loads on Metallic Bridges as denned in the 
 
 Regulations of August 29, 1891 109 
 
 PART II 
 Tests of Metallic Bridges as required by the Regulations of August 29, 1891 . .111 
 
 PART in 
 
 Imposed Loads and Tests stipulated in the Regulations of February 17, 1903, for 
 
 Metallic Station Buildings 112 
 
 BIBLIOGRAPHY .... . .... 113 
 
 INDEX 117 
 
INTRODUCTION 
 
 THE Commission on Reinforced Concrete was instituted by a Ministerial order 
 dated December 19, 1900, and was charged "to study the questions relative to 
 the employment of Reinforced Concrete and to proceed to the necessary researches 
 to determine as far as possible the Regulations which might be framed for the 
 employment in Public Works of this mode of Construction." 
 
 The following gentlemen constituted the Commission : Monsieur Lorieux, 
 President ; Monsieur Considere, Reporter ; MM. Bechmann, Harel de la Noe, Rabut, 
 Resal, Mesnager, Hartmann, Boitel, Hermant, Gautier, Coignet, Hennebique, 
 Candlot. 
 
 At its first meeting on February 16, 1901, the Commission appointed three 
 Sub-Commissions to undertake preparatory work. 
 
 The first Sub-Commission, presided over by M. Rabut, undertook the testing to 
 destruction of certain of the reinforced concrete structures of the Paris Exhibition 
 of 1900. 
 
 The second Sub-Commission, presided 'over by M. Considere, was appointed to 
 study the following questions : 
 
 1. Safe limits for tensile and compressive stresses in the concrete. 
 
 2. Information to be produced in draft schemes to demonstrate that the different 
 parts of the works are within these limits of security. 
 
 3. Time which must elapse between completion of work and application of 
 tests, conditions and duration of tests and the nature of results to be obtained. 
 
 This Commission resorted to experimental methods in order to give its proposi- 
 tions an unassailable foundation. It established the programme of the numerous 
 tests carried out under the direction of M. Mesnager at the Laboratory of the 
 School of Bridges and Roads. 
 
 The third Sub-Commission, presided over by M. Bechmann, studied questions 
 relative to 
 
 1. The production and qualities of the cement, sand and gravel, the preliminary 
 tests intended to indicate the quality of the cement, the proportions of the materials, 
 the quantity of water employed, the methods of mixing, etc. 
 
 2. The qualities of the reinforcement. 
 
 3. The practical limits of percentage. 
 
 The three Sub-Commissions had finished their labours by the commencement of 
 1905. On April 17, 1905, the Commission nominated M. Considere reporter, 
 and undertook the discussion of the results obtained by the Sub-Commissions. 
 Finally, on January 19, 1906, the Commission presented the following proposi- 
 tions to the Minister of Public Works : 
 
 1. Draft circular to accompany the regulations for structures in Reinforced 
 Concrete. 
 
 2. Draft Regulations for structures in Reinforced Concrete. 
 
 3. Report in support of these Regulations, followed by complementary notes by 
 M. Considere. 
 
xiv INTRODUCTION 
 
 The Minister of Public Works further submitted the work of the Commission 
 to the General Council of Bridges and Roads, on behalf of which it was examined 
 by a Commission composed of M. Maurice Levy, President, and MM. de Preaudeau 
 and Vetillart. 
 
 This Commission presented to the General Council a new draft, which, after 
 some amendments arising out of the discussion, was approved by the Council, and 
 accepted by the Minister of Public Works. 
 
 The arrangement of sections adopted in the French edition 1 has not been 
 adhered to, and the regulations, or "Instructions" as they are called, are given 
 only in their final form in the English edition. 
 
 1 " Experiences, Kapports et Propositions Instructions Ministerielles relatives a 1'emploi du 
 Be"ton Arme," published by H. Dunod et E. Pinat, Quai des Grands Augustins 49, Paris (6 e ). 
 
REINFORCED CONCRETE 
 
 CHAPTER I 
 
 INSTRUCTIONS RELATIVE TO THE USE OF REINFORCED CONCRETE 
 
 PART I 
 DATA FOR DESIGN 
 
 A. Imposed Loads. 
 
 Article 1. Bridges in reinforced concrete shall be designed to support the 
 vertical externally applied loads and the wind loads stipulated by the regulations 
 of August 29, 1891. * 
 
 Article. 2. Superstructures in reinforced concrete shall, unless exception can be 
 justified, be submitted to the imposed loads stipulated in the regulations of 
 February 17, 1903. 1 
 
 Article 3. The floors and other parts of buildings, retaining walls, conduits 
 under pressure and all other works in which the public safety is involved shall be 
 designed in view of the greatest imposed loads to which they will be exposed in 
 service. 
 
 B. Limits of Stress. 
 
 Article 4. The compressive stress allowed in the calculations for reinforced 
 concrete ought not to exceed 0'28 of the crushing resistance acquired by non- 
 reinforced concrete of the same composition after ninety days' setting. The estimated 
 value of this resistance, as measured on cubes of 7*88 inch side, shall be stated in 
 the calculations for each project. 
 
 Article 5. When the concrete is spiralled, or when transverse or oblique 
 reinforcements are introduced and so arranged as to resist more or less efficiently 
 the transverse swelling of the concrete under the influence of compression, the 
 limit of the compressive stress set forth in the preceding article will be increased in 
 a greater or less degree depending on the volume and the efficiency of the trans- 
 verse reinforcements, provided that the new limit, whatever the percentage of metal 
 employed, shall not exceed 0*60 of the resistance to crushing of the non-reinforced 
 concrete as it is defined in Article 4. 
 
 Article 6. The limit of stress in shear, in the longitudinal slipping of the 
 concrete on itself and in the adhesion of the metal of the reinforcements to the 
 concrete will be O'lO of the limit of compressive stress defined in Article 4. 
 
 1 See Appendix, p. 109. 
 R.C. B 
 
. . 
 
 n^IJi REINFORCED CONCRETE 
 
 Article 7. The limit of the compressive and tensile stresses in the metal of the 
 reinforcements shall be 0'50 of the apparent limit of elasticity, as denned in the 
 calculations for each project. 
 
 For members exposed to shocks or submitted to stresses alternating in sense, 
 such as in some floors, this limit will be reduced to 0'40 of the said apparent limit 
 of elasticity. 
 
 Article 8. In members submitted to very variable stresses, the limits of stress 
 defined above shall be reduced to an extent depending on the variation of 
 stress. This diminution need not exceed in any case 25 per cent, of the values 
 above stated. 
 
 The limits of stress shall also be reduced for members exposed to causes of 
 fatigue or enfeeblement, of which the calculations of resistance do not take account, 
 e.g., members such as rail bearers exposed to violent dynamic action. 
 
 PART II 
 CALCULATIONS OF RESISTANCE 
 
 Article 9. In the calculations of the resistance of works in reinforced concrete 
 there shall not only be taken into account the greatest external forces, including the 
 action of the wind and snow, that the works will have to resist, but also the thermal 
 effects and the effects of the contraction of the concrete in those cases where the 
 concrete is prevented from contracting or expanding freely in the theoretical sense 
 of the word, or where experience does not show that they may be regarded as 
 approximately such. 
 
 Article 1 0. The calculations of resistance shall be made according to scientific 
 methods resting on experimental data, and not by empirical processes. They shall 
 be deduced either from the principles of resistance of materials or from principles 
 offering at least the same guarantees of exactitude. 
 
 Article 1 1. The resistance of the concrete to tension will be taken into account 
 in the calculation of the deformations. To determine the stress, however, in any 
 section this resistance shall be regarded as zero in that section. 
 
 Article 1 2. It must be ensured that compression members are not exposed to 
 buckling. That precaution may be dispensed with when the ratio of the height to 
 the least transverse dimension is less than 20, and where the stress does not exceed 
 the limit specified in Article 4. 
 
 Article 13. The description must indicate the qualities and the proportions of 
 the materials entering into the composition of the concrete. The proportion of 
 water employed in gauging ought to be supervised with care, and should be only 
 sufficient to give the concrete the necessary plasticity for the proper covering of 
 the reinforcements, and the filling of all the voids. 
 
 PART III 
 
 EXECUTION OF WORKS 
 
 Article 14. The framing and the setting of the reinforcements must present 
 sufficient rigidity to resist without sensible deformation the loads and the, shocks to 
 which they will be exposed during the execution of the work up till the removal of 
 the framing. 
 
 Article 15. Unless in exceptional cases where the mixture would be poured 
 
INSTRUCTIONS RELATIVE TO USE OF REINFORCED CONCRETE 3 
 
 slow-setting cement shall be used. The concrete shall be rammed with the greatest 
 care in beds of which the thickness will be in proportion to the dimensions of the 
 aggregate used and the spacing of the reinforcements, and shall not exceed 
 2 inches after ramming, unless stones are used as aggregate. 
 
 Article 16. The distances between the reinforcements themselves- and to the 
 faces of the frames shall be such that they permit the perfect ramming of the 
 concrete and the complete surrounding of the reinforcements by the latter. The 
 distance between the reinforcements and the framing, even when mortar without 
 gravel or pebbles is used, ought always to be at least from 0*6 inch to 0*8 inch 
 in order to protect the reinforcement from the weather. 
 
 Article 17. When specially shaped sections are employed for reinforcements 
 instead of round bars, special precautions shall be taken to ensure the complete 
 covering of the reinforcements on all their perimeter, and particularly on any 
 re-entrant angles. 
 
 Article 18. When the concreting of a reinforced concrete member has been 
 interrupted, which should be avoided as much as possible, the old concrete shall be 
 cleaned to the solid and thoroughly moistened in order that it may be completely 
 saturated before fresh concrete is put in contact with it. 
 
 Article 19. In time of frost work shall be suspended if efficient arrangements 
 cannot be made to obviate harmful effects. On restarting the work all parts of 
 the concrete injured by the frost shall be removed, and the procedure will then be 
 as described in the preceding article. 
 
 Article 20. For fifteen days at least, after its execution there shall be main- 
 tained in the concrete sufficient humidity to ensure setting under good conditions. 
 
 The removal of the framing shall be done without shock by purely static 
 forces and only after the concrete has acquired the necessary resistance to support, 
 without damage, the forces to which it will be exposed. 
 
 PART IV 
 
 TESTS OF WORKS 
 
 Article 21. Works in reinforced concrete which concern the public safety will 
 be tested after completion. The conditions of the tests as well as the interval 
 which must elapse before the works are put into service shall be inserted in the 
 general conditions of the contract. The maximum deflections in the various parts 
 of the works which ought not to be exceeded shall also as far as possible be stated 
 in the general conditions. 
 
 The age that the concrete ought to have at the moment of the tests will also 
 be fixed by the general conditions. It will be at least ninety days for large 
 works, forty-five days for works of average importance and thirty days for floors. 
 
 Article 22. The engineers shall record at the time of the tests not only 
 the measurements of deformation and such other measurements as are necessary 
 for the verification of the general conditions of the contract, but also as far 
 as possible any other measurements which might be of service to engineering 
 science. 
 
 For works of importance registering apparatuses shall be employed. 
 
 Article 23. Bridges in reinforced concrete shall be tested in the manner 
 prescribed for metallic bridges by the regulation of August 29, 189 1. 1 
 
 1 See Appendix, p. 111. 
 
 B 2 
 
4 REINFORCED CONCRETE 
 
 If it appears desirable to obtain any amendments to the prescription of 
 this regulation, these amendments ought to be justified and inserted in the general 
 conditions. 
 
 Article 24. Superstructures shall be tested in the manner prescribed by 
 the regulation of February 17, 1903, unless amendments are justified. 
 
 Article 25. Floors shall be submitted to a test consisting of the application 
 of the loads and the superloads intended, either to the whole of the floor or 
 at least to an entire span. 
 
 The test loads ought to remain in place for at least twenty-four hours, and 
 the deflections ought not to increase at the end of fifteen hours. 
 
LIST OF SYMBOLS 
 
 CHAPTER II 
 
 A CIRCULAR ISSUED BY THE FRENCH MINISTRY OF PUBLIC WORKS IN EXPLANATION 
 OP THE INSTRUCTIONS, GIVING DETAILED METHODS OF CALCULATING RESISTANCES 
 AND CHECKING DESIGNS (ABRIDGED) 
 
 LIST OF THE SYMBOLS USED IN CHAPTERS II AND III 
 
 V 
 V 
 
 m' 
 
 A 
 
 A c 
 A, 
 
 N 
 
 G 
 
 C 
 
 Y = G 
 T, = G, 
 Y e = G 
 
 /,,/c 
 
 the volume of the concrete in unit length of prism. 
 
 the volume of the transverse or oblique reinforcements in unit 
 
 length of prism, 
 coefficient varying with the spacing of the transverse or oblique 
 
 reinforcements and the efficiency of the transverse connection 
 
 established between the longitudinal bars, 
 the modulus of elasticity of steel. (Young's modulus.) 
 the modulus of elasticity of concrete in compression. 
 
 E 
 
 the ratio -^T. 
 
 &c 
 
 the equivalent homogeneous section replacing the heterogeneous 
 
 section composed of concrete and steel, 
 the sectional area of the concrete, 
 the sectional area of the longitudinal reinforcements. As A is 
 
 generally small in comparison with A c , A c + A 8 , the total area, is 
 
 frequently taken instead of A c . 
 the total compression normal to the section applied at the centre of 
 
 gravity and consequently uniformly distributed, or the value of 
 
 the compression applied halfway between the extremities of a 
 
 section if it varies across the section, 
 the unital stress in the concrete. 
 
 the unital stress in the reinforcement on the compression side, 
 the unital stress in the reinforcement on the tension side, 
 the centre of gravity of the equivalent homogeneous section, the 
 
 position of which is to be found. 
 
 the known centre of gravity of the longitudinal reinforcements, 
 the known centre of gravity of the concrete section, 
 the centre of pressure of the resultant force on the cross section, 
 the ordinate of G from an axis xx' chosen at will. (See Fig. 1.) 
 the ordinate of G a from the axis xx'. (See Fig. 1.) 
 the ordinate of G c from the axis xx '. (See Fig. 1.) 
 the second moments of area (the moments of inertia) of the 
 
 geometrical sections of the steel and concrete respectively in the 
 
 cross section of the member, about the axis XGX ' . 
 the second moment of area of the equivalent homogeneous section 
 
 about XGX'. 
 the shear on any section, i.e., the component, tangential to the 
 
 section, of all the exterior forces, including the support reactions 
 
 which lie on one side of the section. 
 
EEINFORCED CONCRETE 
 LIST OF THE SYMBOLS USED IN CHAPTERS II AND III continued. 
 
 M 
 
 P 
 
 s 
 
 h 
 
 b 
 
 b' 
 
 t 
 
 w 
 
 d 
 
 w' 
 
 d' 
 
 L 
 p 
 
 i 
 k 
 
 K 
 
 the bending moment applied to the cross section, i.e., the sum of 
 the moments of the exterior forces relatively to G, the centre of 
 gravity of the equivalent section. 
 
 lie unital stress on the concrete distant x from the axis XGX '. 
 
 the unital stress on the steel distant x from the axis XGX '. 
 
 the co-ordinate of the centre of pressure (or point of application of 
 relative to the axis XX'. 
 
 the distance from the extreme edge of the concrete and from the 
 reinforcement respectively to the axis XGX', reckoned negative 
 when measured to the side of XX' on which the bending moment 
 produces tension. 
 
 the co-ordinate of the neutral axis relatively to the axis XX' . 
 
 the radius of gyration of the equivalent section relatively to XX' . 
 
 the minimum radius of gyration. In a symmetrical section either 
 about the axis of symmetry or an axis normal to the latter. 
 
 the imposed load per unit length of span. 
 
 the effective span (centre to centre of bearings). 
 
 the overall depth of slab and rib. 
 
 the width of the slab. 
 
 the width of the rib. 
 
 the thickness of the slab. 
 
 gross section of the compression reinforcement. 
 
 its mean distance to the compression face. 
 
 net section of the tension reinforcement. 
 
 its mean distance to the tension face. 
 
 the distance of the neutral axis from the compressed face. 
 
 the distance of the neutral axis from the centre of pressure C. 
 
 the distance of the point of application of the resultant of the 
 exterior forces from the compressed face. 
 
 the spacing centre to centre of the ribs. 
 
 the perimeter of the longitudinal reinforcements. 
 
 the length of a column. 
 
 a numerical coefficient depending on the end conditions of a column. 
 
 the "angular coefficient" of the line A'B' in Fig. 3, numerically 
 M R 
 
 equal to 
 
 or 
 
 NOTE. The quantities must be expressed in the same units throughout. The most generally 
 convenient units are the inch and the lb., with their derivatives, the inch-lb. and the Ib. per 
 square inch. These units are applicable without conversion to the formulae throughout the 
 volume. 
 
 Imposed Loads and Working Stresses. 
 
 Article 3. At first sight this article seems simply to be the statement of 
 the very evident necessity of designing a reinforced concrete structure so that 
 the elastic resistances called into play in the various members by the action 
 of the external forces only attain a determined fraction of those which would 
 endanger the stability or the life of the structure. This pre-determined fraction is 
 called the coefficient of security or factor of safety. 
 
 The article is really directed, however, against a method in use by certain 
 specialists. This consists, not in determining the elastic resistances called into 
 
WORKING STRESSES 
 
 play to balance the actual loads, but in attempting to determine the proportion 
 in which it would be necessary to imagine the external loads multiplied in order 
 to produce rupture. This coefficient of amplification is called by them the 
 factor of safety. 
 
 This procedure will be disallowed in preparing designs, as it is held not 
 necessarily to offer a sufficient guarantee of security. No work has ever 
 perished by the proportional amplification of the loads, but always by accidental 
 cause or by some internal flaw the development of which proved fatal. 
 
 Article 4. The following table provides a comparison of working stresses in 
 compression allowed by foreign regulations with those permitted by the French 
 instructions : 
 
 TABLE No. 1. 
 
 Composition of Concrete. 
 
 (For conversion 1 cubic foot of loose cement was taken 
 as weighing 85 Ibs.) 
 
 Average crushing resistance 
 in Ibs. per square inch esti- 
 mated by the Commission. 
 
 Working 
 stresses 
 allowed by 
 Foreign 
 Regulations, 
 25 per cent, 
 of (a), Ibs. per 
 square inch. 
 
 Working 
 stresses 
 allowed by 
 French 
 Instructions, 
 28 per cent, 
 of (&), Ibs. per 
 square inch. 
 
 (a) 
 After -28 days. 
 
 (&) 
 
 After 90 days. 
 
 6 cwts. cement, 28 - 7 cubic feet of gravel, 
 14-4 cubic feet of sand or 1 of cement, 
 3*5 of gravel, and 1'75 of sand by 
 measure. 
 
 1520 
 
 2275 
 
 380 
 
 637 
 
 7 cwts. cement, 28 '7 cubic feet of gravel, 
 14*4 cubic feet of sand or 1 of cement, 
 3-12 of gravel, and T56 of sand by 
 measure. 
 
 1706 
 
 2560 
 
 426 
 
 717 . 
 
 8 cwts. cement, 28' 7 cubic feet of gravel, 
 14-4 cubic feet of sand or 1 of cement, 
 2'75 of gravel, and 1/37 of sand by 
 measure. 
 
 1890 
 
 2846 
 
 470 
 
 798 
 
 The French instructions thus permit a working compressive stress of very 
 much higher value than that allowed by foreign regulations. It is pointed out 
 that these regulations are of earlier date, and when they are modified the change 
 will, without doubt, be in the direction of the French figures. 
 
 Article, 5. When concrete is prevented from swelling laterally under a 
 longitudinal compression by transverse or oblique reinforcements, or by spiralling, 
 the crushing resistance is augmented. 
 
 Experiments made by the Commission indicate that transverse reinforcements 
 and spirals multiply the crushing resistance by the quantity 
 
 1 + ' y. 
 
 m' varies with the degree of efficiency of the transverse connections established 
 between the longitudinal bars. 
 
 When the transverse reinforcement consists of ligatures forming rectangles on 
 a transverse section of the prism, the coefficient might vary from 8 to 15, the 
 
8 EEINFORCED CONCRETE 
 
 minimum value being applied when the spacing of the transverse reinforcements 
 attains a value equal to the least transverse dimension of the member considered, 
 the maximum value being applied when the spacing of the transverse reinforce- 
 ments is reduced to at least one-third of that dimension. 
 
 When the transverse reinforcement consists of a spiral tie, the coefficient might 
 vary from 15 to 32. The minimum should be applied when the pitch of the 
 spirals is two-fifths of the least transverse dimension of the piece considered, and 
 the maximum when this spacing is reduced to 
 
 one-fifth of that dimension for a compression of 711 Ibs. per square inch, 
 one-eighth of that dimension for a compression of 1,422 Ibs. per square inch. 
 
 Whatever the value of the quantity 1 + TT~ or the percentage of metal, 
 
 the compressive stress must not exceed 60 per cent, of the resistance of non-rein- 
 forced concrete as defined by Article 4. This ensures that the stress does not 
 exceed half the value at which superficial cracking of the concrete commences, 
 which, according to the experiments of the Commission, varies from 25 per cent, to 
 GO per cent., depending on the case, of that which produces crushing of the 
 reinforced concrete. 
 
 Calculations of Resistance. 
 
 Article 10. This article sets aside all purely empirical processes of calcula- 
 tion. The principles of resistance of the materials employed afford here, as in 
 ordinary structures, more sure solutions. 
 
 The experiments described in Chapter IV. show that the principle of Navier 
 relative to the plane deformation of transverse sections is applicable within the 
 limits of the experiments. This, combined with the application of the principle of 
 the proportionality of stresses to the deformation suffices, in the case of compression 
 members. 
 
 Each heterogeneous section may be replaced by an equivalent section having 
 the same mass as the real heterogeneous section by attributing to the parts of the 
 section formed by the concrete a density 1 and to the parts formed by the longi- 
 tudinal reinforcements 1 a density m. 
 
 Hypothetically 
 
 This ratio within the limits of the loads defined by Article 4 is about 10. It 
 grows with the stress in the concrete and might be doubled or tripled at the 
 moment of rupture, if failure took place by the crushing of the concrete. On the 
 other hand, it would diminish if failure took place by excess of load on the 
 reinforcements. 
 
 This fact alone shows how uncertain would be the calculations of resistance 
 based on the imaginary increase up to rupture of the actual loads, a method 
 previously referred to. 
 
 It is preferable to regard the coefficient m as a figure derived from experience 
 and not as representing exactly the ratio of the moduli of elasticity of the metal 
 and of the concrete separately found. In every case the experiments to determine 
 the modulus of elasticity E c were carried out in non-reinforced concrete, and it is 
 
 The transverse reinforcements do not figure here. Their essential rdle has already been 
 considered and allowed for by the increase (Article 5) permitted in the limit of crushing stress 
 of the concrete. It is in the augmentation of the resistance to crushing due to the opposition to 
 lateral swelling in which their efficacy resides. 
 
CALCULATIONS OF RESISTANCE 
 
 doubtful if the value thus found is the true value of the modulus of the concrete in 
 reinforced members owing to the difficulty experienced in ramming the concrete 
 between the reinforcements and the moulds. 
 
 It may be taken that this coefficient might vary from 8 to 15. The minimum 
 value will be applied when the longitudinal bars have a diameter equal to one-tenth of 
 the smallest dimension of the member, the transverse interties being spaced at this 
 latter dimension and the longitudinal bars being slightly shorter than the 
 column. The maximum will be applied when the diameter of the longitudinal 
 bars is one-twentieth of the smallest dimension of the member and the transverse 
 interties spaced at one-third of this same dimension. 
 
 The greater number of authors allow for "m" a fixed value, which is often 
 taken equal to 15. There is thus attributed in many cases, without doubt, to the 
 metal a greater part of the resistance than it actually takes, and to the concrete a 
 less. Trouble might thus arise owing to the fact that the stress in the concrete is 
 greater than the calculation assumes, and consequently the coefficient of security is 
 lower than was intended. By varying " m " as above described, a more accurate 
 determination of the stresses is made, which is necessary in view of the high values 
 allowed in Article 4. 
 
 Once the coefficient m has been chosen, the formulae to be applied may easily 
 be put into the classical form which applies to a homogeneous solid. 
 
 Simple Compression. 
 
 A = A c + m A, 
 
 (2) 
 
 If E c be given, A can be calculated from it. Consequently by the help of (2), and 
 knowing the actual total section of the member, A s the total section of the rein- 
 forcements, or * the percentage reinforcement, may be found. 
 
 Compression with Bending. 
 
 When the total compression N is not uniformly distributed, it is necessary to 
 consider, besides the area A of the equivalent section, the position of its centre of 
 gravity and its moment 
 of inertia (more properly 
 its second moment of area) 
 relative to the axis passing 
 through its centre of 
 gravity and normal to the 
 plane of bending. - & 
 
 Fig. 1 is a sketch of 
 a section, supposed to be 
 symmetrical about an axis 
 y'y passing through its 
 centre of gravity. 
 
 The centres of gravity 
 G s and G c of the reinforce- 
 ment and of the concrete are known, as are also Y 8 and Y c , their distances from 
 an axis xx 1 chosen at will, the abscissae Y s and Y & etc., being reckoned positive 
 on one side xx f , negative on the other. 
 
10 REINFORCED CONCRETE 
 
 A, the area of the equivalent section, is given by (2). Y and the position of 
 the axis XGX' is then determined from the following equation ; 
 
 A Y = \Y C + m A,r. . . (4) 
 
 I s and I c are then calculated, and / is then determined by equation (5) : 
 
 I=l e + ml t . . (5) 
 
 As previously pointed out, it is more convenient in practice to deal with A t , the 
 total area of the member, than with A c , the area of the geometrical section of 
 concrete, and the error thereby introduced is, almost without exception, negligible : 
 
 A, = A c + A,. 
 
 Consequently we also deal with G t and / respectively, the centre of gravity of 
 the total area of the cross section and the second moment of that area relative to 
 an axis parallel to XGX 1 passing through G t . 
 
 Formulae (2), (4) and (5) are then rewritten 
 
 A = A, + (m - 1) A s . . . . (2'; 
 Ar=A e r< + (m-l)A,r,. . . . (4') 
 /=/ + A t (Y--Y t )* + (m- I)/, . (5') 
 Now if in addition to N y there is applied a bending moment M t 
 
 N . M 
 
 HC = A + 7 * ..... ^ ^ 
 
 and if at the point considered there is found a longitudinal reinforcement, the 
 compression it would carry would be 
 
 n, = m n c ...... (6) 
 
 In (5a) x must be reckoned positive when it represents the distance to points 
 lying to that side of XGX' on which the bending moment produces compression. 
 For example, when the bending moment produces compression between G and K, 
 and tension between G and D, then x must be reckoned positive for all points 
 between G and K and negative for all points between G and D. 
 
 The maximum compression in the concrete will then be given by (7) : 
 
 N . M m 
 
 n c = - + jx c . . (7) 
 
 Its least compression will be 
 
 N M ,- N 
 
 * = A " 7 * ' ' ( ' a) 
 
 The compressions in the reinforcements will be obtained by substituting the 
 appropriate values of x- 8 in (7) : 
 
 M 
 
 IN M \ 
 
 Us ~ m \A ~~ T x ) ' ' ' ^ 
 
 It is an essential condition for the correct application of these formulae that 
 compression exists throughout the cross section, or that in (7a) and (8a) n c and n s 
 are positive, If in these formulae the resultant stress was negative or a tension, 
 the formulae would no longer apply, since the laws of tension in concrete differ 
 widely from those expressing the phenomena of its compression. In that case the 
 procedure will be as explained later. 
 
CALCULATIONS OF RESISTANCE 11 
 
 If the centre of pressure of the cross section considered were known, by 
 definition 
 
 M=Nx . (9) 
 
 and 
 
 / = A i* . (10) 
 
 we have 
 
 The neutral axis would by definition be obtained when n c = o, that is when 
 
 x' being the coordinate defining the position of that axis. 
 Formula (7 a) becomes with these notations 
 
 Comparison of (12) and (13) indicates that there is only compression throughout 
 the cross section when x' > % that is when the neutral axis falls outside the 
 section. 
 
 The preceding formulae suppose that N and M are known for each cross section 
 of the member. That is the case for a column carrying a central load that is, 
 where the load is applied to the centre of gravity G of the equivalent section, and 
 consequently M = o, or when the load is eccentric and M = Nx . This is the 
 case of a dam where the curve of pressures gives N and x for each section. 
 
 When, however, these values are not directly furnished by statics, the procedure 
 will be as indicated in the much more general case where members provide a 
 resistance composed simultaneously of compression and tension. That is the case 
 which really justifies the employment of reinforcements. 
 
 Article 11. When the ordinary principles of statics furnish the normal and 
 tangential components of the external forces acting on each cross section of the 
 member considered, and also the bending moment at that section, the calculations 
 necessary for the design of a reinforced concrete member may be proceeded with, 
 without any reference to the elastic deformations of the member. 
 
 But in the case of continuous beams, or beams wholly or partially built in or 
 arched ribs working in tension, the provisions of Article 1 1 are applicable. 
 
 The Administration are prepared to accept the method of calculation in common 
 use, although it is not at all accurate. It consists in attributing the same 
 coefficient of elasticity in tension as in compression. Once this hypothesis is 
 allowed the formulae established above, under the restriction that there is only 
 compression on any cross section, become general. 
 
 Now, by virtue of the intervention of the equivalent section A, these formulae 
 bring back the resistance of a reinforced concrete member, that is to say, of a 
 heterogeneous member, to that of the resistance of an equivalent homogeneous piece. 
 All the general and classical results which apply in the case of the latter are in 
 consequence capable of application to the former. Thus to determine the values 
 of N 9 M and T in the case of an arch, or of M and T and the support reactions in 
 the case of a straight beam loaded transversely (where N = o), it suffices to adopt 
 the well-known values which apply to homogeneous members. 
 
12 REINFORCED CONCRETE 
 
 Thus for a reinforced concrete beam built in at both extremities, the greatest 
 bending moment will be at the building in, and will have for its value 
 
 S ; ..... <"> 
 
 The bending moment at the middle of the span, of sign contrary to the preceding, 
 will be in absolute value 
 
 For partial building in an intermediate value between the latter value and ~, 
 
 the value of the bending moment in a simply supported beam must be chosen. 
 
 For continuous span bridges the well-known expressions are applicable to 
 reinforced concrete structures. 
 
 In the case of a double-hinged arch the thrust is readily obtained from tables 1 
 relative to homogeneous arches, and for a built-in arch the tables recently published 
 by M. Pigeaud 2 give similar information. If it is considered that there is only 
 partial constraint, intermediate values between those furnished by the tables must 
 be chosen. 
 
 Once the thrust is known, all the necessary data to determine J/, N and T 
 graphically or by calculation are obtained for each of the sections it is desired to 
 consider. 
 
 A more correct interpretation of the regulation is obtained by taking into 
 account the actual elastic behaviour of concrete in tension. As a result of different 
 experiments it is known that the coefficient of elasticity of reinforced concrete in 
 tension only conserves a value sensibly constant up to a limit of stress, which is the 
 same as the limit of the resistance to extension of a similar concrete non-reinforced. 
 Beyond this limit the concrete becomes in effect plastic, that is, it extends without 
 its resistance to tension being modified, owing to its connection with the reinforce- 
 ments. There is no difficulty theoretically in building up on this hypothesis, 
 together with that of Navier relating to the plane deformation of plane sections, 
 expressions for the resistance of materials, but the expressions become much more 
 complex. 
 
 By one or other of the above methods the values of N, J/and T will be found. 
 
 From these the unital stresses, at least on the more highly stressed sections, 
 must be determined. In this latter calculation Article 1 1 prescribes the abstraction 
 of all the resistance to extension of the concrete. This is not in the least contra- 
 dictory to that which prescribes the taking account of that resistance in the 
 calculations of deformation, since in the latter the abstraction of all the resistance 
 to extension of the concrete would lead to excessive values being put on the 
 deformations and consequently on N, M and T, which depend on the calculated 
 values obtained ; on the other hand, the local stresses must be determined on a 
 hypothesis representing the most unfavourable conditions which may possibly 
 supervene in practice. In fact, the concrete cracks more or less from the tension 
 side of each member. These microscopic cracks, or even a fissure at any one place, 
 have very little effect on the deformation of the member as a whole, although the 
 local stress in the reinforcement at the fissure will be materially increased owing 
 to the complete annulling of the tension resistance of the concrete. 
 
 1 Tables de Bresse, published by Gauthier Villars, 55, Quai des Grands Augustins, Paris (6 e ). 
 
 2 "Annales des Fonts et Chaussees " (Deuxieme trimestre 1905, et troisieme trimestre 1906). 
 Obtainable from H. Dunod and E. Pinat, 47, Quai des Grands Augustins, Paris (6 e ). 
 
CALCULATIONS OF RESISTANCE 
 
 13 
 
 Example of the Application of the above Principles to a Slab of T Section 
 and to a Beam of Rectangular Section, 
 
 The cross section of the member dealt with is shown in Fig. 2. 
 If there are no compression reinforcements w must be made equal to zero. In 
 Fig. 3 the ordinates of the straight line A'B' give the stresses in the concrete, and 
 
 i b - JL 
 
 F"" 
 
 <; 
 I 
 
 * 
 
 FIG. 2. 
 
 the appropriate ordinates multiplied by " ra " give the values of the stresses in the 
 reinforcements. 
 
 (a) Simple Bending. 
 
 N = o, the algebraic sum of the elastic forces normal to the cross section is 
 consequently zero. From this equation the unknown distance yi to the neutral 
 axis is determined. We may therefore write 
 
 o = -fi- + (b b') t Ux - j + m w ( yi d) miv' (h d' yi ) (16) l 
 
 in which the only unknown is yi. Also the angular coefficient K is determined 
 thus : 
 
 m w' (hd r - yi } (h d') . . . . (17) 
 where K is the only unknown value. 
 
 These formulae implicitly suppose that the neutral axis falls in the rib. If it 
 falls in the slab, it suffices to make b' =b in the above formulae, which become 
 
 , 
 o = -- + 
 
 w 
 
 = - + m w 
 
 d) m w' (h d' y} . . . (18) ! 
 
 d) d m 10' (h d' y^ (h d') . (19) 
 
 1 For a ribbed slab with both tension and compression reinforcements in which the neutral 
 axis falls in the rib (see expression 18a, p. 14) 
 
 When the neutral axis falls in the slab or for a member of rectangular section with both 
 tension and compression reinforcements, b b' and 
 
 m(w + to') ) 2 2m{wd + w'(Ji d'~)} m(w + w') (i\ 
 
 J> i ' ~^~ ~ ft 7 "" 
 
 In the latter case when there is only tension reinforcement in either the ribbed slab or 
 member of rectangular section, w = o, and 
 
 //7/iM/\ 2 2//tM)'(/t d') mw' 
 
 l ~V\"F~j' f ~~V~ ~~b~ 
 
14 REINFORCED CONCRETE 
 
 To know where the neutral axis falls, and in consequence whether its position 
 is determined by (16) or (18), it suffices to replace yi by t in the right-hand member 
 of (18), which gives 
 
 if + m lv ( t d) m iv' (h d' t). . . (18a) 
 
 If this expression has a positive value, the neutral axis falls in the slab and is 
 determined by (18). When its value is negative the neutral axis falls in the rib 
 and is determined by (16). 
 
 Formulae (18) and (19) apply also to a rectangular section of base b and height h. 
 
 When the two unknowns (18) and (19) are determined, the maximum values of 
 the unital stresses are : 
 
 ' s = m K (h d' 
 
 (b) Composite Flexion (or Flexion Combined with Thrust). 
 
 In addition to M and T, as in the previous case, JVis also known, as is the centre 
 of pressure (7, which is distant c from the compressed face, reckoned positive if it 
 falls in the section and negative if it lies outside the latter. In the following 
 calculations it is better to determine in the first place the position of the neutral 
 axis by its distance XC (y a ) from C rather than by y lf its distance from the 
 compressed face (Fig. 3). 
 
 Since the resultant of the elastic forces coincides with TV", the sum of the moments 
 of the elastic forces relatively to C is zero, which gives the following equation to 
 determine % : 
 
 - G + a + <> - *> 
 
 d' c) = o (22) 
 which is of the form 
 
 y* + p y* + q = o ..... (23) 
 
 where 
 
 (24) 
 
 The term in y is missing, which facilitates the solution and justifies the use of y 2 
 in preference to y^, 
 
 When ^2 nas been found, the unknown auxiliary K is obtained immediately by 
 the equation 
 
 TT ' n I 
 
 -/!_ Zi 
 
 -\- m w [y z + c d] m w' [h d' c y 2 ] . (25) 
 where K is the only unknown. 
 
 Formulas (22) to (25) inclusive assume that the neutral axis falls in the rib. If 
 it falls in the slab, as also in the case of a beam of rectangular section, base b, 
 height h, it suffices to make b f = b, which gives 
 
 _ _ 3 C 2 _ 6 m M; , _ 6 m t^ y __ __ 
 
CALCULATIONS OF RESISTANCE 
 
 15 
 
 = - 2 c 3 - 
 
 6 m w 
 
 (c - if - 
 
 (h d' c? 
 
 (27) 
 
 In the case of a ribbed slab, to know if the neutral axis falls in the rib or in the 
 slab it is sufficient to determine whether or not the first member of the equation 
 (23) has or has not contrary signs at the upper and lower extremities of the rib. 
 
 When the unknowns y 2 an( i K are determined, there is obtained from the former 
 
 y\ = y* + c 
 
 for the distance of the neutral axis to the compressed face. The values of the 
 unital stresses on the concrete and reinforcements are then determined, as previously, 
 by formulae (20) and (21). 
 
 Remarks on the Calculation of Slabs. 
 
 When a floor is formed of a slab with ribs (Fig. 4), a rib is considered with 
 a part only of the slab c c', d d r , of width cd = b, without taking into account the 
 help derived from the neighbouring parts. 
 
 This width b should bear a relation to the span and spacing of the ribs and 
 
 | Roadway \ * \ 
 
 Fillin "\ 
 
 C 
 
 
 1 
 
 
 C 
 
 I 
 
 ->K- 
 I 
 
 I \ 
 
 c 
 
 - L - 
 
 \ 
 
 
 
 d' 
 
 ^\ 
 
 
 
 Cross Section. 
 
 "T 
 
 i 
 ! 
 i 
 
 1 
 
 i 
 
 i 
 i 
 i 
 
 
 *1 
 
 y 
 
 *- e ---* 
 
 
 
 Plan 
 
 FIG. 4. 
 
 
 the thickness of the slab. It should never exceed one-third of the span s of the 
 ribs, nor three-fourths of their spacing L. 
 
 If the floor has to support concentrated loads between the ribs, it ought to be 
 provided with two series of reinforcements at right angles. There is generally 
 given to the feebler reinforcement a total section per metre of width of slab at 
 least equal to one-half of the stronger section per metre length of slab. 
 
 To calculate the thickness t of the slab, an isolated load might be replaced by 
 a load uniformly distributed on a rectangle having this load as centre, its sides 
 parallel to the ribs and at a distance apart e equal to the sum of the thicknesses of 
 the slab itself, and of the filling and of the pavement which it carries, its sides, 
 
 perpendicular to the ribs, having for spacing e + . The load thus distributed 
 
 o 
 
 is supposed to be carried by a band of the floor slab of width e -|- and of span L, 
 
 u 
 
 supported on two consecutive ribs. 
 
16 
 
 REINFORCED CONCRETE 
 
 When a floor is supported by two sets of ribs at right angles, spaced at spans 
 L and L' respectively, the bending moment in the span L may be obtained, in the 
 absence of a better method, by calculating it as if the ribs spaced L apart alone 
 existed, and by multiplying the figure so obtained by the coefficient of reduction : 
 
 1 
 
 2 
 
 r\i 
 
 (L') 
 
 The bending moment in the span L' is obtained by a similar process and by 
 changing the letters in the coefficient of reduction. 
 
 Resistance to Slipping of Reinforcements (Adhesion). 
 
 If it has been found that in two neighbouring sections AB, A'B' of a member 
 (Fig. 5), spaced As apart, there are unital stresses of R s ' and ft", the . total 
 
 stresses on these sections will be w'R s ' and w'It s " 
 respectively, and the tendency of the reinforcement 
 to slip in its sheath of concrete is measured by the 
 difference 
 
 <- As --> 
 
 w - 
 
 The tendency to slip, per unit of surface of the 
 
 reinforcement, will then be 
 
 w' (JR.' - ./') 
 
 and 
 
 P . As 
 
 it is this ratio which must not exceed the limit 
 imposed by Article 6 of the instructions, viz., one- 
 tenth of the maximum compressive stress, or O028 
 of the crushing strength of the concrete after ninety 
 days' setting. 
 
 When stirrups or other transverse reinforcements 
 are attached to the longitudinal reinforcement in 
 such a manner that slipping of the latter cannot 
 take place without shearing the former, then the 
 shearing resistance F of the transverse pieces 
 occurring on the length As of the longitudinal 
 reinforcement considered as the product of the 
 section in shear by the allowable shearing stress for the metal ought to be deducted 
 from the slipping force w r (fi s f R"\ It is then sufficient that the ratio 
 
 FIG. 5. 
 
 w 
 
 " F 
 
 P. As 
 
 does not exceed the limit allowed for adhesion. 
 
 When there are only simple ties between the transverse and longitudinal rein- 
 forcements, these are not sufficient to bring the shearing strength of the transverse 
 pieces into action as a reinforcement lent to the resistance to slipping of the 
 longitudinals. Consequently no account ought to be taken of the shear resistance 
 of the transverse reinforcements. The ties, however, serve other purposes and 
 ought to be provided. 
 
 Longitudinal Slipping of the Concrete on Itself and Shearing Resistance. 
 
 Consider a portion of the member lying between two transverse sections AB 
 and A'B', distant apart As, and having a longitudinal reinforcement a'b' in the 
 tension side of the member. Consider a horizontal section of the member in the 
 
CALCULATIONS OF RESISTANCE 
 
 17 
 
 stretched part of the concrete, that is, between the reinforcement and the neutral 
 plane and parallel to the latter. Let w c be the area of this section. 
 
 As the tensions in the concrete normally to mB and nB' are not taken account 
 of, the portion m n BB' of the member is in equilibrium under the influence of the 
 tensions w'R 8 ' and w'R" of the longitudinal reinforcements and of the longitudinal 
 shearing stress on the plane mn. The value of this longitudinal shearing stress 
 per unit area is 
 
 w' (R,> - R,) 
 
 w c 
 
 and ought not in any case to exceed the stress allowed for the shearing of the 
 concrete. 
 
 This stress (28) remains constant up to the neutral plane. Above that plane 
 it diminishes by the effect of the compression, so that what has been taken account 
 of here represents the maximum stress. 
 
 If transverse reinforcements are employed to resist efficiently the longitudinal 
 slipping, they might be taken account of as described in the discussion of adhesion. 
 
 The vertical shearing stress at each point is besides, as is well known, the 
 same in magnitude as the longitudinal slipping force just considered. 
 
 Buckling of Compressed Pieces. 
 
 Article 12. To ensure that buckling of compressed pieces will not occur, the 
 following inequality, which expresses Rankine's formula, must be satisfied : 
 
 + fojsb)<* (^) 
 
 The varying values of k to suit the different end conditions met with in practice 
 are as follows : 
 
 TABLE No. 2. 
 
 A 1 
 
 End conditions. 
 
 Kemarks. 
 
 Built in at one end, free at the other 
 Jointed at both ends 
 Jointed at one end, built in at the 
 other. 
 
 Built in at both ends 
 
 If the building in is imperfect, a mean 
 value between J and 1 should be 
 chosen. 
 
 If the building in at one end is im- 
 perfect, a mean value between ^ and 
 \ should be taken. If it is imperfect 
 at both ends, a mean value between 
 and 1 should be chosen. 
 
 When the compression member is of great length, it happens that unity is 
 
 k I 2 
 
 negligible in comparison with the number 
 
 
 inequality which 
 
 expresses the condition of stability might be simplified thus : 
 
 or 
 
 A ' 1 0,000 r 
 -10,000 
 
 (30) 
 
 R.C. 
 
18 REINFORCED CONCRETE 
 
 The average value of R c is about 710 Ibs. per square inch, and the coefficient 
 of elasticity of concrete about on the average one-tenth that of steel, that is, 
 E c = 2,844,000 Ibs. per square inch. 
 
 The product 10,000 R c = 7,100,000 Ibs. per square inch. 
 
 2 ~p 
 
 The product - - = 7,030,000 Ibs. per square inch. 
 These are sensibly equal, so that (30) may be rewritten : 
 
 which is Euler's formula with a coefficient of security of 4. It is thus seen that 
 the indications furnished by this formula agree with those of the Rankine formula 
 for very long pieces. 
 
 If in addition to the purely compressive stress on the member there is a bending 
 moment, the effect of which cannot be considered negligible, e.g., the case of an 
 eccentrically loaded column, or of a long column exposed to wind pressure, the 
 maximum compressive stress due to this bending moment must be introduced into 
 the inequality (29) in order to completely state the conditions of stability. 
 
 The stress due to this bending moment is expressed by 
 
 ^c=^ ...... (31a) 
 
 o^I *<=^ ...... (314) 
 
 Rankine's formula is then represented by one or the other of the following 
 inequalities : 
 
 Execution and Tests of Works. 
 
 The Commission point out that comment on the remaining articles of the 
 Instructions is superfluous. They limit themselves to the remark regarding the 
 execution of works that in reinforced concrete construction, perfection of execution 
 is the essential condition of success. Accidents which have happened are in general 
 due to the mediocre quality of the materials used or their improper employment. 
 It is necessary to exercise a special supervision over the production and the purity 
 of the materials used, their mixture, the quality and the quantity of the water used 
 in the manufacture of the concrete, the ramming and placing of the concrete 
 round the reinforcements, and the stability of the latter till the enveloping 
 concrete is properly in position. 
 
CHAPTER III 
 
 ANNEX TO THE EXPLANATORY CIRCULAR BY THE FRENCH MINISTRY OF PUBLIC 
 WORKS, BEING A REPORT ON THE DRAFT REGULATIONS OF THE GOVERNMENT 
 COMMISSION BY THE COMMISSION NOMINATED BY THE GENERAL COUNCIL OF 
 BRIDGES AND ROADS (abridged). 
 
 As explained in the Introductory Note, this commission, consisting of M. Maurice 
 Levy as President and Reporter, and MM. de Preaudeau and Vetillart, reconsidered 
 the whole question of the draft regulations presented to the Minister of Public 
 Works by the larger Government Commission, and as a result of their labours the 
 regulations took the form which appears in Chapter I. 
 
 They suggested the substitution of the word " Instructions " for the word 
 "Regulations," as conveying a sense of less permanence and finality without losing 
 any of the obligatory character of the latter. 
 
 They also reconsidered the propriety of authorising the high working stress 
 proposed by the Government Commission. After much consideration and discussion, 
 they came to the conclusion that, taking into account the methods of calculation by 
 which the stresses would be arrived at, tjie limits defined in Articles 4 and 5 
 would be safe in practice. 
 
 The fundamental premise of all calculations in reinforced concrete is the ratio 
 expressing the equivalence of equal sections of reinforcement and of concrete repre- 
 sented by the symbol "m." The Government Commission did not come to a 
 unanimous decision on the value of m. Two members, MM. Rabut and Mesnager, 
 were of opinion that this number should be taken equal to 10, whilst the majority 
 of the commission decided that it should have a value ranging from 8 to 15. The 
 German and Swiss regulations, as well as the majority of French and Belgian 
 writers, adopt the value 15. 
 
 Hypothetically m is the ratio between the moduli of elasticity of the reinforce- 
 ment and of the concrete. From the experiments of M. Mesnager, which agree 
 closely with those of Professor Bach of Stuttgart, this ratio up to a stress of 850 Ibs. 
 per square inch on a concrete composed of 6 cwts. Portland cement to 14*3 cubic 
 feet of sand to 2 8 '7 cubic feet of gravel, has the value 10. With the value 15 
 there is often attributed to the metal a greater share of the load than it really takes, 
 so that the concrete is more highly stressed than the calculations indicate. Danger 
 thus arises from the use of a fixed value of m. 
 
 The following considerations concerning the closely interrelated quantities, "m," 
 the working stress and the coefficient of security, lead the Commission nominated by 
 the General Council of Bridges and Roads to agree to the figures appearing in the 
 circular accompanying the instructions. 
 
 Consider a column of reinforced concrete in which the calculated stress is 7 1 Ibs. 
 per square inch. A test cube of the same concrete not reinforced broke after 
 ninety days' setting under a load of 2,840 Ibs. per square inch. The column would 
 
 c 2 
 
20 
 
 REINFORCED CONCRETE 
 
 9 .Q4 H 
 
 7-09" 
 
 0-276" Dia.m 
 
 then be said to have a coefficient of security of 4. This is, of course, only a con- 
 ventional value. The real value of the coefficient of security can only be determined 
 by the testing to destruction of the actual structure. 
 
 This actual coefficient of security was determined in the case of five experimental 
 columns on which very precise rupture experiments were carried out by Professor 
 Bach of Stuttgart. The breaking loads experimentally determined were compared 
 with the calculated stresses resulting 
 
 1. From the employment of the working stresses allowed by foreign regulations 
 
 and m constant and equal to 15. 
 
 2. From the employment of the 
 working stresses allowed by the 
 instructions, taking advantage of the 
 
 / P 7 \ 
 
 coefficient of increase ( 1 -f~ m r -y \ 
 
 and making m vary from 8 to 15. 
 
 The columns tested had the cross 
 section shown on Fig. 6 and a length 
 of 3 9 '3 7 inches. The area of each 
 column was thus 96'9 square inches. 
 Each was reinforced with four rods 
 varying from 0'59 to 1*18 inches in 
 diameter and spaced at 7 '09-inch 
 centres. These longitudinal rods were 
 united in pairs by rods of 0-276 inch 
 diameter, forming double transverse 
 ligatures, forming the four sides of 
 a square and spaced longitudinally 
 V, the volume of each set of four 
 
 FIG. 6. 
 
 from 2 '46 inches to 9 '8 4 inches apart. 
 ligatures, was 3 '8 3 cubic inches. 
 
 Table No. 3 is a resume of the five series of experiments. 
 
 TABLE No. 3. 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 No. of 
 Experiment. 
 
 Diameter of 
 Longitudinal 
 Keinforcements. 
 
 Spacing of 
 Transverse 
 Reinforcements. 
 
 Mean Value of the 
 Breaking Load. 
 
 Total Cross 
 Section of the 
 Longitudinal 
 Reinforcements. 
 
 1 
 
 Inches. 
 0-59 
 
 Inches. 
 9-84 
 
 Lbs. per square inch. 
 2,390 
 
 Square Inches. 
 
 MO 
 
 2 
 
 0-59 
 
 4-92 
 
 2,520 
 
 MO 
 
 3 
 
 0-59 
 
 2-46 
 
 2,915 
 
 MO 
 
 4 
 
 0-79 
 
 9-84 
 
 2,420 
 
 1-95 
 
 5 
 
 1:18 
 
 9-84 
 
 2,700 
 
 4-39 
 
 The breaking stress of a non-reinforced concrete column was found to be 
 2,020 Ibs. per square inch and that of a cube of this concrete 2,500 Ibs. per 
 square inch. 
 
21 
 
 Supposing m 15 and taking R c = 500 Ibs. per square inch, which would 
 conform to the German regulations, 
 
 N = 500 (96-90 + 15 w). 
 
 TABLE No. 4. 
 
 No. of 
 Experi- 
 ment. 
 
 15 w. 
 
 (96-90 + 15 to). 
 
 N. 
 
 N 
 96-9' 
 
 Breaking 
 Loads. 
 
 Effective 
 Co-efficient 
 of Security. 
 
 
 
 
 
 Lbs. per 
 
 Lbs. per 
 
 
 
 (Inches). 2 
 
 (Inches.) 2 
 
 Lbs. 
 
 inch. 2 
 
 inch. 2 
 
 
 1 
 
 16-4 
 
 113-3 
 
 56,400 
 
 582 
 
 2,390 
 
 4-1 
 
 2 
 
 16-4 
 
 113-3 
 
 56,400 
 
 582 
 
 2,520 
 
 4-3 
 
 3 
 
 16-4 
 
 113-3 
 
 56,400 
 
 582 
 
 2,915 
 
 5-0 
 
 4 
 
 29-3 
 
 126-2 
 
 62,800 
 
 648 
 
 2,420 
 
 3-5 
 
 5 
 
 65-7 
 
 162-6 
 
 81,000 
 
 834 
 
 2,700 
 
 3-2 
 
 It is seen that the effective coefficient of security is a very variable quantity. 
 It varies between 5 and 3 '2, which indicates that the hypothesis of m = 15 
 might lead to serious miscalculations. 
 
 Now in terms of Article 4 of the instructions, allowing a stress of 710 Ibs. 
 per square inch instead of 500 Ibs. per square inch, as in the above calculations, 
 and in virtue of Article 5 we increase this stress according to the coefficient of 
 
 ncrease 
 
 which leads to 
 
 ' V 
 1 + m 
 
 R c = 710 
 
 V' 
 
 + m' 
 
 The safe working loads N for the various columns are given by the formula 
 
 N = JK (96-9 + m . w). 
 
 The values of m f and m indicated in the circular are adopted and are given 
 in Table No. 5. 
 
 TABLE No. 5. 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 11. 
 
 Nos. 
 
 m. 
 
 m w. 
 
 96-90 + mw. 
 
 Spacing of 
 Transverse 
 Reinforce- 
 
 m'. 
 
 V 
 
 y ' 
 
 K ' = y, 
 
 710 (l + m' y\ 
 
 N. 
 
 N 
 96-9' 
 
 Effective 
 Coefficient 
 of 
 
 
 
 
 
 ments. 
 
 
 
 
 
 
 Security. 
 
 
 
 
 
 
 
 
 
 
 Lbs. per 
 
 
 
 
 (Inches. )2 
 
 (Inches.) 2 
 
 (Inches). 
 
 
 
 
 Lbs. 
 
 inch.2 
 
 
 1 
 
 10 
 
 11-01 
 
 107-91 
 
 9-84 
 
 8 
 
 0-00401 
 
 734 
 
 79,200 
 
 818 
 
 2-9 
 
 2 
 
 12 
 
 13-18 
 
 110-08 
 
 4-92 
 
 12 
 
 0-00802 
 
 779 
 
 85,800 
 
 886 
 
 2-8 
 
 3 
 
 15 
 
 16-43 
 
 113-33 
 
 2-46 
 
 15 
 
 0-01604 
 
 882 
 
 121,800 
 
 1,258 
 
 2-8 
 
 4 
 
 9 
 
 17-52 
 
 114-42 
 
 9-84 
 
 8 
 
 0-00401 
 
 734 
 
 105,900 
 
 1,094 
 
 2-8 
 
 5 
 
 8 
 
 35-03 
 
 131-93 
 
 9-84 
 
 8 
 
 0-00400 
 
 734 
 
 96,850 
 
 1,000 
 
 2-7 
 
 The figures in column 11 display a remarkable constancy and admit of 
 fidence in the values of "m" and "m f " 
 also justify the use of the high- working stress. 
 
 confidence in the values of "m" and " m' '" set forth in the Instructions, and 
 
CHAPTER IV 
 
 SHORT DESCRIPTION, WITH RESUME OP THE RESULTS, OF THE EXPERIMENTS CARRIED 
 OUT AT THE LABORATORY OF THE NATIONAL SCHOOL OF BRIDGES AND ROADS 
 UNDER THE PROGRAMME OF THE SECOND SUB-COMMITTEE. 
 
 1. Measurement of Contraction during Setting. 
 
 To measure the contraction during the setting of cement concrete, four 
 prisms, each 3 '2 8 feet long and of approximately 6 -inch side, were moulded 
 vertically, two reinforced and two without reinforcement. One of the non-rein- 
 forced prisms was kept in the Court of the Laboratory covered with sacks and 
 watered from time to time, the others were kept dry on supports in a closed shed. 
 
 The results are discussed in Chapter V., p. 70. 
 
 2. Measurement of Elasticity of Concrete without Reinforcement. 
 
 Two prisms of concrete, containing 6 cwts. Portland cement, 28*7 cubic feet 
 of gravel and 14'4 cubic feet of sand mixed to a plastic consistency, each 3*28 feet 
 long and of square section of 1'64 feet side, were subjected to compression in a 
 hydraulic press after setting for about 10^ months. 
 
 Table No. 6 gives the results obtained. 
 
 TABLE No. 6. 
 
 Compressive Stress. 
 
 Modulus of Elasticity. 
 
 Load Applied Normal to Planes 
 of Ramming. 
 
 Load Applied Parallel to Planes 
 of Hamming. 
 
 Lbs. per square inch. 
 
 From 64 to 580 
 From 64 to 970 
 From 64 to 1,360 
 
 Lbs. per 
 square inch. 
 4-20 x 10 6 
 4-01 x 10 
 3-87 x 10 6 
 
 Tons per 
 square inch. 
 1,875 
 1,790 
 1,728 
 
 Lbs. per 
 square inch. 
 3-83 x 10 6 
 3-77 x 10 6 
 3-60 x 10 6 
 
 Tons per 
 square inch. 
 
 1,710 
 1,683 
 1,608 
 
 3. Determination of the Resistance to Crushing of Cement Concrete 
 prepared in Different Degrees of Plasticity. 
 
 Three prisms each 7'87 inches square and 19'68 inches long were cast verti- 
 cally in moulds, the concrete consisting of 12 cwts. of Portland cement to 28'7 
 cubic feet of gravel and 14 -4 cubic feet of sand. 
 
DETERMINATION OF SETTING STRESSES 
 
 23 
 
 Prism No. 1. The concrete was mixed with 11 '6 per cent, of water by weight 
 of dry mixture and was sufficiently wet to pour into the mould, which was 
 completely filled in that way. 
 
 1 Prism No. 2. The mould was filled for three-quarters of its height with 
 material similar to that in Prism No. 1 ; the remainder of the mould was filled with 
 successive layers of dry mixture strongly rammed. 
 
 Prism No. 3. The mould was filled with ordinary plastic concrete rammed. 
 
 The tests in each case were made fifty-four days after moulding. 
 
 TABLE No. 7. 
 
 
 Cross 
 
 
 
 
 
 Sectional 
 Area of 
 Prisms in 
 
 Weight in Lbs. per cubic foot of Concrete 
 of Prisms. 
 
 Resistance 
 to Rupture 
 by Crushing. 
 
 
 square inches. 
 
 
 
 
 
 
 
 
 Lbs. per 
 
 
 
 After 7 days. 
 
 After 26 days. 
 
 After 54 days. 
 
 square inch. 
 
 Prism No. 1 
 
 63-24 
 
 140-8 
 
 138-4 
 
 137-7 
 
 2,092 
 
 Prism No. 2 
 
 63-23 
 
 143-2 
 
 142-2 
 
 141-8 
 
 > 2,510 2 
 
 Prism No. 3 
 
 62-46 
 
 141-6 
 
 140-0 
 
 139-5 
 
 2,440 
 
 4. Influence of the Percentage of Keinforcement on the Stresses 
 developed during Setting. 8 
 
 Nine pairs of cylinders were manufactured, each 19 '7 inches long and 3 -9 
 inches in diameter, each pair containing a similar reinforcing rod, the area of which 
 varied throughout the series from a percentage of 0-23 to 9'0. One cylinder 
 of each pair consisted of 6 cwts. of Portland cement, 2 8 -7 cubic feet of gravel 
 and 14*4 cubic feet of sand, the other of 10 cwts. of Portland cement to the same 
 quantities of sand and gravel. The cylinders of the former mixture were kept 
 in air, those of the latter in water. 
 
 No very definite results were obtained ; but at the end of seven months it 
 was found that the shortening of the reinforcements of the test cylinders kept 
 in air was 0-018 per cent, when the percentage reinforcement was 0'23, 
 and O'OIO per cent, when the percentage reinforcement was 9. The 
 corresponding percentage elongations of the reinforcements of the cylinders kept 
 in water were O'OIO per cent, and 0*009 per cent, when the percentage rein- 
 forcements were 0*23 and 9-0 respectively. 
 
 The shortenings and elongations were measured on a length of 1*64 feet. 
 
 5. Tension Tests. 4 
 
 Four prisms of square section 3 -94-inch sides and 78*8 inches long, rein- 
 forced with four round rods, each 0*24 inch diameter, giving a percentage reinforce- 
 ment of 1'13, were made of concrete consisting of 6 cwts. of Portland cement, 
 28*7 cubic feet of gravel and 14-4 cubic feet of sand, and gauged with 8-8 percent, 
 of water by weight of dry mixture. 
 
 1 See note on p. 74. 
 
 3 This stress only produced fissures without leading to total rupture. 
 8 For notes on these tests by M. Considere, see pp. 105, 106. 
 
 4 For notes on these tests by M. Considere, see Chapter VII., 1. 
 
24 
 
 REINFORCED CONCRETE 
 
 Prism No. 1 was tested by a gradually increasing load until cracking was 
 observed. Under a load of 550 Ibs. per square inch, when the elongation 
 reached 0*135 per cent, of the original length (measured on one metre), fissures 
 were observed. 
 
 Prism No. 2 was tested by repeatedly removing the load and 
 reapplying it. Twenty-five repetitions were made. The last load applied was 
 293 Ibs. per square inch, which produced an elongation of O'OGl per cent, of 
 the original length without producing any visible cracks. The permanent 
 deformation under this load was 0'0265 per cent, of the original length. 
 
 The reinforcing rods were carefully cut out and the concrete of the prism 
 subjected to bending tests. The breaking load in the first of these bending 
 tests corresponded to a tension of 133 Ibs. per square inch, and in the second 
 to a tension of 126 Ibs. per square inch. 
 
 Prism No. 3. This prism was tested similarly to No. 2. After the tenth 
 loading the permanent deformation found on unloading was observed not to 
 
 increase, and after the twentieth 
 loading the load was allowed to 
 remain on for fifteen hours. No 
 appreciable increase in the exten- 
 sion took place. The load applied 
 in each case was 255 Ibs. per square 
 inch, and the extension due to the 
 twenty-fifth application was 0'0165 
 per cent, of the original length. 
 The total extension from the com- 
 mencement of the experiment was 
 
 ["*_"" ~ I 0*0435 per cent, of the original 
 
 length without any appearance of 
 fissures. 
 
 Prism No. 4. This prism was 
 tested as was Prism No. 1 by a 
 gradually increasing load. When 
 the load had reached 540 Ibs. per 
 square inch and the elongation 
 0'13 per cent, of the original 
 length, fissures appeared uniformly 
 over the whole length of the 
 
 prism at intervals of from 3 to 
 FIG. 7. . , 
 
 b inches. 
 
 From a portion of the concrete of Prism No. 1 which had been loaded to 
 550 Ibs. per square inch, the coefficient of elasticity of concrete in compression 
 was determined and the following values were obtained : 
 
 For stresses between 
 
 70 and 700 Ibs. per square inch, 2'105 X 10 6 lbs. per inch 2 or 940 tons per inch. 2 
 700 and 1,140 Ibs. per square inch, 2 '180 X 10 6 Ibs. per inch 2 or 973 tons per inch. 2 
 
 70 and 1,140 Ibs. per square inch, 2'130 X 10 6 Ibs. per inch 2 or 951 tons per inch. 2 
 
 The steel wire used in the manufacture of the prisms had an apparent limit 
 
 of elasticity of 19-8 tons per square inch, a breaking strength of 27 tons per 
 
 square inch, with an elongation of 20'5 per cent, on 7 '87 inches, and a 
 
 modulus of elasticity of 13,000 tons per square inch. 
 
 K 8' * 
 
 <--4'-f- ->J 
 
 t^-Line of Fracture 
 of Concrete 
 
 
 
 L/ne of Fracture / 
 of Concrete ' 
 
 *^Art/F,cia/ Shear Plane 
 
 o- ' 
 *-"' - o > 
 
TESTS OF SHEAR RESISTANCE 
 
 25 
 
 6. Shearing Tests. 
 
 Six rectangular prisms, each 11*8 inches X 11 '8 inches X 23*6 inches long, were 
 made in three series, each consisting of concrete containing 6 cwts. of Portland 
 cement, 28 '7 cubic feet of gravel and 14'4 cubic feet of sand. 
 
 The prisms were moulded in wooden boxes in two halves, with the reinforce- 
 ments vertical. As soon as the first half of each prism was set it was turned in the 
 mould and the other half formed, a sheet of oiled paper being placed between the 
 halves to secure a division plane. 
 
 Fig. 7 shows the prism with division plane and the method of applying the 
 shear, and Table No. 8 gives a resume of the results obtained. 
 
 The planes along which fissuring took place are indicated by dotted lines on the 
 diagram. 
 
 1st series of prisms were reinforced with six sheet-iron straps 1-575 inches 
 X 0-084 inch, giving a percentage reinforcement of the cross section of 0-57. 
 
 2nd series of prisms were reinforced with two round rods each 0'716 inch 
 diameter, giving a percentage reinforcement of 0'58. 
 
 3rd series of prisms were reinforced with six rods of 0*394 inch diameter, 
 giving a percentage reinforcement of 0'52. 
 
 TABLE No. 8. 
 
 Shearing Effort Applied to 
 the Division Plane. 
 
 Total Stress. 
 
 Lbs. 
 
 Unital Stress 
 per square 
 
 inch of 
 Reinforce- 
 ment. 
 Tons. 
 
 Mean Relative 
 
 Displacement 
 
 of the two 
 
 halves. 
 
 Inches. 
 
 Remarks. 
 
 29,730 | 16-57 
 
 809 
 
 6,590 
 
 13,550 
 
 14,690 
 
 20,700 
 
 0-45 
 3-68 
 7-56 
 8-13 
 11-53 
 
 SERIES I. 1st Prism. 
 0-50 | Maximum load attained. 
 '2nd Prism. 
 
 7,750 
 
 4-32 
 
 
 
 Stress beyond which a movement 
 
 imper- 
 
 
 
 
 ceptible to the eye was indicated. 
 
 
 18,640 
 
 10-41 
 
 
 
 Relative displacement became visible. 
 
 
 25,600 
 
 14-29 
 
 
 
 Sudden displacement. 
 
 
 28,600 
 
 14-94 
 
 0-50 
 
 Maximum load. Concrete fissured. 
 
 
 SERIES II. 1*2 Prism. 
 
 0-0005 
 0-0044 
 0-0163 
 0-0263 
 0-70 
 
 Prism fissured. 
 
26 
 
 REINFORCED CONCRETE 
 
 TABLE No. 8 (continued). 
 
 
 Mean Eelative 
 
 
 Shearing Effort Applied to 
 the Division Plane. 
 
 Displacement 
 of the two 
 
 
 
 halves. 
 
 
 
 Unital Stress 
 
 
 Remarks. 
 
 
 per square 
 
 
 
 Total Stress. 
 
 inch of 
 
 
 
 
 Reinforce- 
 
 
 
 
 ment. 
 
 
 
 Lbs. 
 
 Tons. 
 
 Inches. 
 
 
 SERIES II. 2nd Prism. 
 
 6,590 
 
 18,850 
 23,280 
 
 3-68 
 
 10-42 
 12-89 
 
 0-36 
 
 Stress beyond which a movement imper- 
 ceptible to the eye was indicated. 
 Visible displacement took place. 
 Concrete fissured. 
 
 SERIES III. 1st Prism. 
 
 13,550 
 25,300 
 
 8-27 
 15-50 
 
 0-33 
 
 Relative displacement became visible. 
 Concrete fissured. 
 
 2nd Prism. 
 
 17,020 
 24,870 
 
 10-43 
 15-27 
 
 0-43 
 
 Relative displacement became visible. 
 Concrete fissured. 
 
 The steel reinforcing the prisms used in the shearing tests had the properties 
 indicated by the following figures : 
 
 TABLE No. 9. 
 
 
 Practical 
 Elastic Limit. 
 
 Breaking Load 
 on Original 
 Section. 
 
 Elongation 
 per cent, on 
 8 inches. 
 
 Modulus of 
 Elasticity. 
 
 
 Sheet steel, 1-57 inches 
 X 0-084 inch. 
 
 Tons per inch. 2 
 20-7 
 
 Tons per inch. 2 
 27-5 
 
 21-5 
 
 Tons per inch. 3 
 
 13,000 
 
 Round rod, 0-394 jnch 
 diameter. 
 
 18-8 
 
 26-5 
 
 25-7 
 
 15,500 
 
 Round rod, 0-717 inch 
 diameter. 
 
 15-8 
 
 24-0 
 
 33 
 
 14,800 
 
TESTS OF SHEAR RESISTANCE 
 
 27 
 
 7. Torsion Tests. 
 
 Two cylinders, each 39'37 inches long and 4*21 inches diameter, were reinforced 
 longitudinally by four steel wires placed symmetrically in the section about 0*47 inch 
 from the surface. The concrete was of the same proportions as that described on 
 p. 25. The moulds were placed vertically and filled in three parts, one 
 immediately after the other. 
 
 As soon as the cylinders were removed from the moulds, square heads for the 
 purpose of applying the torsion were moulded on each extremity. 
 
 In the application of the test the cylinders were kept horizontal and the torsion 
 applied by means of a lever. The variations in length of the cylinders during the 
 test were measured on one of the reinforcing rods, the ends of which projected 
 beyond the concrete. 
 
 The results obtained were the following : 
 
 TABLE No. 10. 
 
 Moment of 
 Torsion. 
 
 Foot-lbs. 
 
 Total Elongations 
 per cent, of 
 Original Length. 
 Measured on 
 39-37 inches. 
 
 Remarks. 
 
 36 
 
 108 
 253 
 290 
 
 36 
 108 
 253 
 325 
 360 
 
 1. Cylinder with Reinforcements 0-213 inch diameter. 
 
 0-0 
 0-002 
 0-010 
 0-013 
 
 Rupture took place when torsion was increased 
 beyond this value. 
 
 Cylinder with Reinforcements 0'300 inch diameter. 
 
 0-0 
 
 0-001 
 
 0-005 
 
 0-010 
 
 0-016 
 
 A crack appeared at this load. 
 Rupture took place immediately after this torque 
 was applied. 
 
 The direction of the principal fissures with the generator of the cylinder was 61 
 for the first cylinder and 45 for the second. 
 
 8. Resistance to Slipping of Reinforcements. 
 
 1. Four test pieces, consisting of mild steel cylinders 4*18 inches diameter, 
 rough from the rolls, were enveloped for a length 7*87 inches in a square block of 
 concrete of 1 2 "20-inch side, otherwise not reinforced. The composition of the concrete 
 was 6 cwts. Portland cement 28*7 cubic feet gravel, 14*4 cubic feet sand, and it was 
 filled into the mould by ramming. 
 
 In the case of two of the test pieces tension was applied to the steel cylinder 
 and in the other two a thrust was applied. 
 
28 
 
 REINFORCED CONCRETE 
 
 The age of the concrete at the time of the test was seventy-two days, and failure 
 took place by the splitting of the concrete block, in the case of the first test piece, 
 when a load was applied corresponding to a stress of 97 Ibs. per square inch of area of 
 contact of the metal and concrete. In the case of the second, failure took place at 
 190 Ibs. per square inch, and in the case of the third and fourth test pieces to which 
 a thrust was applied at stresses of 215 Ibs. per square inch and 235 Ibs. per 
 square inch respectively. The low stress obtained in the first case is accounted for 
 by a defect in the testing apparatus. 
 
 2. Four test pieces similar in all respects to the above, but having the concrete 
 surrounding the steel cylinder reinforced with two rings of sheet steel 1'18 inches X 
 
 0*23 inch, and with three longitudinal 
 wires 0'98 inch diameter, were similarly 
 tested. After six months' setting slip- 
 ping took place when stresses of 347 
 and 360 Ibs. per square inch of area of 
 contact between the concrete and the 
 steel had been applied by tension and 
 when stresses of 356 and 464 Ibs. per 
 
 ! : i 
 
 -I-4-- 
 
 075'tol" 
 
 FIG. 8. 
 
 square inch had been applied by 
 thrust. In each case no cracking of the 
 enveloping cylinder of concrete occurred 
 when the first slipping of the cylinder 
 through its concrete envelope took place, 
 which slipping amounted to about 
 0*08 inch. The cylinder was able after 
 
 this initial slipping had occurred to resist a stress tending to cause further 
 slipping amounting on the average over the four specimens to 303 Ibs. per 
 square inch. 
 
 3. Test pieces representing parts of beams and formed as indicated in Fig. 8 
 were prepared. They were divided into three series according to the proportions 
 of cement employed in the concrete : 
 
 Series I. 3 cwts. cement, 28*7 cubic feet gravel, and 14'4 cubic feet sand. 
 Series II. 6 28'7 14'4 
 
 Series III. 10 28'7 14'4 
 
 They were tested by tension applied to the projecting end of the reinforcement. 
 
 The test pieces were non-reinforced as at "a," reinforced with ordinary 
 (Hennebique) stirrups as at "6" or reinforced with open stirrups as at "c." 
 
 The results obtained are given in Table No. 11, p. 29. 
 
 In the case of the test pieces without stirrups a crack occurred in each case 
 along the middle of the lower face following the reinforcing bar at the moment of 
 slipping. In none of the others were fissures observed. 
 
 4. Additional Tests on the Slipping of Reinforcements in Concrete made ivith 
 French Quick-setting Cements. Six test pieces were made of the form and 
 dimensions shown in Fig. 8, of type " a," without transverse reinforcements of any 
 kind. The concrete in each case was of the proportions of Series II. 
 
 With a cement setting of which commenced in nine minutes and was complete 
 in thirteen minutes, the average resistance to slipping per square inch of the surface 
 of contact of reinforcement and concrete was 60 Ibs. per square inch after twenty- 
 four hours, and 232 Ibs. per square inch after twenty-eight days. 
 
 With a cement which commenced setting in air in one hour and was set in two 
 
TESTS OF RESISTANCE TO SLIPPING 
 
 29 
 
 hours, the resistance was 31 Ibs. per square inch after twenty-four hours and 91 Ibs. 
 per square inch after twenty-eight days. 
 
 5. Tests were made of the resistance to slipping of the wires in an old 
 reinforced concrete sleeper. The diameter of the wires was 0*197 inch. 
 
 TABLE No. 11. 
 
 
 
 
 Average Stress 
 
 
 _ 
 
 Stress which 
 produced the 
 First Slipping 
 
 Maximum 
 Stress under 
 which Slipping 
 ceases after 
 
 under which 
 the Reinforce- 
 ment leaves 
 its Bed, when 
 
 Age of Test 
 Piece. 
 
 
 Reinforcement. 
 
 the First 
 Slipping. 
 
 the Displace- 
 ment reaches 
 
 
 
 
 
 0-2 inch. 
 
 
 
 Lbs. per 
 square inch. 
 
 Lbs. per 
 square inch. 
 
 Lbs. per 
 square inch. 
 
 Months. 
 
 (a) Without stirrups . 
 
 (b) With ordinary stirrups 
 
 (c) With open stirrups 
 
 (a) Without stirrups 
 
 SERIES I. 
 
 317 
 
 102 
 
 60 
 
 3 
 
 267 
 
 236 
 
 182 
 
 3 
 
 304 
 
 182 
 
 142 
 
 3 
 
 SERIES II. 
 
 (6) With ordinary stirrups . 
 
 (c) With open stirrups 
 
 400 
 
 155 
 
 115 
 
 422 
 
 161 
 
 141 
 
 230 
 
 158 
 
 119 
 
 102 . 
 
 91 
 
 115 
 
 283 
 
 232 
 
 202 
 
 411 
 
 311 
 
 284 
 
 300 
 
 245 
 
 200 
 
 404 
 
 300 
 
 272 
 
 284 
 
 245 
 
 245 
 
 240 
 
 215 
 
 182 
 
 305 
 
 262 
 
 226 
 
 472 
 
 353 
 
 312 
 
 556 
 
 357 
 
 313 
 
 365 
 
 298 
 
 259 
 
 424 
 
 383 
 
 302 
 
 SERIES III. 
 
 (a) Without stirrups . 
 
 433 
 
 146 
 
 148 
 
 3 
 
 (6) With ordinary stirrups . 
 
 579 
 
 483 
 
 417 
 
 o 
 
 (c) With open stirrups 
 
 454 
 
 375 
 
 326 
 
 3 
 
 Longitudinally the wires were not straight, but presented considerable undula- 
 tions. Slipping of the reinforcement took place generally about 1,150 Ibs. per 
 square inch of the surface of contact, although in one case slipping took place at 
 
30 
 
 REINFORCED CONCRETE 
 
 820 Ibs, per square inch. In three cases the wire broke outside the concrete 
 before slipping had taken place when the stress had reached 1,050, 1,310 and 590 Ibs. 
 per square inch respectively of the surface of contact between the wire and the 
 concrete. 
 
 9. Bending of Beams. 
 
 Twenty-three specially manufactured beams were tested, and a resume of the 
 results obtained is given in Table No. 12, pp. 32-38. 
 
 Fig. 9 shows in outline the method of applying the test loads to the beams 
 A to G inclusive. By this arrangement there is obtained a uniform bending 
 moment between the points of application of the load, and a uniform shear between 
 the latter and the points of support of the beam. 
 
 The sand and gravel used were carefully measured by weight, allowance being 
 made for moisture in the sand and for sand and moisture in the gravel. When 
 
 T 
 
 
 
 aratuses for Measuring Strajns 
 
 3 28' -4 
 
 < 6-23' i 
 
 3-28 H 
 
 G 23' 
 
 FIG, 9. 
 
 beam A was prepared the sand contained 4 per cent, of its weight of water and the 
 gravel 2*7 per cent. The results of this method, however, were sensibly the same 
 as those obtained by the volumetric methods used in practice. 
 
 The granulometric composition of the materials used was as follows : 
 
 Sand. 
 
 Weight per cubic foot = 9 9 '7 Ibs. 
 Granulometric composition, weights per cent. 
 0*197 inches diameter to 0'079 inches diameter 
 0-079 0-0197 . 
 
 0-0197 0-0 
 
 Gravel. 
 
 Weight per cubic foot = 9 3 '4 Ibs. 
 Granulometric composition, weights per cent. 
 0*984 inches diameter to 0*787 inches diameter . 
 0*787 0*394 . 
 
 0*394 0*197 
 
 100 
 
 3-5 
 71*7 
 
 24-8 
 
 100 
 
 For the tests of beams J to U inclusive an alteration in the spacing of the points 
 of support and of application of the loads was made, giving the ends of the beam a 
 
TESTS OF BEAMS 
 
 31 
 
 greater overhang. The effect of the projection of reinforcements beyond the points 
 of support can thus be studied. The arrangement is outlined in Fig. 10. 
 
 In beam H, the whole load was applied as a concentrated load midway between 
 the points of support, whilst in beams /, V and W the points of application of the 
 load, were 3' 2 8 feet apart. 
 
 Manet-Rabut apparatuses for measuring strains were fixed to the beams in the 
 positions indicated in Figs. 9 and 10 by rods built into the concrete. The strains 
 in the reinforcements were measured by similar apparatuses fixed directly to the 
 latter, which were exposed for a short length by careful chiselling. 
 
 The relative slipping of the concrete and the reinforcement was obtained in 
 either of three ways : 
 
 1. By the use of an apparatus fixed to the concrete at the end of the beam, 
 operated by a rod from the end of the reinforcement, bared for the purpose. 
 
 2. By means of an apparatus fixed to the concrete, and measuring the relative 
 movement of the reinforcement in a vertical plane normal to the beam 1J inches 
 distant. 
 
 3. By means of a microscope fixed to the concrete, and reading on a reference 
 mark on the reinforcement in the plane of the microscope. 
 
 The deflections were measured by means of a Rabut recording apparatus 
 
 .Apparatuses for Measuring /\ 
 ...... Strain" 
 
 
 J 
 
 FIG. 10. 
 
 fixed to each face of the beam midway between the tie rods, whilst the extension 
 of the latter and the deflections of the loading system were also recorded, so that 
 the actual values of the deflections of the beam were obtained. 
 
 All the beams had a length over-all of 13' 12 feet, with the exception of beams U 
 and F, which had an over-all length of 9*84 feet. 
 
 The ends of the longitudinal reinforcements of beams A, B, C, D, F and G 
 were fish-tailed according to the Hennebique practice, whilst in beam E they pro- 
 jected 2 inches at each end for measurement purposes. In beams H to ^inclusive, 
 with the exception of /, the longitudinal reinforcements were cut to a uniform 
 length, \\ inches shorter than the beam, and left simply with square-cut ends, whilst 
 in beams 7, U, V and W each end of the longitudinal reinforcements was returned 
 square upwards for a length of 2J inches. 
 
 Beams A to G inclusive had measuring apparatuses attached to the vertical 
 faces of the beams near the upper and lower faces and also at the neutral axis for 
 the purpose of verifying Navier's hypothesis, viz. that plane sections remain plane 
 during bending. The result obtained in the case of beam 7> is graphically repre- 
 sented in Fig. 11, p. 39. 
 
 Beams H to M inclusive give a comparison between flat and round stirrups of 
 equal sectional area. 
 
 Beams M t N t allow of the study of the effect of the splitting up to the trans- 
 verse reinforcement into a greater or less number of stirrups. 
 
REINFORCED CONCRETE 
 
 tfl 
 
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TESTS OF BEAMS 
 
 33 
 
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 The cracks observed during the 
 hardening under load were only 
 visible to the magnifying glass 
 after unloading. During the 
 loading tests a maximum load of 
 7'6 tons or a moment of 
 11-22 foot-tons produced new 
 fissures and extended the old 
 ones into the beam. 
 
 Under a total load of 7-6 tons or 
 a bending moment of 11-22 foot- 
 tons a fissure on the tension side 
 of the beam appeared, and 
 under a total load of 14-73 tons 
 or a bending moment of 21-75 
 foot- tons the beam failed by 
 cracking all over, and by slip- 
 ping of the reinforcement at 
 one end. 
 
 Under a total load of 5 - 12 tons or 
 a bending moment of 7'55 foot- 
 tons two cracks on the tension 
 side appeared, and under a load 
 of 10-08 tons or a bending 
 moment of 14-88 foot-tons the 
 beam failed by cracking all over. 
 
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34 
 
 REINFORCED CONCRETE 
 
 
 
 
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TESTS OF BEAMS 
 
 35 
 
 
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36 
 
 REINFORCED CONCRETE 
 
 a a 
 
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TESTS OF BEAMS 
 
 37 
 
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 middle of span. 
 Perished by crushi 
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 near middle of s 
 Perished by crush ii 
 
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38 
 
 REINFORCED CONCRETE 
 
 
 rH 
 
 S 
 
 .3 
 
 1 
 
 Remarks. 
 
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 flllllliPllSi 
 
 S-2S-s^-ij"^"g 
 
 lla^lfl^lfsll! 
 
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 8* S |f 8 Sl lS J5-Si 
 
 I-*ll!ilillll?-g 
 
 l3gi 3 :- a ll s -.S 
 
 ^^ c2-s e sog.2^-T3floj 
 
 S F T3aj c3 Kr ?MaJa; ( i> f -' 
 
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 125 
 
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TESTS OF BEAMS 
 
 39 
 
 The influence of the percentage of vertical reinforcement may be studied in 
 beams M, P and Q. 
 
 The comparison of vertical stirrups with reinforcements inclined at 45 degrees 
 may be made in beams Q, R, S and T. 
 
 The utility of returning the reinforcements at the extremities was studied in 
 beams /, U, V and W. 
 
 Beams V and W were also intended to show the condition of the concrete in a 
 reinforced concrete beam after it had been stressed. 
 
 Table No. 13 gives an indication of the quality of the cement used in the various 
 beams. In every case a good result was obtained in the soundness tests. 
 
40 
 
 REINFORCED CONCRETE 
 TABLE No 13. 
 
 
 Time of Setting in Humid Air. 
 
 Average Tensile Strength of 
 Neat Cement (Ibs. per 
 square inch). 
 
 
 Commencement. 
 
 Termination. 
 
 7 days. 
 
 28 days. 
 
 84 days. 
 
 Beams A G . 
 
 20 minutes 
 
 4J- hours 
 
 370 
 
 518 
 
 687 
 
 Beams H U 
 
 3 hours 
 
 5J hours 
 
 549 
 
 653 
 
 646 
 
 Beams V and W 
 
 If hours 
 
 6J hours 
 
 469 
 
 550 
 
 654 
 
 Diagram for Final Loading. 
 
 Diagram For Initial Loading. 
 
 Deformations. Elongations or Shortenings. Indicated Thus. 
 Observed Deflections at Middle of Span . 
 
 Scale to Deformations. 
 
 TO 0-01 002 003 004 005 006 007 008 009 010 
 1 I I 1 1 I 1 I I 1 1 
 
 020 per Cent of 
 
 " 
 
 DOS 
 
 4- 
 
 Scale to Deflections, 
 
 4- 
 
 03/rfcftes 
 
 FIG. 12. 
 
 The steel used was mild steel, having a practical limit of elasticity varying with 
 the diameter of the rod of from 15 to 20 tons per square inch, a breaking strength 
 
TESTS OF BEAMS 
 
 41 
 
 of from 23 to 28 tons per square inch, and an elongation of from 17 per cent, to 34 
 per cent, on a length of 7*87 inches. 
 
 In addition to the information given in Table No. 1 2, the actual strains on the 
 tension and compression faces and at the neutral line were measured and also the 
 variations in length due to the setting of the concrete in many of the beams. 
 These are fully recorded in Chapter IV. of the French edition of the Report. 
 
 In the case of beam M, the extension and shortening of the concrete on the 
 tension and compression faces respectively at the level of the reinforcements 
 
 Initial Loading * 
 
 <:> '"? \s 
 
 Tensile Strain (7.) of Concrete on Line Inclined 45 Indicated Thus 
 
 Elongation of the Tension Reinforcement. 
 Deflection of Beam. 
 
 Scale to Elongation of Reinforcement a.nd Tensile Strair 
 apt 002 003 004 005 006 007 008 O09 010 
 
 longa.tic 
 006 007 
 ~\ 1 I I I I 
 
 rCent of 
 
 Inches 0/0 
 
 Scale lo Deflection 
 010 
 
 030 Inches 
 
 FIG. 13. 
 
 measured on a length of 3 - 28 feet, where the bending moment was uniform, together 
 with the observed deflections at the middle of the span, are given in Fig. 1 2. 
 
 In the case of beam Q, the deflection at mid span, the elongation of the tension 
 reinforcements measured on a length of 19'68 inches, and the elongation on a line 
 inclined at 45 to the length of the beam are graphically represented in Fig. 13. 
 
 The elongations on a line inclined at 45 were measured on a length of 19*68 
 inches and are stated as percentage alterations of original length, and are plotted in 
 the curve in Fig. 13 marked " Tensile Strain (/ ) of Concrete on Line inclined 45 C 
 
 ;o 1 
 
 1 In the French edition this curve was marked simply " Shear Strain." Monsieur Mesnager 
 has pointed out to me that this is an error and that the actual shear strains are double the values 
 given by the curve. That is clearly so, since in an elastic material subject to a pure shear the 
 shear strains are each very approximately double the tensile strains measured on a line at 45 to 
 the directions of the shears. Consequently the shear strain, measured in radians, has 
 represented by the figures given divided by 50. N.M. 
 
42 
 
 REINFORCED CONCRETE 
 10. Bending of Flat Slabs. 
 
 Thirteen slabs, each 3-94 inches deep and 19'68 inches wide, reinforced with 
 four rods at 4 "72-inch centres and placed in the slab with 0'79 inches clear between 
 the rods and the lower face of the slab, were tested to destruction in order to 
 compare the resistances obtained under the various conditions described in Table 
 No. 1 4, in which a resume of the results is also given. 
 
 FIG. 14. 
 
 The sand used weighed 99 Ibs. per cubic foot, of which 
 27*4 per cent, was from 0*197 inches diameter to O079 inches diameter, 
 59-6 0-079 0-0197 
 
 13-0 0-0197 0-0 
 
 and contained 6 '2 per cent, by weight of moisture. 
 
 The gravel used weighed 89'1 Ibs. per cubic foot, and 
 
 10 '4 per cent, was from 0'984 inches to 0*787 inches diameter. 
 75-6 0-787 0-394 
 
 14-0 0-394 0-197 
 
 V<- -4-72'- ->*--4-72"->*- * 72"- tu2 -76* 
 
 i jji i i j j , . -j--. ' j- J J 
 
 44 265 706 
 
 IS88 2029 
 
 3352 3733 4234 
 
 SSS7 5998 
 
 Total Loa.ds applied to Slab in Pounds 
 
 FIG. is. 
 
 The gravel contained 6'8 per cent, of its weight of sand and 3*8 per cent, of 
 its weight of water. 
 
 The cement used was of medium setting time, setting in 4J hours, and giving 
 a resistence to tension of 480 Ibs. per square inch after seven days and 580 Ibs. 
 per square inch after twenty-eight days. Slab No. 14 was made of a variety of lime 
 setting in eighteen hours and giving a resistance to tension of 1 40 Ibs. per square 
 inch after seven days, 207 Ibs. per square inch after fourteen days, and 304 Ibs. 
 per square inch after eighty-four days, 
 
TESTS OF FLAT SLABS 
 
 43 
 
 
 
 
 3 
 
 3 
 
 || 
 
 1 
 
 
 
 
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 || 
 
 tl 
 
 & 
 
 
 
 s 
 
 
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 15 "* w 
 
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 'I'll 
 
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 3 S 
 
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 C2 G CD 
 
 if? 
 
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TESTS OF FLAT SLABS 
 
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46 REINFORCED CONCRETE 
 
 The reinforcements of 0*197 inches diameter were of iron having a limit of 
 elasticity of 17 tons per square inch, a breaking strength of 25 tons per square 
 inch, and an elongation of 14 per cent, on 7 '8 7 inches. 
 
 The reinforcements of 0*394 inches and 0*591 inches diameter were of mild 
 steel having a limit of elasticity of 17 tons per square inch, a breaking strength 
 of 25 J tons per square inch and an elongation of 26 per cent., with a modulus of 
 elasticity of 14,200 tons per square inch. 
 
 The slabs were left in the open air from the date of manufacture till the date 
 of the test ; and the loads were applied as indicated in Fig. 14. 
 
 The load in the case of slab No. 1 1 was applied in twenty minutes ; in the 
 other cases the time varied from fifty-five minutes to 2 hours. 
 
 From zero load up to the first load given in the table, the deflection in each 
 case follows a straight-line law, and is directly proportional to the load applied. 
 For loads beyond the first load given, the deflection continues generally to obey a 
 straight-line law, but the rate of increase of the deflection is much greater than up 
 to that load. The results from all the slabs are very similar, and Fig. 15 gives 
 the deflection diagram for slab No. 5, which is typical of the others. 
 
 11. Experiments on Ribbed Slabs. 
 
 Two floors were constructed each of span about 9 feet 6 inches, one 4 feet 
 wide, the other 6 feet 6 inches, and each stiffened by one central rib. The 
 floors were 2*36 inches deep and the ribs had 7*50 inches of additional depth, and 
 were 6 inches wide. 
 
 In the case of the floor 6 feet 6 inches wide the rib had tension reinforcement 
 only consisting of four rods, placed two vertically above two, each of 0*87 inch 
 diameter with 0*5 inch clear between the rods and 0*8 inch clear between the 
 rod and the lower face of beam, and having sheet-iron stirrups of 1*575 inches 
 X 0*085 inch at about 4j inches centres extending nearly to the upper surface of 
 the floor. The floor was reinforced in the middle of its depth by rods of 0*394 inch 
 diameter spaced at about 4J inches centres ; the ribs, very slightly increased in 
 depth, were returned along the ends of the slabs to form a continuous support for 
 the floor. The test load was applied along a width of 9 inches centrally over the 
 rib, and was uniformly distributed in the direction of the length except for two 
 short gaps at the centre, where strain-recording instruments were placed. A 
 maximum load of 20*2 tons was placed on the slab a little less than six months 
 after manufacture. At this load a noticeable crack extended across the tension 
 side of slab and rib. Measurements of the deflection were not made, but the 
 actual strains in the structure w r ere carefully measured. These are fully recorded 
 in the French edition, p. 240. 
 
 In the case of the floor 4 feet wide, the rib had tension reinforcement consisting 
 of four rods, each 0*787 inch diameter, placed two vertically above two, spaced 
 and with sheet stirrups as in the other floor. The method of reinforcing and sup- 
 porting the floor during the test was exactly as in the floor previously described, 
 but the load in this "case was uniformly spread over the whole floor. A total load 
 of 15*26 tons was applied, corresponding to a load of 7*87 cwts. per square foot of 
 total surface, and remained in position for twenty-three hours. After eighteen 
 hours' application of the load no further straining was observed and no cracks 
 of any kind were observed, and on removing the load the strains almost entirely 
 
TESTS OF RIBBED SLABS 47 
 
 The measured strains are given in the French edition, p. 238, and a diagram 
 graphically representing these strains is reproduced in Fig. 1 6. 
 
 The materials employed were similar in character to those used in the manu- 
 facture of the experimental beams. 
 
48 
 
 REINFORCED CONCRETE 
 
 15-75" > 
 
 12. Tests of Columns and Prisms in Compression. 
 
 1. 9 Columns, each 1 6* 4 feet long. 
 
 1. Nine columns, each 16 -4 feet long, seven 15 '7 5 inches square and two 9 -8 4 
 inches square, were tested to destruction. Fig. 16A indicates the typical cross 
 section of the columns, particulars of which are given in Table No. 16 (pp. 50 51) 
 and Table No. 17 (p. 49) together with a resume of the results obtained. 
 
 Each column was reinforced with four round bars placed one at each corner, so 
 as to leave about 0*9 inch clear between each face of the column 
 and the surface of the reinforcement. The reinforcing rods were 
 united by sheet interties 0-118 inch thick, placed 19*68 inches 
 apart in the column and 9 '8 4 inches from either end. 
 
 The columns were manufactured under conditions pertaining 
 in practice. Moulding was effected on the flat. 
 
 The concrete used consisted of 6 cwts. of Portland cement 
 to 14 '3 5 cubic feet of siliceous Seine sand passing through holes 
 0-197 inch in diameter, and 28*7 cubic feet of siliceous Seine 
 gravel passing through holes 0'984 inch in diameter and retained on holes 0'197 inch 
 in diameter. These materials were mixed with water, 8 -2 per cent, of the weight of 
 the mixture of dry materials. The quantities used were obtained by weighing, taking 
 account of the humidity of the sand, about 5 per cent, by weight, and of the gravel, 
 about 3 '5 per cent, by weight as well as the quantity of sand contained in the 
 gravel, 9 per cent, by weight of the latter. The granulometric composition of the 
 sand and gravel was very similar to that of the materials described on p. 30. 
 
 The cement used commenced setting in air in four hours and setting was com- 
 pleted in 6J hours, and it stood the soundness tests satisfactorily. The average 
 resistance to tension of briquettes of neat cement was 528 Ibs. per square inch after 
 seven days and 576 Ibs. per square inch after twenty-eight days. 
 The quality of the reinforcement is indicated in Table No. 15. 
 
 TABLE No. 15. 
 
 FIG. 16A. 
 
 
 
 
 
 Apparent 
 Limit of 
 Elasticity. 
 
 Breaking 
 Load per 
 square inch 
 of Initial 
 Section. 
 
 Elongation 
 per cent, 
 after 
 Rupture ; on 
 7-87 inches. 
 
 Modulus of 
 Elasticity. 
 
 Rod of 1-77 inches 
 diameter. 
 
 Mild steel 
 
 Tons per 
 square inch. 
 14-5 
 
 Tons. 
 22-8 
 
 32% 
 
 Tons pei- 
 square inch. 
 13,650 
 
 Rods 0-47 inch to 
 1'26 inches dia- 
 meter. 
 
 Do. 
 
 17-9 
 
 25-5 
 
 28% 
 
 14,500 
 
 Sheets 0-118 inch 
 thick. 
 
 Do. 
 
 16-9 
 
 22-6 
 
 26-5% 
 
 
 
 Do. ... 
 
 Iron 
 
 16-5 
 
 21-6 
 
 15% 
 
 
 
TESTS OF COLUMNS 
 
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52 
 
 REINFORCED CONCRETE 
 
 2. 12 prisms 7 -87" X 7'87" X 3'28 feet long. 
 
 These prisms were constructed of 6 cwts. Portland cement, 14*35 cubic feet Seine 
 sand passing through 0'197 inch diameter holes, and 28-7 cubic feet Seine gravel 
 passing through 0'984 inch diameter holes. In six of the prisms the concrete was 
 
 121282 564 846 1128 1410 1692 1514 
 Load Pounds per Sq. Inch. 
 
 age 
 00 
 
 19. 
 
 
 282 564 846 1128 1410 1692 1974 2256 2538 2821 3104 
 
 Shortening as Percentage of Original Length. 
 0-01 002 0-03 004 005 006 007 008 009 0-10 01 
 
 
 
 
 
 
 
 
 
 
 
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 mixed with water amounting to 1 1 '2 per cent, of the weight of the dry materials, and 
 was consequently of soft consistency and was simply poured into the moulds. In 
 the other six prisms 8 '2 per cent, of water was used and the concrete rammed. 
 
 Four prisms were made without reinforcement ; in two of these the concrete 
 was simply poured, and in the other two rammed. 
 
TESTS OF PRISMS 
 
 53 
 
 Four prisms were reinforced longitudinally, each by four rods 0*709 inch 
 diameter, placed at 0*787 inch from each face and united by three sheet interties 
 1-575 inches X 0-118 inch thick, the extreme ties being placed about 6| inches 
 from the ends. The longitudinal reinforcement amounted to 2 '5 4 per cent, of the 
 total area, and the interties, reduced to an equivalent rod of the same volume, 
 0*65 per cent., or together to a total of 3*19 per cent. 
 
 Four prisms were spiralled with a wire 0*236 inch diameter at 0-79 inch 
 pitch, of a mean diameter of 7*24 inches. In addition there were six longitudinal 
 rods, each 0'354 inch diameter, placed inside the spiralling. An equivalent rod 
 of the same volume as the spiralling would have an area 2*04 per cent, of the total 
 area of the prism, and adding 0*95 per cent, as the percentage of the longitudinal 
 reinforcement, the total reinforcement is 2*99 per cent., roughly the same as for 
 the longitudinal bars. The spiralling was applied in sections comprising seven to 
 
 7-16" -- 
 
 FIG. 21. 
 
 nine helices, the sections being simply superposed after having reduced the last spiral 
 at each end to half pitch. 
 
 The reinforcement was of mild steel of ordinary quality. The rods of 
 0*354 inch diameter had an apparent limit of elasticity of 18 tons per inch 2 , 
 an ultimate strength of 26 tons per square inch, and a total elongation of 26 per 
 cent, on 7*87 inches. 
 
 In each case the prisms were removed from the moulds forty-eight hours after 
 manufacture, and kept moist by watering for three days. One of each type was 
 then kept dry in the air, the other of that type was kept under a bed of sand 
 frequently watered. A resume of the results is given in Table No. 18, pp. 54 56. 
 
 In Fig. 17 the results of the tests of the prisms with the three types of rein- 
 forcement are exhibited graphically. The three prisms in this group were made 
 from the same wet mixture, and similarly treated after moulding, viz., kept in a 
 dry atmosphere till the date of the tests. 
 
 In Fig. 18 the results obtained are exhibited, when the prisms from a similar 
 wet mixture are kept moist after moulding. 
 
 Figs. 19 and 20 represent graphically the corresponding results when a dry 
 mixture is used and carefully rammed, and the prisms kept in the dry and kept 
 moist respectively. 
 
54 
 
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TESTS OF COLUMNS 
 
 57 
 
 3. 24 columns from 6*5 6 feet long to 13*12 feet long. 
 
 The columns manufactured had a section either square of 7*16 inches side or 
 octagonal with the diameter of the inscribed circle 7*87 inches, as shown in 
 Fig. 21 (p. 53). 
 
 The series of square columns comprised columns not reinforced, and columns 
 reinforced longitudinally as shown on the cross section. The interties were placed 
 at 13 inches centres and 6| inches from the ends. 
 
 The series of octagonal columns included only columns spiralled with a metallic 
 spiral rolled at varying pitches to an exterior diameter of 7 '48 inches. 
 
 In each case the longitudinal reinforcements were about a quarter of an inch 
 shorter than the columns, and they were not flush at either extremity. 
 
 All the columns were cast vertically and were manufactured by workmen under 
 the conditions met with in actual works. 
 
 The columns were made in two series : (a) containing 7 cwts. Portland cement, 
 14'3 cubic feet Seine sand passing through a sieve with holes 0'197 inch 
 diameter, and 28'7 cubic feet of Seine gravel passing through a hole of 0'984 inch 
 diameter ; and (b) containing 10 cwts. Portland cement to those quantities of sand 
 and gravel. 
 
 The water employed in gauging was 8*3 per cent, of the weight of the dry 
 mixture in the former case, and 9 per cent, in the latter. The resulting concrete 
 was plastic ; that is to say, that after being well worked up it moistened on striking 
 with the flat of a spade. During the first fortnight of hardening the columns 
 were watered slightly every two or three days. 
 
 The columns were weighed in order to determine the approximate density of 
 the concrete, and the weights per cubic foot are given in Table No. 19, and for 
 purposes of comparison the weights per cubic foot of the prisms of Series 2 (p. 52) 
 are added. 
 
 TABLE No. 19. 
 
 
 6 cwts. Portland Cement. 
 
 
 
 
 
 7 cwts. 
 
 10 cwts. 
 
 
 
 Portland Cement. 
 
 
 
 Kept in Air. 
 
 Kept Moist. 
 
 
 
 
 
 
 Rammed and 
 
 Rammed and 
 
 
 
 
 
 Poured. 
 
 Rammed. 
 
 Poured. 
 
 Rammed. 
 
 Kept in Air. 
 
 Kept in Air. 
 
 Non-reinforced 
 
 143-5 
 
 150-2 
 
 146-9 
 
 152-5 
 
 149-0 
 
 148-0 
 
 Reinforced to total per- 
 
 
 
 
 . 
 
 
 
 155-1 
 
 154-7 
 
 centage of 2 '13. 
 
 
 
 
 
 
 
 Reinforced to total per- 
 
 153-0 
 
 158-f) 
 
 156-9 
 
 162-2 
 
 
 
 
 
 centage of 3-19. 
 
 
 
 
 
 
 
 Reinforced to total per- 
 
 
 
 . 
 
 
 
 166-3 
 
 164-1 
 
 centage of 4*94. 
 
 
 
 
 
 
 The extremities of each column were ground and rendered as exactly plane and 
 parallel as possible, and the load was applied directly by the heads of the hydraulic 
 press with the interposition of a sheet of cardboard 0'079 inch thick. 
 
 The reinforcements were of mild steel or of iron, of somewhat varying quality. 
 Rods of mild steel of 0'304 inch diameter had an elastic limit of 14'6 tons per 
 square inch, a breaking strength of 2 3 -2 tons per square inch, and a percentage 
 
58 
 
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TESTS OF COLUMNS 59 
 
 elongation on 7*87 inches of 25 per cent., whilst rods of 0*315 inch diameter had 
 an elastic limit of 22*5 tons per square inch, and an ultimate strength of 29 tons 
 per square inch, with an elongation of 21*5 per cent, in 7*87 inches, all the varieties 
 of iron and steel used being between these values. 
 
 The cement used stood the soundness tests satisfactorily ; setting commenced 
 in 2 hours 40 minutes, and was complete in 5 hours 40 minutes. Briquettes of 
 neat cement had a mean resistance to tension of 535 Ibs. per inch 2 after seven days, 
 and 578 Ibs. per inch 2 after twenty-eight days. 
 
 Fig. 22 shows graphically the results obtained with columns 6 '5 6 feet long 
 and 13 '12 feet long, manufactured in both cases with a concrete composed of 
 7 cwts. of Portland cement, 28'7 cubic feet of gravel, and 14'3 cubic feet of 
 sand. 
 
 Fig. 23 shows the results obtained with columns of a similar length, and with a 
 mixture of 10 cwts. of Portland cement to 28*7 cubic feet of gravel, and 14*3 cubic 
 feet of sand. 
 
 Fig. 24 shows the results obtained with spiralled columns of various lengths 
 manufactured with concretes containing 7 cwts. and 10 cwts. respectively of 
 Portland cement, to 28'7 cubic feet of gravel and 14*3 cubic feet of sand. 
 
 The graphs in the above figures do not show the point at which the column 
 actually collapsed, but simply the point at which the readings were discontinued 
 owing to the virtual failure of the column. 
 
 The rupture of the columns having for the most part, and particularly for those 
 of concrete with 10 cwts. of cement, occurred near the extremity corresponding 
 to the upper end of the column during moulding, experiments were carried out to 
 discover to what extent the resistance of the concrete might vary in columns 
 moulded vertically without special precautions. 
 
 In the case of the columns 6*56 feet long, a prism 18*9 inches long was cut 
 from the base and tested by crushing. In the case of the concrete containing 
 7 cwts. of cement, the prisms from the base showed an increase in crushing strength 
 of 420 Ibs. per square inch over the figure for the whole column. In the case 
 of the concrete containing 10 cwts. cement the figure was 1,850 Ibs. per square 
 inch. 
 
 In the case of the columns 13'12 feet long, prisms were cut from the base and 
 from a part of the column 3 feet from its upper end during moulding. The 
 prisms from the base had 570 Ibs. per inch 2 greater resistance to crushing than the 
 upper prism, and about 1,360 Ibs. per inch 2 greater resistance to crushing than the 
 whole column for a concrete containing 7 cwts. Portland cement, whilst for a con- 
 crete containing 10 cwts. Portland cement these figures were 1,350 Ibs. per inch 2 
 and 2,570 Ibs. per inch 2 respectively. 
 
 13. Compression Tests of Spiralled Mortar and Concrete. 
 
 1. Prisms in Cement Concrete, arranged by M. Considere. 
 
 These prisms, of octagonal section of 29'45 square inches area and 1*64 feet 
 long, were submitted to compression tests carried to rupture, the deformations 
 being measured. 
 
 The results are given in Table No. 20 (p. 62). 
 
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TESTS OF COLUMNS 
 
 61 
 
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62 
 
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 TABLE No. 20. 
 
 Description. 
 
 Load Applied 
 to Spiralled 
 Core, 
 Ibs. perinch2 
 
 Shortening 
 per cent,, of 
 Original 
 Length. 
 
 Remarks. 
 
 1. Prism not reinforced ; age, 
 4 months. Stress reckoned 
 on total section. 
 
 307 
 1,050 
 1,168 
 
 0-0128 
 0-0680 
 
 Modulus of Elasticity : 
 From 165 Ibs. per inch 2 to 750 
 Ibs. per inch' 2 =2-18 X 10* 5 
 Ibs. per inch 2 . 
 From 58 Ibs. per inch 2 to 750 
 Ibs. per inch 2 = 2-11 x 10 6 
 Ibs. per inch. 2 
 Rupture. 
 
 2. Prism reinforced with a rod 
 0-236 inch diameter, 
 spiralled to a pitch of 
 1-18 inches, and to an 
 exterior diameter of 5 '51 
 inches. The sectional area 
 of the reinforced core was 
 26-4 square inches. 
 
 344 
 1,502 
 65 
 1,502 
 3,160 
 
 5,770 
 
 0-0160 
 0-0880 
 0-0320 
 0-9400 
 1-2740 
 
 Permanent deformation. 
 
 Covering of spirals progressively 
 detached. 
 Prism completely deformed into 
 S shape. 
 
 3. Prism reinforced with an iron 
 rod 0'161 inch diameter, 
 spiralled to a pitch of 0*59 
 inch, and to an exterior 
 diameter of 5 -51 inches. 
 The sectional area of the 
 reinforced core was 2 6 -4 
 square inches ; the pitch 
 of the spirals was a little 
 irregular, the pitch attain- 
 ing -67 inch in places. 
 
 344 
 1,502 
 65 
 1,502 
 3,610 
 
 6,016 
 
 0-016 
 0-0740 
 0-016 
 0-0660 
 0-6560 
 
 External covering of spiralling 
 detached bit by bit. 
 Maximum load of which the 
 testing machine was capable. 
 Column not broken. 
 
 4. Prism reinforced with a rod 
 0'236 inch diameter, 
 spiralled to an external 
 diameter of 5 '51 inches, 
 and to a pitch of 1'063 
 inches. Average section 
 of core = 26 - 4 square 
 inches. 
 
 344 
 1,502 
 65 
 1,502 
 3,610 
 
 5,635 
 
 0-0020 
 0-0720 
 0-0080 
 0-0768 
 1-5640 
 
 Permanent deformation. 
 
 External covering of spiralling 
 detached bit by bit. 
 Rupture. 
 
 5. Prism reinforced longitudi- 
 nally with 8 rods, 0'315 
 inch diameter, giving 
 sensibly the same per- 
 centage of metal as in 
 the preceding spirally 
 armoured prism. The 
 stresses given are reckoned 
 on the total section of 
 29 '45 square inches. 
 
 1,530 
 1,835 
 
 
 Cracking commenced. 
 Complete failure. 
 
 6. Non-reinforced prism of 
 29 '45 square inches area. 
 Stress reckoned on total 
 area. 
 
 825 
 
 
 Complete failure. 
 
 NOTE. In Prisms 2, 3 and 4 the transverse swelling of the spirals was measured, but 
 no conclusive results were obtained. 
 
TESTS OF SPIRALLED PRISMS 63 
 
 2. Six Prisms in Cement Concrete, as desired by M. Consider e. 
 
 Six octagonal prisms of about 15*5 square inches cross sectional area and 
 1*64 feet long were made. 
 
 Three of the prisms were of a mixture of 8 cwts. of Portland cement to 
 9*56 cubic feet of sand, screened to 0*197 inch diameter, and 28*7 cubic feet 
 of gravel (0*197 inch to 0*984 inch diameter), and water amounting to 9 '3 per 
 cent, of the weight of the dry materials, was used as being necessary and sufficient 
 to obtain a plastic consistency. 
 
 The other three were composed of a mixture of 10*7 cwts. of Portland cement 
 to the above quantities of sand and gravel and 9 -8 per cent, of water. 
 
 In the former series of three prisms, two were spiralled at a pitch of 0*55 inch 
 for about one-quarter of the length from either end and 0*79 inch for the 
 remaining portion in the middle. In the latter the pitch of the spirals for 
 one-fifth of the length of the column at either end was 0*39 inch, whilst 
 the middle portion was spiralled to 0*59 inch pitch. The spiralling was of 
 iron wire 0*169 inch diameter, and the external diameter of the spirals was 
 3*94 inches. In addition, the prisms were reinforced each with eight rods 
 of 0*169 inch diameter, placed in the interior of the spirals and in contact 
 with them. 
 
 The two spiralled prisms, containing 8 cwts. Portland cement, were loaded 
 by small increments to a stress of 1,300 Ibs. per square inch of total section, and 
 showing under that stress an average shortening of 0*0652 per cent, of their 
 original length, with an average permanent deformation of 0*0244 per cent, of 
 their original length when the load was removed. This permanent deformation 
 increased slightly when the load was reapplied and removed. 
 
 From one of the prisms the crust of concrete covering the spiral reinforcement 
 was removed down to the centre of the spiralling rods, and a compression was 
 again applied and removed and the process repeated. At each repetition the 
 stress was carried higher and the permanent deformation measured. At a stress 
 of 2,366 Ibs. per square inch of the core the shortening was 0*16 per cent, of the 
 original length, whilst the permanent deformation was 0*074 per cent. At a stress 
 of 9,270 Ibs. per square inch the deformation was 2*4 per cent., and the permanent 
 set amounted to 1*81 per cent. The maximum stress applied was 9,480 Ibs. per 
 square inch, but as the prism threatened to break, this load was removed before 
 readings were taken. The spiralling was then stripped and the core tested. 
 Crushing took place at 870 Ibs. per square inch. The age of the concrete at test 
 was about ten weeks. 
 
 In the other prism no further compression tests were made as above, but the 
 spiralling was also removed and compression applied. Crushing took place at a 
 stress of 1,670 Ibs. per square inch. 
 
 The third prism of this mixture was made without reinforcement for purposes of 
 comparison, and failed at 1,142 Ibs. per square inch. 
 
 Two of the prisms of the mixture containing 10*7 cwts. Portland cement, one 
 reinforced and the other not reinforced, were tested. The concrete was about four 
 months old at test and had been immersed in fresh water for six weeks previous 
 to it. 
 
 The reinforced prism at a stress of 6,370 Ibs. per square inch of the spiralled 
 core underwent a shortening of 0*582 per cent, of its original length, and on the 
 load being removed showed a permanent deformation of 0*342 per cent. The 
 
64 REINFORCED CONCRETE 
 
 prism ultimately perished by buckling under a stress of 12,700 Ibs. per square 
 inch of the section of the core. 
 
 The prism not reinforced failed at a stress of 2,235 Ibs. per square inch of 
 total section. 
 
 3. Eight Cylinders of Mortar Spiralled for Compression Tests. 
 
 These cylinders had a mean diameter of 3 '3 inches and a length of 
 23-23 inches, but in consequence of the low modulus of elasticity of the 
 mortar they showed a tendency to fail readily by buckling. Some were cut 
 and tested in shorter lengths, but it has not been thought fit to give the 
 detailed results owing to the impossibility of making comparisons. 
 
 The cylinders tested were spiralled, either with single spiral, with two con- 
 centric spirals or with three concentric spirals. When of the same length and 
 when the columns failed by buckling the two concentric spirals only gave an 
 increased ultimate strength of about 11 per cent, over the figure shown by the 
 single spiral. When, however, the column failed more evenly by crushing, the 
 two concentric spirals gave an increase of 24 per cent, of the crushing strength 
 shown by the single spiral, and the three concentric spirals showed an increase of 
 49 per cent, over the crushing strength shown by the single spiral. The stress at 
 which the external covering of concrete on the spirals began to flake off was not 
 appreciably affected by the addition of the concentric spiralling. This stress for 
 cylinders six months old was about 4,550 Ibs. per square inch of the total section. 
 
 4. Cylinders of Annular Section in Cement Mortar. 
 
 Three cylinders, each 2 3 '6 2 inches long, composed of mortar containing 6 cwts. 
 of Portland cement, 11 '8 cubic feet of Seine sand screened to 0'197 inch diameter 
 and gauged with water amounting to 15 '7 per cent, of the weight of the dry 
 materials. The cylinders were kept in air for ten weeks after manufacture ; 
 they were then immersed in fresh water for six weeks, from which they were 
 taken for testing purposes. 
 
 The particulars of the cylinders and the results of the tests are given in 
 Table No. 21. 
 
 5. Two Spiralled Prisms from the Experimental Bridge, built t by M. Considere. 
 
 These prisms were taken from the upper boom of the above bridge, which was 
 of the bowstring type. They were of octagonal section, inscribed circle 9 '8 4 inches 
 diameter, giving a total cross section of 80' 2 9 square inches and an area of spiralled 
 core of 48'67 square inches. 
 
 The first prism tested was 41 inches long. Under a stress of 2,842 Ibs. per 
 square inch of the total section the shortening was 0'0856 per cent, of the original 
 length, and under a stress of 5,684 Ibs. per square inch of the total area or of 
 9,380 Ibs. per square inch of the spiralled core was 0'2 per cent., whilst the outer 
 covering of concrete on the spirals began to fall off. The maximum stress applied 
 was 12,690 Ibs. per square inch of the spiralled core, at which stress the bending 
 of the prism rapidly increased. At the time of the test the prism was about two 
 years old. 
 
 The other prism was 52 inches long and was tested by the application of a 
 load at one-third of the diameter from one face. Up to a stress of 4,670 Ibs. per 
 square inch, reckoned as uniformly distributed over the whole section, no cracking 
 
TESTS OF SPIRALLED PRISMS 
 
 65 
 
 was apparent, and the angle between the end faces of the column wasO'0087 radians. 
 At a stress corresponding to 10,600 Ibs. per square inch, if uniformly spread over 
 the core, the angular deformation was 0*0113 radians, and the column failed by the 
 shearing of the concrete of the core. 
 
 6. Prism of Spiralled Concrete for Compression Test. 
 
 This prism of square section of 10*24 inches side and 37 inches long was 
 composed of fluid concrete poured without any ramming. 
 
 It was reinforced with a spiral of mild steel rod of 0*472 inch diameter 
 
 TABLE No. 21. 
 
 
 
 
 
 
 Results of Test. 
 
 
 No. 
 
 External 
 Diameter 
 
 Internal 
 Diameter 
 
 Area. 
 
 Spiralling. 
 
 Load 
 Applied, 
 Ibs. per 
 
 Mean 
 
 Shorten- 
 ing per 
 
 Remarks. 
 
 
 
 
 
 
 square 
 
 C6nt of 
 
 
 
 
 
 
 
 inch of 
 
 Tr4-ol 
 
 Original 
 
 
 
 
 
 
 
 J. Ot'ft 1 
 
 Section. 
 
 Length. 
 
 
 
 Inches. 
 
 Inches. 
 
 Inches.2 
 
 
 
 
 
 1. 
 
 7*09 
 
 4*92 
 
 20*52 
 
 Iron wire 0*189 inch 
 
 441 
 
 0*016 
 
 
 
 
 
 
 
 diameter in helical 
 
 2,170 
 
 0*096 
 
 The cylinder broke 
 
 
 
 
 
 pitch of 0*787 inch. 
 External diameter 
 
 2,570 
 
 
 in consequence of 
 the failure of the 
 
 
 
 
 
 of spiralling 6*89 
 
 
 
 mortar inside the 
 
 
 
 
 
 inches. 
 
 
 
 cylinder owing to 
 
 
 
 
 
 ' 
 
 
 
 want of support. 
 
 2. 
 
 7-09 
 
 4*53 
 
 23*34 
 
 Iron wire 0*189 inch 
 
 2,300 
 
 
 Do. 
 
 
 
 
 
 diameter in helical 
 
 
 
 
 
 
 
 
 pitch of 0*787 inch. 
 
 
 
 
 
 
 
 
 External diameter 
 
 
 
 
 
 
 
 
 of spiralling 6*69 
 
 
 
 
 
 
 
 
 inches. 
 
 
 
 
 3. 
 
 4*76 
 
 
 17*83 
 
 Not reinforced. 
 
 2,490 
 
 
 Maximum load 
 
 
 
 
 
 
 
 
 supported. 
 
 wound to a mean diameter of 8*39 inches and to a pitch of 1*024 inches, giving a 
 percentage of 4*3, and in addition in the longitudinal direction with seven bars of 
 mild steel of 0*63 inch diameter arranged round the inside of the spiral and in 
 contact with it, giving a percentage of about 2'1. The age of the concrete at the 
 time of the test was about three months. The load was applied axially and the 
 first fissures appeared at a stress of 4,040 Ibs. per square inch of the total area, 
 and the maximum stress supported was 10,200 Ibs. per square inch of the spiralled 
 core. At that stress the shortening was 2 per cent. 
 
 The spiralling was subsequently removed and the resistance to direct crushing 
 of the non-reinforced concrete was found to be 1,124 Ibs. per square inch, measured 
 on a cylinder of 6*89 inches diameter and 18 inches long. 
 
 R.C. F 
 
66 
 
 REINFORCED CONCRETE 
 
 7. Two Prisms Reinforced with Intertwining Spirals. 
 
 These prisms were of the section shown in Fig. 25 and were 19 '68 inches long. 
 
 The spirals were of mild steel wire 0'272 inch diameter, rolled on a cylinder 
 of 5J inches diameter to a pitch of 1 inch. Alternate spirals were wound in 
 opposite directions. Longitudinal reinforcements of mild steel 0'315 inch 
 diameter were placed as shown. 
 
 The concrete consisted of 12 cwts. Portland cement to 14 '3 5 cubic feet of sand 
 sieved to 0'197 inch diameter and 28'7 cubic feet of gravel. In both cases the 
 moulding was done on the flat. For prism No. 1 concrete of a plastic consistency 
 well rammed was employed ; for No. 2 a wetter concrete was used to fill the mould 
 up to the level of the upper side of the spirals, of sufficient fluidity to fill the spirals 
 without ramming between them, the mould was then filled with the mixture of 
 materials quite dry and rammed till the moisture appeared on the surface. The 
 prisms were kept in air for the eight months that elapsed between the time of 
 moulding and the test. 
 
 In both cases at a stress of 4,550 Ibs. per square inch of the total section of the 
 prisms, or 7,110 Ibs. per square inch of the section of the spiralled core, the concrete 
 
 <- 18-5" - ---> 
 
 FIG. 25. 
 
 outside the spiralling began to flake off. The maximum load carried by prism 
 No. 1 was 9,730 Ibs. per square inch of the spiralled core, whilst the maximum 
 stress supported by prism No. 2 was 10,930 Ibs. per square inch of the spiralled 
 core. In both cases the total shortening was 3'6 per cent, of the original length. 
 
 14. Tension Tests on Reinforced Members. 
 
 Two tension members were constructed of twenty-four wires of steel surrounded 
 by a metallic spiral as indicated in Fig. 26, and encased for a length of 6*56 feet. 
 One half of the length of each member was of neat cement, the other half of mortar. 
 
 In member No. 1 the diameter of the longitudinal wires was *177 inch, giving 
 a percentage reinforcement of 5*9. The wires were placed 0'47 inch centre to 
 centre. The mild steel wire in the spiral had a diameter of O'HS inch and a 
 pitch of 1'18 inches. Ten wires were jointed in the member, the junction consist- 
 ing of an overlap of 11 '8 inches, the free ends being bound with soft iron wire. 
 The junctions were -spread over the length of the member. The reinforcing wires, 
 which extended beyond the end of the concrete casing, were gathered together and 
 fixed into a steel cage with spelter, there being a clear distance about 17 inches 
 between the end of the concrete casing and the near face of the metallic anchor block. 
 The concrete casing had a square section of 3 - 15 inches side. 
 
TESTS OF TENSION MEMBERS 
 
 67 
 
 3-IS" 
 
 FIG. 26. 
 
 Member No. 2 was of similar design, but was moulded under a tension of 
 S'9 tons per square inch of the area of the reinforcement, which was maintained 
 up to the moment of the test. The longitudinal 
 wires were OH 8 inch diameter, giving a per- 
 centage reinforcement of 3*4. The mild steel wire 
 constituting the spiralling had a diameter of 
 0-079 inch and a pitch of about half an inch. 
 Five of the wires were in two parts, the junctions 
 being formed by means of a muff consisting of a 
 slightly flattened steel tube 2 inches long, through 
 which the ends of the wires were passed and allowed 
 to project for lengths of 9 inches beyond the muff. 
 The free ends of the wires were in this case moulded 
 into a concrete head. 
 
 The longitudinal reinforcements consisted of a 
 specially hard steel, which had a limit of elasticity 
 in the neighbourhood of its breaking strength. The 
 
 mean resistance to tension for wires of 0'177 inch diameter was 107 tons per 
 square inch, and for wires of 0'118 inch diameter was 115 tons per square inch. 
 
 The cement was Portland cement of French manufacture. Its setting time was 
 4J hours. Its resistance to tension after seven days was 620 Ibs. per square inch, and 
 after twenty- eight days 734 Ibs. per square inch. The mortar consisted of four parts of 
 this cement to five parts by measure of fine siliceous sand passing through a sieve with 
 holes 0'039 inch diameter and without much dust. The division between the 
 mortar and the pure cement was maintained by a sheet-brass diaphragm 0*394 inch 
 thick, with holes to keep the wires at the proper spacings. 
 
 Tension was applied to the member by means of the head of metal in one case 
 and of concrete in the other. 
 
 Member No. 1 was tested after a hardening of one month. This member had 
 several cracks in the part made of pure cement ; none were visible in the part in 
 mortar. In consequence of the difference of inclination of the reinforcing wires 
 between the member and the fixed head the distribution of the load was necessarily 
 very uneven, with the result that the wires began to break one after the other at a 
 stress of 7 4 '3 tons per square inch, calculated as being uniformly spread over the 
 reinforcement. The first fissure in the mortar appeared at a stress of 10 '7 tons per 
 square inch of the reinforcement, assuming the load uniformly distributed. 
 
 Member No. 2 was tested after a hardening of three months. At the time of the 
 test only two small cracks near the extremity in the pure cement were visible. The 
 first crack in the pure cement occurred when a stress of 15*5 tons per square inch 
 of the reinforcement had been applied, and the first fissure in the mortar when that 
 stress was increased to 24 tons per square inch. The tension was not carried 
 beyond 43 tons per square inch of the reinforcement. At that stress the mortar 
 and cement were cracked at right angles to the reinforcement every 4 inches or so. 
 
 P 2 
 
CHAPTER V 
 THE REPORT AND DRAFT REGULATIONS PRESENTED BY THE COMMISSION 
 
 THE Commission arranged its work in the following manner : 
 
 1. It set out to define as precisely as possible the materials constituting rein- 
 forced concrete, the principal conditions they ought to fulfil, and the indispensable 
 precautions to be taken in construction. 
 
 2. It studied the elementary properties of the materials, taken separately and 
 also associated. 
 
 3. The physical and elastic properties thus determined were examined to find, if 
 possible, a rational basis for and a scientific method of calculation. 
 
 4. The results obtained from these processes were compared with successful 
 practice. 
 
 The Report passes in review the principal results obtained from the experimental 
 work of the Commission. 
 
 Variations in Volume Resulting from the Setting of Cement. 
 
 It is known that, extending over some months, mortars and concretes exposed to 
 air undergo contraction during setting, which is greater the higher the proportion of 
 cement. This contraction leads to internal stresses, tension in the concrete and 
 compression in the reinforcement. When this contraction is opposed by external 
 connections, serious cracking frequently results. 
 
 The concrete employed in the tests was of the proportion most frequently 
 employed in open-air work in France viz., 6 cwts. Portland cement, 28 '7 cubic 
 feet of gravel and 14'4 cubic feet of sand, which, when rammed into the work, give 
 about 36 cubic feet of concrete, or about 1^ cubic yards. 
 
 Although the contraction varies somewhat with the length and section of the 
 member, the Commission put it at 0'025 per cent, when it is exposed to the 
 weather immediately after manufacture, and 0'020 per cent, when it is maintained 
 humid for the first three weeks. 
 
 The Commission did not insist that the contraction should be taken account of, 
 except in long members. 
 
 Thermal Variations of Volume. 
 
 No new experiments were made on this subject, tjut it appeared from the 
 collected results of previous experiments that a coefficient of expansion per 
 100 degrees Centigrade of 0*0011, or (HI per cent. (0-00061 per 100 degrees 
 Fahrenheit), might 'without sensible error be adopted, and that the coefficients of 
 expansion of concrete and steel might be taken as equal. 
 
 From measurements made on an arched bridge at Chatelherault, it was demon- 
 strated that reinforced concrete structures are only very slightly sensible to hourly 
 variations of temperature, but that they assume the mean daily temperature. 
 
RESISTANCE TO CRUSHING 69 
 
 Resistance and Deformation of Concrete Submitted to Tension. 
 
 When concrete, not reinforced, is submitted to simple tension, the tension 
 increases proportionally to the elongation until rupture is produced for an 
 elongation of at least, in general, O'Ol per cent. 
 
 When concrete, not reinforced, is submitted to bending, the part in tension 
 has a certain ductility. From a limit which appears very near the maximum 
 elongation when submitted to simple tension, the modulus of elasticity of the 
 concrete in the tension part of the beam diminishes very markedly, and 
 rupture is produced for an elongation which generally lies between O'Ol and 
 0-02 per cent. 
 
 Concrete properly prepared and reinforced becomes much more ductile still. 
 From the experiments of the Commission it was established that the elongation 
 of the concrete before rupture went up to O135 per cent., and it was observed 
 that until an elongation between O'Ol and 0'02 per cent, was reached, the 
 concrete had practically the same modulus of elasticity as concrete not reinforced. 
 Beyond this limit the modulus of elasticity is sensibly zero ; or, in other words, 
 whilst the elongation increases, the tension of the concrete remains very nearly 
 constant and in the neighbourhood of the resistance of concrete not reinforced. 
 
 Resistance to Crushing. 
 
 Table No. 22, pp. 70 -73, contains a resume of the results of the experi- 
 ments made by the Commission and of those made by Professor Bach of Stuttgart. 
 
 In the first six divisions the particulars characterising each series of experiments 
 are indicated. In division 7 is given the increase of resistance in Ibs. per square 
 inch of total section which the reinforcement has produced. The figure relative 
 to each column was found by deducting from its resistance that of a test column 
 not reinforced and made of the same concrete. 
 
 To permit of the comparison of the different types of reinforcement, a common 
 measure has been devised for them as follows : 
 
 Suppose the column to be reinforced with an equivalent bar having the same 
 total volume as all the reinforcements of whatever kind in the column. Divide 
 the total increase of resistance by the area of this equivalent bar. The quotient 
 will represent the increase of resistance of the concrete produced by each square 
 inch of reinforcement. 
 
 The figures given in Table No. 22 call for the following remarks : 
 
 In Series A, in order to study the slipping of the reinforcements, the concrete 
 covering the ends of the longitudinal bars was removed. As a result, the resistance 
 to crushing has been almost exactly the same, although the percentage of metal 
 varied from 0*28 to 3'97 per cent. 
 
 In Series B, prepared conformably to the programme of the Society of German 
 Reinforced Concrete Engineers, the ends of the longitudinal bars were 2 inches 
 from the ends of the columns and left buried in the concrete. The resistance per 
 square inch of the equivalent bars in these cases varied from 6 -6 7 to 12 '3 3 tons 
 per square inch, the former figure being that corresponding to the large longitudinal 
 bars with the interties spaced widely apart, the latter to small bars with more closely 
 spaced interties. 
 
 Experiments A and B having drawn attention to the importance of the end 
 conditions of the longitudinal bars, there was realised in Series C the most perfect 
 arrangement from this point of view. The bars were cut square, and adjusted to 
 
70 
 
 REINFORCED CONCRETE 
 
 
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RESISTANCE TO CRUSHING 
 
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74 REINFORCED CONCRETE 
 
 bear exactly on the heads of the testing machine. The columns of this series, which 
 were made with the minimum quantity of water necessary, have shown an increase 
 of strength of 15-25 tons per square inch of the equivalent bar, whilst those made 
 by pouring the fluid concrete into the mould only showed an increase of 5 '9 7 tons 
 per square inch at the end of twenty-eight days. 
 
 In the tests of Series D, the columns were 6'56 feet and 13 - 12 feet in length. 
 Great differences of resistance were found in the non -reinforced columns of these 
 lengths. 1 This fact diminishes the confidence one might have in the results of 
 this series, and explains to some extent how identical reinforcements have given 
 augmentations of resistance of 6 '4 and 19 '8 tons per square inch in columns which 
 only differ by the proportions of the concrete. There is reason to set aside these 
 extreme values. 
 
 All the columns of the first four series crushed without notable flexion. 
 
 The columns fulfilling the conditions which the Commission judged necessary 
 to assure the efficiency of the spiralling have given the results B', C' and D', 
 which correspond to the Series B, C and D of the columns reinforced with intertied 
 longitudinal bars. 
 
 The columns of Series B' were made with little care in order to determine the 
 minimum resistance one might obtain on works. For example, the spacing of the 
 spirals from centre to centre has varied from half an inch to 3 inches in one single 
 piece, and the longitudinal bars from 1 inches to 5 inches. 
 
 In Series C' it should be noticed that the spiralling has given to concrete 
 
 1 The non-reinforced columns of 6'56 and 13'12 feet long were made at the same time as the 
 columns of Series D and D' to serve as references. They were formed of the same concrete, and 
 were rammed with the same care. Their resistance to crushing without buckling was for 
 concrete containing 
 
 7 cwts. cement 3,440 Ibs. per square inch for columns 6*56 feet long. 
 2,820 do. do. 13'12 do. 
 
 Difference 620 Ibs. per square inch. 
 
 10 cwts. cement 2,630 Ibs. per square inch for columns 6-56 feet long. 
 2,090 do. do. 13-12 do. 
 
 540 Ibs. per square inch. 
 
 To determine the cause of the differences of resistance of the columns 6'56 and 13'12 feet long 
 pieces were cut from the top and the base of each of the columns, and it was found that the 
 resistance of the base of each column exceeded that of the upper part by 1,365 and 2,620 Ibs. per 
 square inch for concrete containing 7 cwts. and 10 cwts. of cement respectively. 
 
 The explanation of these facts appears to be the following. The concrete gives up during 
 the ramming and up till the commencement of setting part of the excess of water, which must 
 in every case be added to facilitate the placing of the concrete. The water which thus comes from 
 the lower beds adds itself in the concrete superposed to that which the latter contains. Thus the 
 higher up one goes in the column the wetter is the concrete, with the above-mentioned result. 
 The effect is the more marked the richer the concrete in cement. For the interpretation of the 
 results of the experiments of Series D', which included columns 7'55, 8'53 and 9'84 feet long, 
 it was observed that the resistance of the concrete in these cases varied according to a linear 
 law between the resistances observed for the concrete of 6-56 feet and 13*12 feet. 
 
 It is important to point out that in order to maintain a uniform quality throughout the whole 
 height of columns it is necessary to employ drier concrete as the work ascends, and it is impor- 
 tant to dispose the reinforcements in such a way as to permit of the employment of concrete 
 gauged without excess of water. 
 
 These facts show how difficult is the comparison of reinforced pieces of different types and 
 of the unreinforced pieces of the same type cast for comparison of the strength of the concrete. 
 Pieces to be compared should have dimensions such that the final degree of humidity of the 
 concrete is the same. 
 
 These facts explain the contradictions existing in experiments apparently comparable, and 
 lead one to take account not of the isolated anomalies, but only of the main lines of the results 
 of experiments. 
 
RESISTANCE TO CRUSHING 75 
 
 poured without ramming and tested after twenty-eight days the same increase of 
 resistance as concrete rammed with care. 
 
 The columns of Series D' were prepared to study the resistance to buckling. 
 Setting aside those indicated as having buckled without crushing, the others show 
 an increase of crushing resistance, per square inch of the cross sectional area of the 
 equivalent bar having the same volume as the longitudinals and spirals together, 
 of 28-5 tons to 40 tons. 
 
 A number of columns tested at Stuttgart did not fulfil the conditions necessary 
 to give to the spiralling the proper efficiency. In one case the longitudinal 
 reinforcements were too feeble, in the other the pitch of the spirals was too great. 
 The results show analogous increases to those of columns reinforced with longitudinal 
 intertied bars. These experiments thus establish a transition between the two 
 types of reinforcement. The following description of the test of a strongly 
 spiralled column, which consequently presents features highly characteristic of this 
 type of reinforcement, is given to enable a clear idea to be formed of the phenomena 
 met with during the loading to destruction of such a column. 
 
 The column was 6 '56 feet long, composed of concrete containing 7 cwts. of 
 cement and reinforced to a total percentage of 4 -91. The first fissures in the 
 concrete covering the spirals were apparent when the pressure had attained 
 4,370 Ibs. per square inch of the total section. The pressure was increased to 
 a maximum of 7,050 Ibs. per square inch, when buckling commenced. The 
 loading was maintained until the moment when the deflection attained a value 
 of 4 inches, the load at this time corresponding to a stress of 4,240 Ibs. 
 per square inch of the spiralled core, the external envelope of concrete over 
 the spirals having by this time almost entirely disappeared. In the column thus 
 bent there was no trace of crushing of^ the spiralled core, but in the parts of 
 greatest curvature radial tension fissures were observed tending to cut the concrete 
 in slices. 
 
 In columns which have crushed without bending, the failure of the column is 
 produced sometimes by the thinning out and rupture of a spiral, sometimes by the 
 shearing of the concrete on oblique planes. 
 
 Both in the columns which failed by flexion and those which ruptured, the 
 concrete of the core away from the vicinity of the rupture presented no traces of 
 alteration. This was demonstrated by cutting out test prisms from the cores of 
 columns which had resisted high pressures. For example, crushing resistances of 
 3,930 and 2,470 Ibs. per square inch were obtained from prisms cut from the base 
 and the top respectively of a column containing 7 cwts. Portland cement and 
 reinforced to 6*34 per cent., and which had resisted a pressure of 9,080 Ibs. per 
 square inch of the spiralled core. A column reinforced to 4'91 per cent., which 
 had resisted a pressure of 8,740 Ibs. per square inch, gave corresponding resistances 
 of 2,260 and 2,030 Ibs. per square inch respectively. 
 
 These facts indicate that cracking takes place prematurely in the outer cylinder 
 of concrete covering the spirals, but that that does not compromise the solidity 
 of the core on which the resistance to crushing depends. Such cracking must, 
 nevertheless, be avoided in practice. 
 
 The experiments of Series D showed that, on the average, the pressure under 
 which the first fissures appeared exceeded by about 940 Ibs. per square inch the 
 resistance of the non-reinforced columns, and that the excess resistance was 
 almost the same for short columns reinforced to nearly 5 per cent., and for 
 long columns only reinforced to 2 per cent. The pressures which spiralled 
 pieces can resist without sustaining any damage whatever depends thus on the 
 
76 REINFORCED CONCRETE 
 
 inherent resistance of the concrete, and is but little augmented with the percentage 
 of metal. 
 
 In the experiments at Stuttgart, the results point to the same conclusions. In 
 that case the resistance at which cracking of the envelope of the spirals took place 
 exceeded by about 1,400 Ibs. the resistance of the non-reinforced columns. 
 
 It may safely be allowed that in ordinary concrete, containing 6 cwt. of cement, 
 for which a resistance of 2,280 Ibs. per square inch may be reckoned on, the load 
 which causes cracking in spiralled members is 2,850 Ibs. per square inch. In 
 members thus proportioned the pressure might thus be limited to 1,440 Ibs. per 
 square inch; that is, to 62 per cent, of the inherent resistance of the concrete, no 
 matter how high the percentage reinforcement might be. 
 
 The pressure being thus limited to 1,440 Ibs. per square inch for concretes of 
 middling quality, and to 1,600 or 1,700 Ibs. per square inch at the most for concretes 
 of the best quality, and on the other hand, the coefficient of security 3, 4 or 5 being 
 applied as regards crushing or buckling phenomena, it is evident that there is no reason 
 for increasing the percentage of metal beyond that necessary to obtain resistances of 
 4,800 to 8,500 Ibs. per square inch. For this reason the experiments made at the 
 Laboratory of the Ecole des Fonts et Chaussees on cylinders very strongly spiralled, 
 in which resistances up to 25, 600 Ibs. per square inch were obtained, have not been 
 described. These experiments, however, show that the useful effect of spiralling 
 extends to very wide limits. 
 
 When compression tests on concrete are made, creaking noises proceed from the 
 concrete when the stress reaches a value which varies within somewhat wide limits. 
 In the non-reinforced columns of Series D noises were heard, sometimes near the 
 crushing load, sometimes when the stresses were less than 720 Ibs. per square inch. 
 In spiralled and longitudinally reinforced pieces the first noises were heard sometimes 
 when the stress was in the neighbourhood of the crushing strength of ordinary 
 concrete, sometimes when that figure had been exceeded by 700 Ibs. per square inch. 
 The cause of these noises is not known, but it is noticed that they precede but slightly 
 the crushing of non-reinforced or longitudinally reinforced columns, and the cracking 
 of the envelope in spirally reinforced columns. It is thus possible that these noises 
 indicate to the ear the commencement of processes which are not visible to 
 the eye. 
 
 The great ductility of spiralled concrete is another phenomenon which falls to be 
 recorded. In short pieces, in which sensible uniformity of quality might be looked 
 for, the shortening observed was from 1 to 3*6 per cent, of the original length. In 
 longer pieces, where there is considerable variation from the top to the bottom, the 
 shortening measured at the middle of the length has varied from 0'5 to 0*75 per 
 cent, in columns 6 feet long, and from 0*3 to 0'4 per cent, in longer columns. The 
 upper part, which had the least resistance, yielded before the concrete elsewhere had 
 resisted the maximum load, and therefore the maximum deformation of which it was 
 capable. The considerable bending observed in spiralled pieces is another proof of 
 the ductility of concrete reinforced in this way. 
 
 Pitch of Spirals. 
 
 The network of spirals and longitudinal reinforcements which constitutes the 
 cage is intended to prevent the transverse swelling of the concrete under the load. 
 It opposes the escape of material between the meshes, and these ought evidently to 
 be the closer, the greater the load designed for. Only experience can dictate the 
 proper arrangement from this point of view. 
 
MODULUS OF ELASTICITY 77 
 
 In the Stuttgart experiments the spacing centre to centre of the spirals was from 
 to in columns which gave medium results, and in those in which the 
 
 resistances were conformable to the draft provisions of the Commission, d being the 
 diameter of the circle inscribed in the octagon forming the transverse section of the 
 column. 
 
 The feebly spiralled columns tried with success by Professor Guidi at Turin had 
 
 the spirals spaced at . 
 o 
 
 In the columns of Series D good results were obtained with a spacing of the spirals 
 
 of for greater resistances, and - for less. 
 8 4'4 
 
 The Commission recommended that the pitch of the spirals be not unduly 
 diminished, owing to the difficulty occasioned thereby of ramming the concrete. 
 
 As all the experiments point to the ramming having a considerable influence on 
 the mechanical qualities of the concrete, it is suggested that the efficiency of the 
 network preventing lateral spreading should be increased for increasing loads by 
 augmenting the section of the longitudinal rods rather than by decreasing the pitch 
 of the spirals. 
 
 Elasticity. 
 
 The irregularity of concrete is still greater from the point of view of elasticity 
 than from that of resistance. From a concrete composed of 6 cwts. Portland 
 cement, 14*35 cubic feet of sand, and 28*70 cubic feet of gravel the Commission 
 has obtained moduli of elasticity under a light load varying from 2-28 X 10 6 
 to 5 '6 9 X 10 6 Ibs. per inch 2 , according to the quantity of water used in gauging and 
 the method of ramming. 
 
 The modulus of non-reinforced concrete diminishes as the load increases, 
 especially beyond a limit in the neighbourhood of one-half or two-thirds of the 
 crushing load, and it is necessary, having regard to buckling, to take into considera- 
 tion the modulus under pressures superior to the working load. Consequently, a 
 modulus of elasticity of 2,130,000 Ibs. per square inch, or 950 tons per square inch, 
 may be properly allowed. 
 
 This irregularity in non-reinforced concrete necessarily shows itself in the tests 
 of reinforced columns. 
 
 In Series A, the non-reinforced column had not the same dimensions as the 
 reinforced one, and the results of this series cannot be compared. Only the columns 
 of 15-75 inch side, in which the percentage varied from 0'28 per cent, to 3*97 per 
 cent., are suitable for purposes of comparison. 
 
 There has been calculated the total resistance per square inch which the 
 different columns gave when their shortenings had the same value of 0'02 per cent. 
 In order to compare two columns the differences of their unital resistances has 
 been divided by the shortening for which the comparison was made, and by the 
 difference in the unital reinforcement. 1 The quotient gives a measure of the 
 useful elastic effect of the excess of reinforcement in the more heavily reinforced 
 column, and it ought, hypothetically, for average quality of steel to be about 
 29,100,000 Ibs. per inch 2 , or 13,000 tons per inch 2 if the reinforced columns were 
 formed of identical materials simply associated in a common shortening. 
 
 1 The unital reinforcement is the area of equivalent reinforcement per unit area of column 
 or the percentage reinforcement -r- 100. 
 
78 REINFOKCED CONCRETE 
 
 On comparing the columns reinforced to 3*97 per cent, and - 28 per cent, 
 respectively, an apparent modulus of elasticity of 1,710,000 Ibs. per inch 2 , or 
 7,600 tons per inch 2 , was found for the metal in excess of 0*28 per cent. 
 
 In Series C and D similar calculations give the apparent modulus of elasticity 
 of the metal as varying from 17,100,000 Ibs. per inch 2 , or 7,600 tons per inch 2 , to 
 10,000,000 Ibs. per inch 2 , or 4,400 tons per inch. 2 
 
 It was found experimentally in series A, that except in the neighbourhood 
 of the ends, relative slipping of the concrete and steel was absolutely negligible. 
 
 These facts lead to the conclusion that since the metal does not slip and in 
 consequence sustains the same shortening as the surrounding concrete, it certainly 
 furnishes resistances corresponding to its modulus of elasticity. Its apparent effect 
 having been much less, we are led to conclude that the modulus of elasticity of the 
 concrete has been less in the reinforced columns in question than in those not 
 reinforced. This weakness in the concrete might be due to three possible causes : 
 either an increase in the quantity of water used in mixing the concrete, owing to the 
 greater ease of working it in the moulds, or the less perfection of ramming owing to 
 the constraint of the reinforcements, or owing to the prevention by the reinforce- 
 ments of the full contraction of the concrete during its setting, and which, perhaps, 
 will hinder it from acquiring all the mechanical qualities of which it is capable. 
 
 The first cause suggested did not operate in any of the experiments made by 
 the Commission, because the quantity of water used was weighed with care, and the 
 second did not affect the columns of Series A, as these were all similar. 
 
 Whilst the experiments of the Commission and also those of Professor Guidi at 
 Turin gave results for the elasticity of the metal inferior to that indicated by the 
 theory of elasticity, the experiments of Professor Bach at Stuttgart, under the 
 auspices of the Society of German Reinforced Concrete Engineers, gave results for 
 the moduli of elasticity of longitudinal reinforcements corresponding sensibly to the 
 figures deduced from theory. 
 
 All that may be affirmed regarding the elasticity of pieces longitudinally 
 reinforced is that in careful experiments the apparent elastic effect of the longitu- 
 dinal bars has varied from less than half the value indicated by the theory of 
 elasticity to values sensibly equal to that value. Under these conditions it 
 seemed reasonable to adopt the simplest solution, which consists in allowing from 
 the point of view of elasticity the coefficient of equivalence between the metal and 
 the concrete which were adopted from the point of view of resistance to crushing. 
 These coefficients vary from 8 to 15, combined with a modulus of elasticity 
 2,130,000 Ibs. per square inch, or 952 tons per square inch ; they attribute to the 
 metal values of the modulus of elasticity varying apparently from 7,616 tons per 
 inch 2 to 14,280 tons per square inch, which agree with the results obtained 
 at Paris, Stuttgart, and Turin. 
 
 The causes indicated above that diminish the coefficient of elasticity act in the 
 same sense on the resistance of concrete to crushing. 
 
 The Commission decided that whilst awaiting further experiments on the 
 effect of transverse reinforcement or spiralling on the elasticity of concrete, it is 
 prudent to entirely neglect any increase which such reinforcement might give. 
 
 Deformation of Plane Sections in Bending. 
 
 Although not rigorously exact, the hypothesis of the conservation of plane 
 sections serves as a rational basis to the theory of resistance of homogeneous 
 materials. Its application to a heterogeneous material such as reinforced concrete 
 
BENDING PHENOMENA 79 
 
 a priori^ open to serious doubt. One might readily understand that the slipping 
 of the reinforcements and the cracking of the concrete in tension would make the 
 hypothesis entirely unworkable. 
 
 A very great number of experiments made on the beams 7*87 inches X 
 15*75 inches, and 13' 12 feet span, have proved that sections originally plane remain 
 sensibly so during bending, except in the immediate neighbourhood of the supports 
 and of the points of application of heavy concentrated loads. 
 
 Away from these exceptional points, where in actual structures it might be 
 useful to consider specially the strength from the point of view of local stresses, 
 the warping of sections originally plane does not modify notably the longitudinal 
 deformations, which serve as a basis for the calculation of deflected pieces. Any 
 deviation from the hypothesis of the conservation of plane sections may thus, 
 without sensible error in the calculation of tensions or compressions, be neglected. 
 
 Application of the Laws of Simple Deformations to the Calculations of Bent 
 
 Pieces. 
 
 In the theory of bending of homogeneous materials, it is allowed that to a 
 certain longitudinal elongation or contraction there corresponds a certain tension 
 or compression in bending and also in traction or thrust. 
 
 To discover to what extent this assumption is applicable to reinforced concrete, 
 the following investigations were carried out: 
 
 A number of prisms were made simultaneously with the beams of 7*87 inches X 
 15*75 inches section, and 13*12 feet span, and the moduli of elasticity of the 
 concrete and the reinforcements respectively were measured. Applying with these 
 figures the above hypothesis, there was determined by calculation the position of 
 the neutral axis, in the period of deformation after the limit of elasticity of the 
 stretched concrete had been passed ; that is, in the period in which the tension of 
 the elongated concrete ought to be constant. Results were found almost rigorously 
 to conform to those given by actual measurement during experiment. 
 
 It has been concluded that the hypothesis in question might, concurrently with 
 the hypothesis of the conservation of plane sections during bending, be safely 
 applied in calculation, assuming at the same time that the laws of deformation by 
 tension or thrust are those already formulated. 
 
 Adhesion of the Concrete to the Metal. 
 
 For simple tension or compression on isolated bars imbedded in concrete the 
 Commission found values of the resistance to unbedding of from 97 to 420 Ibs. per 
 square inch of the surface of contact. For bars surrounded by spirals or placed 
 in the folds of perpendicular stirrups, these figures varied from 225 to 560 Ibs. per 
 square inch. 
 
 These figures give no indication, however, of the tendency to slip in members 
 where bending imposes other stresses on the member. For this information, beams 
 in which failure took place by slipping of the reinforcements were studied, and in 
 doing so it was assumed, according to the usual hypothesis conform to the theory of 
 perfectly elastic bodies, that the slipping stress varied with the shearing stress. 
 Consequently the resistance to slipping furnished by the ends of the longitudinal 
 reinforcement, which projected beyond the supports, was neglected, since there is 
 no shearing force there. The values of the adhesion thus found varied from 185 
 to 213 Ibs. per square inch. Other experimenters applying the same mode of 
 calculation have found similar values. 
 
80 REINFORCED CONCRETE 
 
 Resistance to Shearing Forces. 
 
 The experiments indicate that whilst vertical stirrups are useful in a beam just 
 before the formation of cracks and after cracks have formed, stirrups inclined in the 
 direction of the tension, or longitudinal reinforcing bars bent upwards towards the 
 supports, give much more help to the concrete under working loads. 
 
 Beams which were reinforced in both tension and compression areas, and which 
 had no stirrups, continued to support a load in virtue of the resistance of the 
 reinforcements after the concrete had fissured for J of its full depth in the part 
 exposed to shear. The resistance of the reinforcements to the shearing forces was 
 probably aided by a kind of frictional resistance in the compression area of the 
 beam. 
 
 Experiments on the Eesistance and Deformation of Works Constructed for the 
 
 Exhibition of 1900. 
 
 Experiments were made under the direction of M. Rabut on 
 
 1. Two floor slabs. 
 
 2. A ribbed floor. 
 
 3. A footbridge. 
 
 4. A retaining wall. 
 
 These structures were designed by the Hennebique empirical formulae, and 
 constructed according to the usual practice of that firm. The experiments were 
 carried out to determine 
 
 1. What margin of security might be relied on. 
 
 2. What degree of solidarity there was between the different members. 
 
 3. If any relation could be determined between the loads and the deformations. 
 
 On the first point the experiments showed that in the case of the slabs they 
 carried a surcharge equal to from five to six times that for which they had been 
 designed. The ribbed floor supported without a rupture a load three to four 
 times greater than that for which it had been designed, whilst the retaining wall 
 withstood a very much greater load than that which ought to result from the thrust 
 of the earth. 
 
 On the second point it was observed that concentrated loads were distributed not 
 only on the single rib on which they rested, but sometimes on five and even on as 
 many as seven. 
 
 On the third point, although a precise statement of the relation between the 
 deflections and the stress on the steel or concrete has not been possible, the 
 fact that the deflections under growing loads follows a continuous law, in spite of 
 the formation of cracks, was clearly demonstrated. 
 
 Detailed information regarding the design and construction of these structures, 
 together with the records of the tests and the analyses of the results, form Part I. 
 of the French edition of the Report. 
 
CHAPTER VI 
 
 SOME CONCLUSIONS FROM THE STUDY OF THE ELEMENTARY PROPERTIES OF THE 
 MATERIALS CONSTITUTING REINFORCED CONCRETE 
 
 Calculation of Stresses and Deformations. 
 
 ONCE the hypothesis of the conservation of plane sections is accepted with 
 reference to reinforced concrete structures, the deformations and the stresses under 
 any loading whatever may be calculated from the known properties of the com- 
 ponents, but in every case the calculation is a complicated one and frequently 
 almost insoluble. 
 
 So far as stresses are concerned, the tension in the concrete ought to be 
 neglected, which leads to a very considerable simplification in the calculations, and 
 the Commission suggested that that method should also be applied to the calculation 
 of deformations. The deformations thus calculated are in excess of those to be 
 expected, but the calculated values might be corrected by means of a coefficient 
 of correction, obtained by a comparison of the calculated value with that actually 
 found in a large number of experiments. Such a coefficient would be a function 
 of the percentage reinforcement. 
 
 Coefficients of Security. 
 
 The Commission were of opinion that, taking into account the excellent protection 
 afforded to the metal from abrasion, oxidation, and largely from shocks, and that 
 in well-designed reinforcements holes and grooves are avoided, the metal may 
 safely be stressed by working loads to half its apparent elastic limit. 
 
 The risk incurred in exceeding the limit of elasticity is twofold viz., the rapid 
 increase of the deflection and the destruction of the adhesion. The regulations 
 require the help afforded by the concrete to be neglected in calculating the tension 
 in reinforcements as the reinforcements have to resist the whole tension 
 across any crack that may be formed. Diminution of adhesion as a result 
 of high tension is likely to take place only at the centre of simple spans or over 
 the supports of a continuous beam. In the former case the shear near the middle 
 of the span is generally small, but at the supports of a continuous girder the shears 
 are maxima, so that in this case care must be taken that the slipping stress is not 
 excessive. 
 
 The maximum compression fixed for concrete implies a certain shortening 
 of the latter, and consequently of the steel embedded in it. The compression corre- 
 sponding to this strain of the steel is always well within half the elastic limit. 
 
 The Commission proposed as a factor of safety for the concrete of 3'5, owing 
 to the large influence workmanship has on its qualities. 
 
 Simplification of the Calculations. 
 
 In Table No. 22, on p. 70, in the figures making comparison of the strength 
 
 of columns reinforced with longitudinal bars intertied, the effects of the longitudinals 
 
 and the interties are not separated, and the coefficient of equivalence is taken at the 
 
 same value, 8 to 1 5 for both. This is to some extent justified by an examination 
 
 R.C. G 
 
82 
 
 REINFORCED CONCRETE. 
 
 of the Stuttgart results. There three types of column were tested, which in 
 addition to the longitudinal bars of 0-591 inch diameter, had interties spaced at 
 9*84, 4'92 and 2*46 inches. Differences of resistance were found varying 
 from 8*2 to 14 '6 tons per square inch of the section of the equivalent 
 longitudinal bar, having a volume equal to that of the ligatures. These figures 
 correspond to the figures given by the longitudinal bars. 
 
 On the contrary, longitudinals and spirals produce widely different effects, which 
 must not be confounded in calculations. In order that steel of middling quality 
 may give a resistance of about 16 tons per square inch, which is generally about its 
 apparent limit of elasticity, it must undergo a contraction of about O'l per cent. 
 Spiralled concrete supports before crushing contractions of from 1 to 3 per cent. 
 The resistances provided by the enclosed longitudinal bars are thus not less than 
 16 tons per inch 2 , and are not much beyond this figure, as once the yield point 
 is passed the resistance increases but slowly with the strain. It follows that one 
 is very near the truth in deducting from the total resistance of a spiralled column, 
 first the resistance of the non-reinforced prism of the same dimensions, then the 
 resistance of the longitudinal bars, reckoned at 16 tons per square inch, and 
 attributing the remainder of the effect to the spiralling. 
 
 In Table No. 23 the results are given of this calculation made for the columns 
 figuring in Table No. 22 (division 8, marked (1) to (12)), which fulfilled the conditions 
 indicated by the Commission, and which did not buckle. The second horizontal 
 row gives the increase in strength, after deducting the resistance of the non-rein- 
 forced comparison columns, reckoned in tons per square inch of the equivalent longi- 
 tudinal reinforcing bar, having the same volume as the whole of the metallic 
 reinforcing. The lowest line gives the results when the equivalent longitudinal bar 
 has the same volume as the spirals only, and when in addition to the resistance of the 
 non-reinforced comparison columns, the resistance of the longitudinal reinforcement 
 is also deducted. 
 
 TABLE No. 23. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 32-4 
 
 26-0 
 
 28-3 
 
 36-2 
 
 35-2 
 
 28-6 
 
 39-4 
 
 35-6 
 
 35-6 
 
 33-0 
 
 36-8 
 
 40-0 
 
 65-4 
 
 36-0 
 
 35-2 
 
 45-4 
 
 44-5 
 
 32-4 
 
 49-5 
 
 43-8 
 
 43-8 
 
 49-5 
 
 55-8 
 
 57-8 
 
 These figures complete the elements necessary for the design of compression 
 pieces. 
 
 The Commission pointed out that there is necessarily no hard-and-fast division 
 between longitudinally reinforced columns and spiralled columns ; the two types 
 merge into each other in their extreme examples, but that the role of longitudinal 
 reinforcement is essentially different from that of transverse reinforcement, the 
 former actually resisting the longitudinal stress, the latter simply helping the 
 enclosed concrete to resist it. 
 
 The Commission suggested values of m the coefficient of equivalence of the longi- 
 tudinal reinforcement and the concrete varying from 8 to 15. Similar values for 
 ra' would apply, as previously explained, to the lateral interties between the 
 longitudinals, whilst for spiralling the values of m would vary from 8 to 32. In 
 
CALCULATION OF CRUSHING RESISTANCE 
 
 83 
 
 every case stress was laid on the necessity for keeping the compression of the concrete 
 within 62 per cent, of the resistance of non-reinforced concrete. 
 
 Although in the later stages of the test of a reinforced column the spiralled 
 core alone resists the whole load, it is not advisable, except under certain circum- 
 stances, to complicate the calculations by relating the resistance to the area of the 
 core instead of to the total area of the column. It might be advisable to do so 
 when the ratio of the total section to the core differed from 140 or 150 to 100. 
 
 So long as the ratio of length of a column to its least transverse dimension is 
 not more than 20, no calculations relating to buckling need be made. 
 
 When buckling must be taken into account, either Euler's or Rankine's 
 formula may be used. The former is rigorously applicable only to perfectly 
 straight and symmetrical pieces, and for its application the modulus of elasticity 
 for all the stresses concerned must be known. As the modulus of elasticity of 
 concrete does not fall below 950 tons per square inch, the resistance to buckling 
 of non-reinforced columns may be calculated, using that figure (see p. 17). 
 
 For reinforced columns of the ordinary type the section As of metal may be 
 replaced by a section mAs of concrete and Euler's formula applied, using the above- 
 mentioned value for the modulus of elasticity, m having the values previously 
 defined. 
 
 In the case of a strongly spiralled column, where the stress that might be 
 applied without fear of crushing approaches that at which the limit of elasticity 
 rapidly diminishes, the question is rather more complicated. 
 
 In Table No. 22 there is indicated the resistance attributed to the reinforce- 
 ment, but in studying buckling the total resistance of each column has to be taken 
 into account. This is given in division 4 -of Table No. 24. 
 
 It was pointed out on p. 74 that the resistance of the comparison columns 
 varied from 2,090 Ibs. to 3,440 Ibs. per "square inch. In order to render the 
 figures comparable amongst themselves, it was necessary to correct the observed 
 resistances to those which would have been obtained if the concrete had had a 
 uniform resistance of 2,280 Ibs. per square inch. 
 
 In division 7 of Table No. 24 there is indicated the resistances to crushing, cal- 
 culated by attributing to the concrete a resistance of 2,280 Ibs. per square inch, 
 together with a coefficient of equivalence of 15 for the longitudinal and 32 for the 
 spiral reinforcements. 
 
 TABLE No. 24. 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 Lengths 
 of 
 Columns. 
 
 Percentage 
 of Longi- 
 tudinal 
 Bars. 
 
 Percentage 
 of 
 Spirals. 
 
 Maximum Load 
 Supported in Ibs. 
 per square inch of 
 Total Section. 
 
 Corrected Loads 
 lor Columns 
 which Crushed. 
 
 Corrected Loads 
 for Columns 
 which Buckled. 
 
 Calculated 
 Crushing 
 Resistances. 
 
 Feet. 
 
 
 
 
 Lbs. per 
 square inch. 
 
 Lbs. per 
 square inch. 
 
 Lbs. per 
 square inch. 
 
 6-56 
 
 1-42 
 
 4-92 
 
 7,2806,690 
 
 6,350 
 
 6,110 
 
 6,325 
 
 6-56 
 
 1-42 
 
 3-49 
 
 7,0356,510 
 
 
 
 5,8706,170 
 
 5,290 
 
 6-56 
 
 1-42 
 
 3-46 
 
 6,1105,840 
 
 
 
 4,9505,930 
 
 5,260 
 
 7-54 
 
 1-15 
 
 2-58 
 
 6,2705,830 
 
 5,570 
 
 5,220 
 
 4,550 
 
 8-53 
 
 0-91 
 
 2-05 
 
 5,4604,805 
 
 4,635 
 
 4,510 
 
 4,080 
 
 9-84 
 
 0-69 
 
 1-64 
 
 4,2704,223 
 
 4,135 
 
 3,430 
 
 3,690 
 
 13-12 
 
 0-91 
 
 1-09 
 
 4,3503,780 
 
 3,968 
 
 
 
 3,400 
 
 13-12 
 
 0-91 
 
 1-13 
 
 4,0803,880 
 
 3,5504,070 
 
 3,810 
 
 3,370 
 
 G 2 
 
84 
 
 REINFORCED CONCRETE 
 
 In each case, with one exception, the crushing loads are in excess of those 
 calculated. In the case where the crushing load was actually less than the cal- 
 culated crushing load, the percentage of reinforcement was the greatest, the 
 longitudinals amounting to 1'42 per cent, and the spirals to 4 - 92 per cent. The 
 draft regulations suggested by the Commission indicated that the ratio between 
 the percentage of longitudinal reinforcement and spiral reinforcement should not 
 fall below J. In the column in question this condition was not observed, and, 
 further, the pitch of the spirals (0'39 inch) did not allow of good ramming. 
 
 It may be observed also, taking into account the general behaviour of the 
 phenomena, rather than the anomalies, that the loads which have produced 
 buckling, corrected as above described, are greater than the calculated resistances 
 to crushing. 
 
 If, thus, for a column having the same proportions and the same percentage 
 reinforcement as one or other of the columns tested, the crushing resistance is 
 calculated by the above method, using any given factor of safety from that point of 
 view, then as regards buckling the factor of safety will be at least equal to that 
 chosen against crushing. 
 
 It will be the same in a greater degree for columns less reinforced than those 
 the results of which are tabulated, since the modulus and the limit of elasticity on 
 which depend the resistance to buckling diminish much less quickly with the 
 percentage of metal than the resistance to crushing actual or calculated. 
 
 For analogous reasons buckling precedes crushing for columns more strongly 
 spiralled than those experimented on, but all risk is avoided if the load applied to 
 a column is not allowed to exceed, however high the percentage reinforcement, the 
 safe load for the column of the same proportions in the series of experiments in 
 question. 
 
 This limitation, although not quite logical, will not impose any undue restraint 
 on constructors, because the percentage reinforcement chosen for the columns of 
 various proportions was not arrived at by chance, but as the result of earlier 
 experiment to determine the most efficient percentage for the columns of varying 
 proportions. 
 
 The most efficient percentage for the shorter columns was found to be 
 about 3*5 per cent., and it is possible that for the slenderest column slightly 
 greater resistances might be obtained by higher percentage reinforcement than 
 1'09 or 1-13. 
 
 The limits of load deduced from the experiments are given in Table No. 25 
 and were determined as follows : 
 
 The ratios of length to least dimension were plotted as abscissae, and the load 
 supported by the different columns as ordinates. The mean curve was traced by 
 suggestions of the known forms of the curves of resistance to buckling. The 
 ordinates of this curve divided by 4 gave the values appearing in Table 
 No. 25. 
 
 TABLE No. 25. 
 
 length 
 
 10 
 
 11-5 
 
 13 
 
 15 
 
 17 
 
 20 
 
 3 least dimension 
 
 Maximum working compression, 
 
 1,422 
 
 1,266 
 
 1,138 
 
 995 
 
 924 
 
 853 
 
 Ibs. per square inch. 
 
 
 
 
 
 
 
COMPRESSION WITH BENDING 85 
 
 To indicate the extent of the anomalies observed, it suffices to say that if 
 instead of the mean values obtained by the curve, the actual extreme values had 
 been taken account of, the factor of safety given by the above figures instead of 
 being uniformly 4 would have varied from 3*5 to 4*8. 
 
 The limits of pressure just indicated are suitable for concrete having a 
 resistance of 2,275 Ibs. per square inch when tested in short columns between 
 the heads of an hydraulic press. 
 
 Columns in buildings are under conditions at least as favourable when the 
 members on which they rest as well as those they support, and to which they are 
 strongly bound by the prolonged reinforcements, might be considered as exempt 
 from angular displacements. When the loading in such cases is unsymmetrical, 
 it will be observed that it is less than the maximum in view of which the 
 column has been designed. 
 
 To obtain data for designing a column which has to be subject to a bending 
 moment, the amount of which it is impossible to calculate, such as that due to 
 an eccentricity of the load, the Commission experimented on eccentrically loaded 
 columns. They found that with columns reinforced with intertied longitudinal 
 bars, when the load was applied at a point a quarter of the width of their bases 
 from the centre, the maximum load which they carried was equal on the average to 
 60 per cent, of the maximum load of columns squarely supported between the 
 heads of the press. 
 
 A spiralled column loaded at the outer edge of the middle third, but prevented 
 from acquiring an inclination of more than 3 '4 in 100 at the ends, conditions 
 worse than any to be met with in practice, the resistance was not sensibly inferior 
 to that of a similar column centrally loaded. 
 
 The Commission concluded that it would be prudent to reduce the average load 
 on columns which have not been calculated from the point of view of flexion to 
 60, 70 or 80 per cent, of the load allowed for centrally loaded columns, according 
 as the column is placed in the angles, the fa9ades or symmetrically under beams in 
 structures. 
 
 Members Subject to Compression and Bending. 
 
 The Commission recommended for the design of such members the method 
 which attributes to each element of the material a stress proportional to the 
 product of its longitudinal deformation and its corresponding modulus of 
 elasticity. 
 
 We have previously seen that all longitudinal bars of metal might be replaced 
 by cylinders of concrete of section m times greater than that of the metal, and 
 that this coefficient of equivalence might receive the same value, whether it was 
 applied to resistance or elasticity. These experimental results are equally 
 applicable to bending or compression. 
 
 Experiment proves that concrete is capable of greater shortenings without crush- 
 ing in bent beams than in columns, so that the reinforcements in the former develop 
 more fully the resistances of which they are capable, and there is no reason to 
 suppose that even in slabs which support compression in conjunction with the 
 bending of a beam are the values of the resistances less than in columns strongly 
 reinforced. The maximum value of m should thus be applied to members under 
 simple bending. 
 
 On the other hand, it may be necessary to reduce the value of m if 
 precautions are not taken to assure maximum efficiency to the longitudinal bars, 
 
86 REINFORCED CONCRETE 
 
 when the ratio of the compression produced by the longitudinal resultant of the 
 exterior forces to that produced by the bending moment rises. 
 
 It has been previously explained that the elastic effect of transverse reinforce- 
 ments is small, and even although the resistance of a properly spiralled member 
 is great, yet the modulus of elasticity at high stresses is low. There is 
 consequently no reason to take account of the elastic effect of the transverse 
 reinforcements in rcembers subjected to bending, whilst the elastic effect of the 
 longitudinals is fully accounted for by the equivalent increase of section of the 
 concrete from the point of view of resistance. 
 
 To simplify the calculations, the compressive stress in members subject to 
 bending is taken as proportional to the deformation, and the tensions in the 
 concrete are not taken account of. It is evident that the tensions should not be 
 taken account of, because at the crossing of the minute cracks which cannot always 
 be avoided, the whole load is taken by the reinforcements. In other respects the 
 tensions of the concrete are not negligible, as they influence not only the deforma- 
 tion of the neutral line, but its position in the cross section. It is established by 
 experiment that within the limits of working stress, cracks have no sensible 
 influence on the deformations of bent members or on the crushing of compressed 
 members. From this point of view the concrete ought to be treated as if it produced 
 everywhere the tension of which it was capable. 
 
 When the tensions in a member subject to bending are not taken account of, 
 the total calculated compression must be augmented to furnish the necessary 
 moment of resistance, so that the calculated value of the maximum compression is 
 increased above what is really its actual value. The error is the greater the 
 greater the proportion the tension omitted from the calculations bears to the 
 tension value of the reinforcement i.e., the error is the greater the lower the 
 percentage of reinforcement. 
 
 This error may to some extent be compensated for in the choice of the value 
 of the ratio m. By increasing the value of m above its true value i.e., by 
 exaggerating the superiority of the elasticity of metal over that of concrete, the 
 extensions calculated for the former are reduced and the shortenings calculated for 
 the latter are increased. A greater cross-sectional area of concrete is thus required 
 over which the compression component of the resisting moment is distributed. The 
 result of using such an inflated value of m is virtually to lower in the beam the 
 calculated position of the neutral axis, and to reduce the calculated value of the 
 maximum compressive stress. The absolute values of the two kinds of contrary 
 errors thus committed vary, if not proportionally, at least in the same sense : both 
 are maxima in slabs and beams of rectangular sections and minima in beams of T 
 section formed of a slab and rib. 
 
 The error committed in neglecting the tensions of the concrete is less as the 
 percentage of the reinforcement is increased, whilst the error resulting from the 
 exaggeration of m is less as the ratio of thickness of slab to height of rib is 
 reduced. These errors compensate in a sufficiently satisfactory manner in slabs 
 and beams of whatever proportions. 
 
 In fixing on 15 as the value of m, the ratio between the modulus of elasticity 
 of steel to that of concrete in compression, the following considerations influenced 
 the Commission : 
 
 The modulus of elasticity of concrete in compression varies from 1,020 tons per 
 square inch to 2,540 tons per square inch under light loads, the former applying 
 to concrete gauged with excess of water and imperfectly rammed, the latter 
 containing only the water necessary for its use and thoroughly rammed. 
 
ADHESION 87 
 
 A high modulus of elasticity is generally accompanied by a high resistance, and 
 vice versa. 
 
 It must be remembered that as the stress increases, the value of the modulus 
 of elasticity is reduced, and, consequently, the lowest value which can be met 
 with under working circumstances must be used. This has been taken as 933 tons 
 per square inch, and as the modulus of elasticity of the steel generally used is about 
 14,000 tons per square inch, the value of m is 15. The value of the compressive 
 stress to be allowed in the concrete is closely related to the value of m. The 
 higher the value of m chosen, the lower the compressive stress which ought to be 
 reckoned on. 
 
 Adhesion of the Concrete to the Metal. 
 
 Assuming, according to the elementary theory of perfectly elastic bodies, that 
 the tendency to slip at any section is proportional to the shearing stress on that 
 section, the resistance offered to the slipping of the longitudinal reinforcements 
 has been calculated, in the beams of the first series which failed in that way, at 
 from 170 to 213 Ibs. per square inch of the area of contact. In many existing 
 works the same mode of calculation indicates values as high as 142 Ibs. per square 
 inch as the measure of the tendency to slip. 
 
 The Commission carefully considered the question whether common practice in 
 this respect ought to be modified, keeping in view the difficulty of doing so without 
 largely increasing the cost or hindering the ramming. 
 
 Experiment showed that in the relative slipping of the reinforcement and the 
 concrete, as in the other deformations of reinforced concrete, a gradual diminution 
 in the modulus of elasticity took place as the stress was augmented, and after the 
 real elastic adhesion was destroyed, the frictional resistance to slipping was still 
 considerable. 
 
 In the second series of bending tests it was found that with beams similar 
 in all respects to those of the first series, but supported about 1 foot 4 inches 
 from one end instead of about 4 inches as in the first series, failure did not take 
 place by slipping of the reinforcements. This fact is explained by the additional 
 resistance to slipping which the reinforcements obtained from the part beyond the 
 supports. According to theory, however, the shearing stress was zero there, 
 and in consequence there should have been no additional resistance to slipping 
 obtainable from this part. 
 
 To investigate this point, the longitudinal slipping was measured in two places, 
 one between the support and the load when the shear and presumably the 
 tendency to slip was maximum and constant, the other in the projection beyond the 
 support when the shear was everywhere zero. It was found that, up to a certain 
 limit, the observed facts agreed with the theory. The slipping was zero outside 
 the supports, but between the load and the support it had quite an appreciable 
 value, which varied with the load. Beyond a certain value, slipping occurred 
 throughout. 
 
 These facts led to the following conclusions : 
 
 So long as the elasticity as regards slipping is intact, the hypothesis that the 
 slipping forces are proportional to the shearing forces is nearly correct. When, how- 
 ever, the elasticity has been reduced or broken down at a part, the slipping spreads 
 itself over the whole length of the reinforcement, and equilibrium is established with 
 the maxima stresses sensibly inferior to those indicated by the formula. This would 
 explain the phenomena observed in the experiments, and this interpretation may be 
 exhibited graphically by Fig. 27 for the case of a beam with a concentrated load or 
 
88 
 
 REINFORCED CONCRETE 
 
 with a distributed load. The ordinates of the full straight line represent the shear 
 at the various sections in the half span, those of the dotted curved line the slipping 
 stress at these sections, and in the part of the beam overhanging the support. 
 
 These considerations have led the Commission to the view that a low unital 
 stress should be adopted for slipping where no additional resistance can be given ; 
 but where additional resistance to slipping is obtainable, while its exact calculation 
 
 Diagram For Concentrated Load. 
 
 K 
 
 Diagram for Distributed Load . 
 FIG. 27. 
 
 may not be possible, some allowance should be made by increasing the stress 
 allowed. 
 
 Transverse Reinforcement of Members subject to Bending. 
 
 In ribbed beams transverse reinforcements, either alone or with the help of 
 longitudinal tension reinforcement raised up towards the ends calculated to resist 
 the shear, are generally used, whilst in slabs where the ratio of the depth to span 
 is not excessive no transverse reinforcements are generally employed. 
 
 The Commission thinks the practice justified for the following reasons : 
 The ribs are generally executed several days before the slabs, and unless great 
 care is exercised, and even then, the junction between the two portions forms a decided 
 plane of weakness, and slipping can only be prevented by reinforcements passing 
 across this plane. These reinforcements should be capable of resisting the whole 
 of the tendency to slip on that plane, and consequently they must be able to resist 
 the shearing force. 
 
TRANSVERSE REINFORCEMENT 89 
 
 On the other hand, slabs are usually put in in one operation, and it is thus only 
 from the point of view of rupture across the full concrete that their resistance to 
 shear ought to be assured. 
 
 So long as it is not fissured concrete resists shearing, and when the reinforcement 
 is less than 1 per cent., a stress of 65 Ibs. per square inch may be resisted. The 
 resistance of intact slabs is thus generally assured by the concrete alone. The 
 experimental slabs loaded to destruction perished not by oblique shearing, but by 
 elongation of the reinforcements and crushing of the concrete. The beam P, on p. 36, 
 without transverse reinforcements continued to resist shear after the formation of 
 oblique fissures cutting across more than five-sixths of the section. The shearing force 
 could only have been equilibrated in the planes of the cracks by the transverse 
 resistance of the longitudinal reinforcements, and by a kind of friction developed in 
 the particles of the compressed concrete remaining in contact in the prolongation of 
 the fissures. 
 
 In this connection it may be pointed out that the resistance longitudinal reinforce- 
 ments present to shearing, vertical or oblique, is always superior to the shearing 
 effort, aiid that except in beams carrying all the load concentrated in a single point, 
 the tension of the reinforcements diminishes as the shearing effort increases to such 
 an extent that there remains sufficient free resistance in the metal to resist the 
 shear. 
 
 The longitudinal reinforcements are thus almost always sufficient to prevent 
 rupture on oblique planes in beams of whatever dimensions if the solidity of the 
 enveloping concrete is assured. The danger of the concrete itself breaking up is 
 less when the percentage reinforcement is low, and when it is split into as many 
 bars as possible. 
 
 Slabs are thus well conditioned from both these points of view, and it is not 
 generally necessary to employ transverse reinforcements, the number and weakness 
 of temporary fixing of which, render ramming difficult. If, however, the ratio of 
 depth to span is great, and consequently the longitudinal reinforcements small in 
 respect to the shearing effort, there should be added transverse reinforcements 
 calculated to resist the shearing effort with the help of the concrete and the 
 longitudinal reinforcements. 
 
 Empirical Formulae. 
 
 The Commission recognised the necessity, in structures where the calculation 
 of the dimensions from a purely theoretical basis would be too complicated for 
 practical purposes, of the use of empirical expressions. The following observations 
 were made regarding the basis on which such expressions should rest so as not to 
 be irrational or to conflict with known facts. 
 
 In a structure of ribs and slabs, the ribs impose almost completely their 
 longitudinal deformations on the contiguous portions of the slabs they support, 
 the effect dying out with distance from the rib. 
 
 It is covnenient, as previously described, to allow that for a fixed width on 
 both sides of each rib the slab is completely solid with it from the point of 
 view of bending, the solidarity ceasing abruptly outside this width. 
 
 In the case of highly concentrated loads, such as a wheel load, the pressure 
 is transmitted not only vertically but obliquely, forming a kind of cone, the 
 base of which has greater dimensions the greater the total thickness of causeway, 
 filling and slab. The unloaded parts outside this imaginary conical zone participate 
 in the support of the latter, and the deformation extends transversely the greater 
 the span of the slab. Any expression for the distribution of such a load ought 
 
90 REINFORCED CONCRETE 
 
 thus to contain as variables the combined thicknesses of causeway, filling and slab 
 and the span of the latter. The coefficients should be determined by the analysis 
 of experimental results, and so as to give results conform to successful practice. 
 
 In the case of slabs carried by two sets of beams at right angles, the 
 problem, analogous to that of a plate supported or fixed along all four sides, is 
 complicated by the heterogeneity of the material. Any expression used should give 
 the results as for ordinary beams when the spans are infinitely different, and when 
 they are equal should give results agreeing with successful practice. 
 
 In considering the division of the loads between parallel beams, it is not possible 
 to do more than keep in view the principle of the solidarity of the main beams, the 
 secondary beams and the slabs, which can only be applied by reference to experi- 
 ments on analogous works. 
 
 Tests. 
 
 The importance of rapid tests by rolling load has been drawn attention to in 
 the regulations, as the deformations resulting from variations of temperature during 
 tests of longer duration are frequently of the same order as those produced by dead 
 loads. 
 
CHAPTER VII 
 OF NOTES PRESENTED BY M. CONSIDERS 
 
 A. Tension Tests on Prisms of Reinforced Concrete. - 
 
 THE description and particulars of the tests are given in Chapter IV., 5, p. 23, 
 and the results are exhibited graphically in Fig. 28, p. 92. 
 
 Precautions were taken to prevent any twisting of the test pieces, and the 
 measurements taken showed that they were successful, consequently the variations 
 produced by the loading and unloading give reliable information. 
 
 In the test pieces the area of the concrete was 15*5 square inches and the area 
 of the metal 0*175 square inch, and its modulus of elasticity 29 '1 x 10 6 Ibs. per 
 square inch. 
 
 An elongation d I in the prism, which produces the total augmentation of tension 
 d T, produces in the reinforcement an algebraical augmentation of tension dt m , equal 
 to d I X 0-175 X 29-1 X 10 6 Ibs., and the difference d T dt m is the increase in 
 the tension in the concrete which the elongation has produced. To deduce from 
 the variations of tension thus determined the absolute tensions of the concrete 
 or the steel, it is necessary to know the reciprocal and equal reactions between 
 the associated materials at the beginning or the end of the period during which the 
 variations have been studied. 
 
 The twenty-fifth and last unloading of an experimental prism (No. 3 prism), during 
 which the total tension was reduced from 3,945 Ibs. to 441 Ibs., the minimum 
 load necessary to keep the whole apparatus taut, may be taken as an example. 
 
 The point where the pencil stopped is indicated on Fig. 28 by the letter .4, and 
 if the irregularities due to the apparatus are overlooked, it is seen that the curve 
 of unloading differs little from a straight line, so that without appreciable error it may 
 be taken that if the unloading had been finished, the curve of unloading would 
 have been a straight line terminating at B. 
 
 To determine the reciprocal reactions between the concrete and the reinforce- 
 ment, the length of one of the reinforcements, the ends of which projected beyond 
 the ends of the prism, was measured. The concrete overlying this reinforce- 
 ment was then very carefully removed, and the reinforcement slackened in its bed, 
 but without destroying the latter, so as to conserve the curves which would influence 
 its length. The increase in length was found to be '00433 inch on a length of 
 55-12 inches. The contraction which the adhesion between the concrete and the 
 reinforcement had imposed on the latter even after twenty-five applications of a 
 load of 3,945 Ibs. was thus 0-008 per cent. 
 
 To completely annul the compression which the contraction of the concrete 
 had imposed on the reinforcement, it would have been necessary to have increased 
 the length of the prism by 0*008 per cent. ; that is, to take it to the point marked 
 C on the diagram. If through this point of equilibrium of the reinforce- 
 ments a straight line FF' is drawn having an inclination to the horizontal of 
 0-175 X 29-1 X 10 6 to 1, then each vertical intercept between FF' and 00' 
 represents algebraically the tension in the reinforcement at that phase. 
 
92 
 
 REINFORCED CONCRETE 
 
 The tension produced by the concrete at any deformation is measured by the 
 intercept between the deformation curve and the line FF'. 
 
 9000 
 
 7000 
 
 5000 
 
 3000 
 
 1000 
 
 /oool, 
 
 2000 
 
 5000 
 3000 
 
 1000 
 
 
 1000^ 
 2000 
 
 Prism N I 
 
 0-05 
 
 0-10 
 
 O-I5 
 
 Prism N9 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -^==- 
 
 ^ F 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 ^. - 
 
 
 
 
 / 
 
 > 
 
 r ./ 
 
 ^* 
 
 ^x 
 
 
 
 
 
 
 
 
 
 
 j-^"* 
 
 
 //^ 
 
 ^x" 
 
 >^x 
 
 
 
 ^~~~ 
 
 
 
 
 
 
 
 A 
 
 X 
 
 // / 
 
 & 
 
 
 --^ 
 
 
 
 
 
 
 
 
 
 
 - 
 
 ^*^~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 F 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0-10 
 
 0-14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . - 
 
 
 3000 
 
 
 ^x- 
 
 *^~~ 
 
 ^ 
 
 ? H 
 
 
 
 
 J ^- ' 
 
 ^- - 
 
 
 
 
 
 Y 
 
 
 
 ^y 
 
 
 
 . 
 
 . **" 
 
 
 
 
 
 
 1000 
 
 1 
 
 
 ^^ 
 
 S 
 
 ~ ' 
 
 ^- -- 
 
 
 
 
 
 
 
 
 
 o f 
 
 
 
 
 
 
 
 
 
 
 
 
 -/?' 
 
 
 
 1000 
 
 ~ 
 
 >] 
 
 r-- 
 
 
 
 
 
 
 
 
 
 
 
 (7 
 
 F~~ 
 
 D 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0- 
 
 05 
 
 
 
 
 o-y 
 
 o 
 
 o- 
 
 12 
 
 8000 
 6000 
 4000 
 
 2000 
 
 1000 
 
 
 
 1000 
 
 Prism N? 4 
 
 0-05 
 . Elongation per Cent, of 
 
 FIG. 28. 
 
 0-10 
 
 0-14 
 
 Since the prisms were made of the same materials with equal care and by the 
 same workmen, it might be allowed without sensible error that the line FF' has 
 the same relation to the origin of the four deformation curves. 
 
ANALYSIS OF TENSION TESTS 93 
 
 The following inferences can be drawn from the four graphs : 
 
 1. Initial State. 
 
 To obtain the true origin the deformation curve must be continued back to the 
 zero load-line at the inclination it has immediately above the 440 Ibs. load-line. 
 The intercept OD measures the tension in the concrete due to its being prevented 
 by the adhesion of the reinforcements from taking its full contraction. This 
 tension amounts to 1,146 Ibs., or about 74 Ibs. per square inch. The compression 
 in the reinforcements due to the same cause is 1,146 Ibs., or 6,540 Ibs. per square 
 
 inch. This compression in the metal corresponds to a strain of ' -g ; i.e., 
 
 jy* 1X10 
 
 of 2-25 X 10~ 4 , or 0-000225, or a shortening of 0-0225 per cent. 
 
 2. Elongation ivithout Cracking oj the Concrete. 
 
 Prism No. 1 underwent an elongation of 0-135 per cent, before the first crack 
 was apparent to the eye. Prism No. 2 underwent a maximum elongation of 
 0'061 per cent., with repetitions of smaller elongations, without apparent injury. 
 The reinforcements were removed, and it was not till almost the end of the operation 
 of cutting out that a crack was observed which cut the prism into two parts 29 and 
 10 inches long respectively. The operators thought that this crack was the result 
 of the cutting out of the reinforcement. 
 
 Non-reinforced concrete of the same quality as the above prism does not appear 
 to undergo without breaking an elongation of more than 0*008 per cent., or about 
 one-eighth of the elongation undergone by prism No. 2 without breaking. The two 
 portions of this prism were subjected to bending, and gave tension resistances 
 calculated by the usual formulae of 125 and 133 Ibs. per square inch, figures which 
 are not far removed from the initial tension resistance of the concrete employed, 
 and which had not been previously stressed. 
 
 Reinforced concrete should thus take without breaking, and at the same time 
 conserving a large part of its resistance, elongations much superior to those 
 demanded of it in structures ; but it is also evident that cracks might in certain 
 places be present beforehand or develop during loading of which it will be 
 necessary to take account in the calculations of resistance. 
 
 3. Law of Deformation oj Reinforced Concrete. 
 
 Measuring from the different graphs the tension produced by the concrete, which 
 is indicated by the intercept between the graph and the line FF' t we find that for 
 elongations of 0'004 per cent., 0-02 per cent., 0'06 per cent, to 0-135 per cent., the 
 tensions in the concrete were 170, 213 to 242 and 200 to 185 Ibs. per square inch. 
 
 During the elastic period, corresponding to an elongation of less than 0'004 per 
 cent., the tension had values growing regularly till a limit of 170 Ibs. per square 
 inch had been reached, which would be the limit of the resistance to tension if there 
 were no reinforcement. 
 
 As the elongation increases from 0*004 per cent, to 0'02 per cent, the tension 
 increases till it exceeds from 30 to 40 per cent, the resistance to tension of non- 
 reinforced concrete. This increase disappears on further increasing the elongation 
 to 0'06 per cent, approximately, and afterwards the tension remains constant and at 
 
94 REINFORCED CONCRETE 
 
 the value of the resistance of non-reinforced concrete until a much greater elongation, 
 about 0'135 per cent., was realised. 
 
 If for simplicity the temporary increase of resistance above referred to is 
 neglected, it might be said that the modulus of elasticity of reinforced concrete is 
 the same as that of non-reinforced concrete, so long as the applied stress does not 
 exceed the resistance to tension of the latter. When that tension is exceeded the 
 modulus of elasticity is reduced to zero, and in the places where there are no 
 cracks the help it gives to the reinforcements is not zero but constant. The 
 variations of tension in the reinforcements during this period are equal to the 
 total variations of tension in the prism, since the resistance of the concrete 
 remains sensibly constant. They are equal to the product of the variations of 
 their lengths by the coefficient of elasticity of the metal, and might thus be 
 calculated whether there are cracks in the concrete or not. 
 
 4. Loading and Unloading. 
 
 As will be observed from Fig. 28, the unloading curve is very different from 
 the curve of first loading. It is almost rectilinear, and presents inclinations 
 slightly greater at the ends than elsewhere. 
 
 The curve of reloading differs little from that of unloading ; the slight curva- 
 tures at the ends are in opposite directions. The mean modulus of elasticity is the 
 inclination of a straight line through the extreme ends of these lines, and the 
 greater the previous elongation the lower the value of the mean modulus. 
 
 5. Effects of Tension on the Resistance and Elasticity of Concrete to Compression. 
 
 In some structures, e.g., arches, the concrete might be submitted alternatively 
 to tensions and to compressions, and it is important to know the influence that 
 elongations exceeding the elastic limit exercise on the properties of the concrete 
 from the point of view of compression. 
 
 A portion of prism No. 1, which had undergone the considerable elongation 
 of 0*0135 per cent., was submitted to compression. It was found that its resistance 
 to compression, which before the tension stress was applied was between 1,800 and 
 2,000 Ibs. per square inch, had fallen to between 1,570 and 1,650 Ibs. per square 
 inch. The modulus of elasticity was reduced from' 1,900 tons per square inch 
 to 950 tons per square inch. 
 
 These results are reassuring, because the diminutions of resistance and elasticity 
 in question, of which the former is small and the second presents no danger, except 
 from the point of view of buckling, were produced by an elongation five to eight 
 times greater than that experienced in structures. 
 
 6. Effect of Repetition of Loading. 
 
 Prism No. 3 was submitted to the application, repeated twenty-five times, of a 
 tension of 3,950 Ibs., and it was observed that towards the end of the experiments 
 the deformations no- longer sensibly increased. By the method already described of 
 measuring the ordinates from the graph to the line FF\ it is observed that the 
 tension in the concrete is reduced from 235 to 185 Ibs. per square inch i.e., to 
 80 per cent, of its initial value. 
 
 The tests made at Quimper showed that the final value was reduced to 0*70 of 
 the initial value after many thousand repetitions. 
 
ANALYSTS OF TENSION TESTS 95 
 
 7. Final State after Unloading. 
 
 This state ought to be considered from two points of view, of which the first 
 throws light on the second : 
 
 1. The reciprocal reactions of the concrete and the metal. 
 
 2. The final deformations of the metal. 
 
 In order to determine by means of the graph of prism No. 3 the state of interior 
 equilibrium which compete unloading would produce, the curve of unloading HA 
 must be continued to B. The intercept between B and FF' gives the tension in 
 the concrete, which divided by the area of the reinforcements gives the unital 
 compression in the latter. 
 
 It is evident that even after elongations of 0'03 to 0'04 per cent, the reinforce- 
 ments still retained a small amount of the initial compression imposed on them by 
 the concrete. 
 
 In prism No. 2, after an elongation of 0'061 per cent., the original interior 
 stresses were annulled, and stresses of a contrary sense and of small amount were 
 produced. 
 
 In prism No. 1 the interior state of equilibrium was determined by measuring 
 one of the reinforcements which projected beyond the ends of the prism, then 
 releasing it from the concrete and measuring it again. The shortening observed 
 was 0-01 per cent. It follows that after this prism had undergone the considerable 
 elongation of 0*135 per cent., the original compression in the reinforcements was 
 replaced by a tension of O'Ol X 100 X 29'1 X 10 6 i.e., 2,910 Ibs. per square 
 j nc h which equilibrated a compression of 33 Ibs. per square inch in the concrete. 
 
 The inference from these results is that the interior reactions produced by the 
 contraction of the concrete are reduced by the effect of the deformations, and may 
 even be replaced by reactions of a contrary sense when the elongations exceeded a 
 limit of from 0'05 per cent, and 0*06 per cent., which is greater than the elongations 
 met with in actual structures. 
 
 This fact agrees with the alteration of the elasticity of concrete by large 
 elongations. It is, of course, in virtue of its elasticity that concrete reacts against 
 the reinforcements either in tension or compression, and it follows when this 
 elasticity is reduced the property previously possessed by the concrete of imposing 
 stresses on the reinforcements is diminished or lost. 
 
 It is evident that, since the effects of large but not excessive tensions is to 
 allow the reinforcements to return to their normal length, the contraction of con- 
 crete kept in air imposes strains of the same order on the reinforcements as the 
 external tensions. 
 
 Where the concrete has been immersed in water, the deformations due to the 
 contraction of the concrete are much less than when the concrete is kept in air. 
 
 The Quimper experiments confirm the above facts. It may be mentioned that 
 the average reinforced concrete used in construction is not submitted to elongations 
 greater than from 0'015 to 0'030 per cent. 
 
 B. Bending Experiments in large Reinforced Concrete Beams. 
 
 All the beams considered here are 13' 12 feet long, 15*75 inches deep and 7-87 
 inches wide. The resume of the methods and results of the experiments are given 
 in Chapter VI., section 9, on pp. 30 41, and only the main features of the results 
 and the deductions from them are considered here. 
 
96 REINFORCED CONCRETE 
 
 1. Initial State. 
 
 The contraction of the reinforcing bars, 0*874 inch diameter, was observed 
 during the setting of the concrete by measuring the over-all length of one of the 
 reinforcements from time to time. The reinforcement showed a progressive 
 shortening averaging 0*0264 per cent, on the length of the bar, and since the 
 contraction at the ends was necessarily zero, the maximum shortening which would 
 occur at the middle would not be less than 0*031 per cent. Further contraction 
 took place after these results were recorded, so that it is probable that the shorten- 
 ing of the reinforcement exceeded considerably '031 per cent, at the middle of 
 the span when the tests were made. 
 
 As a check this figure was also arrived at by an entirely different method. 
 The permanent elongation sustained, by the reinforcement during the test was 
 measured, and was found to be 0*015 per cent, at the centre of the span. The 
 reinforcement was freed from the concrete and a further elongation of 0*033 per 
 cent, was recorded, making a total of 0*048 per cent, in the middle part of the beam. 
 Thus, making allowance for unavoidable inaccuracies, it is concluded that for 
 concrete of these proportions the contraction due to setting in the middle part of a 
 beam reinforced as described would be from 0*035 per cent, to 0*040 per cent. ; and 
 if the metal had a modulus of elasticity of 31*3 X 10 6 Ibs. per square inch, a 
 compressive stress of about 11,000 Ibs., or about 5 tons per square inch, would be 
 produced. 
 
 This figure is much greater than that found for the stress in the tension test 
 pieces. The difference is partly due to the greater dimensions of the beam and 
 partly to the better quality of the concrete. It is evident, of course, that the 
 tension a concrete might exercise in setting would be proportional to its resist- 
 ance. 
 
 2. Deformation of Plane Sections. 
 
 Four beams Avere studied from this point of view, two without visible fissures 
 and two having the tension part of the beam cut through by the interposition of 
 a double sheet of tin foil. 
 
 In all the beams, slit or otherwise, the indications of the apparatuses 
 measuring the deformations of the concrete gave, when plotted on a diagram, 
 almost rigorously straight lines, conformably to the hypothesis of the conserva- 
 tion of plane sections during bending. 
 
 In the beams not slit, the elongations of the reinforcements agreed also almost 
 rigorously with the same hypothesis ; that is to say, were sensibly equal to those of 
 the layers of concrete at the same distance from the neutral axis of the beam as 
 the reinforcement. 
 
 It was otherwise, however, for the slit beam, where it was found that slipping of 
 the reinforcements was taking place towards the middle of the span, and gradually 
 increasing with increasing bending moment. In the part of the beam under 
 observation, owing to the method of applying the loads, there were no shearing 
 stresses. 
 
 The observations made showed very considerable warping in different parts 
 of the beam. 
 
 3. Position of the Neutral Axis. 
 
 It is important to compare the observed positions of the neutral axis with those 
 given by the formulae based on the hypothesis of the conservation of plane sections, 
 
ANALYSIS OF BENDING EXPERIMENTS 
 
 97 
 
 and on the application to flexion of the laws of deformation of reinforced 
 concrete. 
 
 From the tension tests previously dealt with it is observed that the deformation 
 of concrete in tension presents two phases separated by a short transition period. 
 
 In the first, which corresponds to very small elongations, the concrete behaves 
 as a perfectly elastic body. In beams reinforced only on the tension side, such as 
 those under consideration, the neutral axis ought to be situated a little above the 
 middle of the height, in virtue of the superiority of the elasticity of the metal over 
 that of the concrete which it replaces. 
 
 In the second phase, the tension of the stretched concrete remains constant. 
 The position of the neutral axis corresponding to the additional deformations 
 produced during this phase ought thus to be the same as if the tension of the 
 concrete was zero. 
 
 It is given by the formula : 1 
 
 when 
 
 x = n _ 
 
 distance from centre of tension reinforcement to neutral axis 
 
 x is - ; - 
 
 A, the distance from centre of reinforcements to the upper surface of the 
 
 beam ; 
 mw' 
 
 n ' bh> 
 
 6, the width of the beam ; 
 w\ the section of the tension reinforcements ; 
 
 modulus of elasticity of tension reinforcement 
 
 m. the ratio : -r-. : : * 
 
 modulus of elasticity of concrete in compression 
 
 To calculate the position of the neutral axis in the beams experimented on, it 
 is necessary to introduce the value of m appropriate to the concrete employed. 
 
 The mean value of the modulus of elasticity of a test prism made of the same 
 concrete was equal to 3 -41 X 10 6 Ibs. per inch 2 when the compression was between 
 570 and 1,420 Ibs. per square inch, as these were stresses approximately marking 
 the second phase of the bending in question. The modulus of elasticity of the steel 
 was known to be 32*5 X 10 6 Ibs. per square inch, m therefore had the value 9 -5. 
 
 Table No. 26 affords a comparison of the positions of the neutral axis as observed 
 and as calculated for the various percentages and for the variations of bending 
 moment set out in the Table. 
 
 TABLE No. 26. 
 
 
 
 
 Distance from the Neutral Axis to 
 
 2 Reference 
 
 Percentage of 
 
 Variations of the Bending 
 
 the Centres of the Reinforcements. 
 
 i . j 
 
 Mpl-fll 
 
 TV1" J_ 
 
 
 
 
 
 Actual 
 
 Calculated. 
 
 
 
 Foot-tons. 
 
 Inches. 
 
 Inches. 
 
 G. 
 
 0-50 
 
 7-56 to 13-05 
 
 10-709 
 
 10-630 
 
 F. 
 
 0-98 
 
 7-56 to 14-90 
 
 9-134 
 
 9-410 
 
 A.B. 
 
 1-94 
 
 7-56 to 16-73 
 
 7-795 
 
 7-953 
 
 C.D. (slit) 
 
 3-14 
 
 8-83 to 19-40 
 
 6-614 
 
 6-772 
 
 1 This formula applies where there are tension reinforcements only. 
 
 2 See Table No. 12, pp. 32, 38, for particulars of beams. 
 
 R.C. 
 
98 
 
 REINFORCED CONCRETE 
 
 It is seen that the results of experiment accord closely with the values calcu- 
 lated according to the hypothesis of the conservation of plane sections applied to 
 the phase in which the tension is zero, and that even for a beam cut by a 
 transverse fissure and notwithstanding the slipping of the reinforcements. 
 
 4. Law of Deformation of Reinforced Concrete. 
 
 Table No. 27 shows the results of some calculations made on one of the beams 
 to verify the law of deformation obtained by the direct tension tests. 
 
 The bending moments applied to the beam are given in column 1. The 
 elongations of one of the reinforcements, which were measured directly and 
 without possibility of error, are given in column 2 ; in column 3 the unital stress 
 obtained by multiplying the observed strain by the modulus of elasticity of the 
 metal, 32-4 X 10 6 Ibs. per square inch ; and in column 4 the total tension supplied 
 by the reinforcements, the area of which was 2 '4 sq. ins. In column 5 the distance 
 from the centre of the reinforcements to the centre of compression, determined 
 from the calculated position of the neutral axis, is given. In column 6 the 
 moments of resistance obtained by multiplying the figures of column 4 by those 
 of column 5 are given. 
 
 By subtracting the moment of resistance due to the reinforcement from the total 
 applied bending moment, the moment of resistance due to the tensions in the 
 concrete is obtained. These are given in column 7. 
 
 TABLE No. 27. 
 
 1 
 
 2. 
 
 3. 
 
 4. 
 
 0. 
 
 6. 
 
 7. 
 
 
 
 "Variations of Tension of 
 
 
 Variations of Moment 
 
 Total 
 Applied 
 
 Percentage 
 
 the Reinforcement. 
 
 
 of Resistance. 
 
 Bending 
 
 Elongation of 
 
 
 Lever Arm. 
 
 
 
 
 
 
 Moments. 
 (Foot-tons.) 
 
 Reinforcement. 
 
 Tons per 
 Square Inch. 
 
 Total Tons. 
 
 Ins. 
 
 Due to 
 Metal. 
 
 Due to 
 Concrete 
 in Tension. 
 
 
 
 
 
 
 Foot-tons. 
 
 Foot-tons. 
 
 3-43 
 
 0-00365 
 
 0-53 
 
 1-26 
 
 11-496 
 
 1-21 
 
 2'22 
 
 7-09 
 
 0-01030 
 
 1-49 
 
 3-59 
 
 11-811 
 
 3-54 
 
 3-56 
 
 12-60 
 
 0-02725 
 
 3-95 
 
 9-47 
 
 12-126 
 
 9-58 
 
 3-03 
 
 18-08 
 
 0-04350 
 
 6-10 
 
 14-63 
 
 12-165 
 
 14-85 
 
 3-24 
 
 Similar results were found in the cases of the other beams tested. 
 
 It will be observed that the moment of resistance produced by the stretched 
 concrete increases at first very rapidly so long as the deformation is small. After 
 attaining a maximum value it diminishes slightly, and thereafter remains sensibly 
 constant. These, facts agree well with the inferences drawn from the direct tension 
 tests. In bending, there is not observed immediately beyond the limit of elasticity 
 the transient augmentation of resistance noticed in the direct tension tests. This is 
 explained by the fact that the various layers of concrete in tension are not equally 
 elongated at the same instant ; in fact, most of the layers are not stressed at all 
 beyond the tension at which the modulus of elasticity becomes constant. 
 
ANALYSIS OF BENDING EXPERIMENTS 99 
 
 The final moment of resistance of 3 - 24 foot-tons supplied by the concrete 
 corresponds to a tension of about 135 Ibs. per square inch. This is the increase in 
 tension caused by the mechanical test, and is additional to the initial tension 
 resulting from the presence of the reinforcements. This latter tension might be 
 put at 213 Ibs. per square inch. Thus the total tension of the concrete during 
 bending after the limit of elasticity had been passed would be about 350 Ibs. 
 per square inch, and would be constant at this figure. 
 
 5. Adhesion and Slipping of the Reinforcements. 
 
 From the experiments of the Commission this very conspicuous fact emerges, 
 that the extremities of the reinforcements are not sensibly displaced relatively to 
 the concrete before the adhesion had been completely destroyed elsewhere, and also 
 that in the neighbourhood of the application of concentrated loads there were 
 important relative displacements. 
 
 Three different phases of the phenomenon united by short periods of transition 
 were clearly marked in the bending experiments recorded on pp. 32, 38. 
 
 In the first, which extended to a bending moment of about 11 '30 foot-tons and 
 to a slipping of the reinforcement of 0*00113 per cent., the displacement of the 
 reinforcement was small and increased proportionately to the load. 
 
 In the second phase, comprised between bending moments of 18 and 29 foot- 
 tons and between slippings of 0'004 per cent, and 0*012 per cent., the slip- 
 pings still increased proportionately to the load, but with a progression six or seven 
 times more rapid than in the first phase. 
 
 Between these two phases of rectilinear displacement there is a curve of tran- 
 sition. In the third phase, which immediately preceded the failure of the beam 
 by the destruction of the adhesion between the reinforcements and the concrete, 
 the adhesion seems to have gradually "disappeared outwards from the point of 
 maximum stress over the whole length of the reinforcements. 
 
 Omitting this last period of doubtful and complex nature, it was found that at 
 the end of the second phase the reinforcement had slipped 0'012 percent, relatively 
 to the concrete which surrounded it. 
 
 The deformation of the concrete was necessarily the greater as the reinforce- 
 ment was approached, and from closely approximate calculations the maximum 
 slipping of the concrete in contact with the reinforcement was about 0'6 
 per cent. 
 
 This high figure, which would have been rejected a priori as inadmissible 
 before knowing the laws of the deformation of the concrete, appears within the 
 bounds of probability, since it is known that concrete might without breaking 
 undergo elongations greater than 0'2 per cent, when submitted to tensions or 
 shortenings of 2 or 3 per cent, when spiralled and compressed. 
 
 This property which concrete possesses of slipping without breaking, appears to 
 play an important role in reinforced pieces of permitting the distribution over great 
 lengths of intense shearing stresses, which tend to be produced on certain points in 
 the neighbourhood of concentrated loads. 
 
 In a beam on which the bending moment was increased till cracking commenced , 
 then removed and re-applied thirty-nine times, it was found that, although the 
 elongations and contractions of the concrete ceased to grow, the slipping was 
 progressive. The load imposed on the adhesion of the concrete to the reinforce- 
 ments in these repeated loadings thus exceeded the limit of elasticity, and even, 
 it seemed, that of stability, although the bending moment was only half that of 
 
 H 2 
 
100 REINFORCED CONCRETE 
 
 the moment which on its first application determined the slipping of the reinforce- 
 ment in another identical beam. 
 
 Considered by itself, this fact is rather disquieting ; but it is known from other 
 sources that beams in which the adhesion has been highly stressed have supported 
 a great number of repetitions of bending moments without the deterioration or 
 deformation growing indefinitely. A prism tested at Quhnper underwent more 
 than 132,000 repetitions of a load which stressed the adhesion highly. 
 
 It would seem that the maximum stress imposed on adhesion by the application 
 of a concentrated load is at first localised, and that it gradually propagates itself 
 along the reinforcement till at no place its value exceeds what the concrete can 
 carry without the slipping progressing indefinitely. Further experimental informa- 
 tion however is required on this point. 
 
 In those beams tested up to the point at which slipping took place, an attempt 
 was made to obtain information regarding the resistance opposed to the slipping 
 of the reinforcement in bent pieces, but only indications without scientific precision 
 are obtainable. In fact, the law of the distribution of the slipping stresses was 
 ignored on the length of the reinforcements, and consequently no account was 
 taken of the maximum values the stresses attained in the most highly stressed 
 places. It was thus a purely conventional mode of calculation, to the results of 
 which no scientific value is attributable, but which may be useful for the checking 
 of design and the interpretation of the results of experiments. 
 
 If the concrete produced no tension, one of the components of the resisting 
 couple would be furnished solely by the reinforcements, and the slipping tendency 
 of the tension reinforcements would be at each point proportional to the shearing 
 effort. In the beams experimented on as the loads were concentrated at about 
 3 feet from the abutments, the shear was constant between the point of appli- 
 cation of the load and the abutment, and the total slipping tendency was thus 
 equal to the maximum tension in the reinforcement, so that the slipping stress 
 per unit area of the surface of the reinforcements was easily arrived at. 
 
 In this way a resistance to slipping of 185 Ibs. per square inch was found for 
 the beam with four bars each 0'874 inch diameter, and 213 Ibs. per square inch 
 for the beam with two bars each 1'57 inches diameter. In both cases the reinforce- 
 ments were placed in the folds of vertical sheet-iron stirrups. An examination of 
 the cracks led in both cases to the view that the displacement of the reinforce- 
 ments may not have taken place by the failure of the resistance to slipping 
 properly so called, but by the dislocation of the bed of concrete covering the 
 reinforcements. 
 
 From experiments made by M. Mesnager on the tearing and driving of rods 
 from cubes of concrete, values of from 190 to 235 Ibs. per square inch were 
 obtained, cracking of the concrete preceding or accompanying failure by slipping. 
 
 These facts show clearly that the values obtained by experimenting with rods 
 buried in very large blocks of concrete which have shown resistances as high as 
 640 Ibs. per square inch cannot be applied to the case of slipping in ordinary 
 reinforced concrete where the section of concrete used is never large enough to 
 prevent cracking before slipping. 
 
 6. Influence of Fissures on the Resistance of the Compression Areas. 
 
 In order to determine whether the hamstringing that takes place in beams 
 does not provoke the premature crushing of the concrete, two beams were manu- 
 factured with an artificial fissure extending across 65 per cent, of the section. 
 
ANALYSIS OF BENDING EXPERIMENTS 101 
 
 With a view to causing rupture by crushing of the concrete, the reinforcement 
 consisted of two 1'57 inches diameter rods, giving the abnormal percentage of 3'14. 
 
 The beams, however, collapsed by the slipping of the reinforcements, and the 
 only inference that could be drawn was that the compression in the concrete at the 
 moment of collapse was not the maximum compression that might have been 
 resisted. Assuming all the tension required was furnished by the reinforcements, 
 the mean compression on the compression area was about 1,250 Ibs. per square inch. 
 If the elasticity had remained constant, and consequently the distribution of stress 
 linear, the maximum intensity of stress would have been 2,500 Ibs. per square inch. 
 The elasticity, however, is reduced, but nevertheless the maximum stress should not 
 be evaluated at less than 1,850 Ibs. per square inch. 
 
 The resistance to direct crushing of blocks of the same concrete not reinforced 
 did not exceed 2,000 Ibs. per square inch. It would seem, therefore, that the 
 fissuring which occurs in the sagging of bent prisms does not hasten in an 
 appreciable manner the crushing of the part of the concrete subject to 
 compression. 
 
 This fact is perhaps explained by the ductility that concrete presents from the 
 point of view of slipping, and by the help derived by the compressed areas from 
 the increased resistance to transverse swelling which precedes crushing. 
 
 C. Effects of Transverse Bemforcements. 
 1. Bending Experiments. 
 
 The opinion has been expressed that in consequence of the inequality of the 
 limits of elasticity which concrete presents after it has been submitted to tension 
 or to compression, shear ought to produce a transverse swelling which would put 
 a tensile stress on the vertical reinforcements, and thereby allow them to 
 produce a useful effect in resisting the shear of the concrete. 
 
 In order to obtain information on this question the experimental method was 
 resorted to. Measuring apparatuses were placed vertically on the lateral faces of 
 two of the beams, with the usual vertical reinforcements. In one case the swelling 
 was only 0'005 per cent., which represented a mean stress in the stirrups of about 
 0'6 ton per square inch. In another, in which failure took place by shearing, the 
 swelling did not exceed O'Ol per cent, before the appearance of cracks, which 
 indicates at the most a tension of 1*4 tons per square inch of the vertical 
 reinforcements. 
 
 The measuring apparatuses were placed in vertical planes equally distant from 
 the support and the point of application of the load, where the beam resisted both 
 the maximum shear and a considerable bending moment. In the height of the 
 beam on which measurements were made, there was comprised both tension and 
 compression areas, so that the variation ascertained in the total height would 
 result from the superposition of the effects of shearing in the whole section on 
 the vertical contraction in the tension area, and on the vertical swelling on the 
 compression area. It is thus certain that if the resultant vertical deformation in 
 the whole depth of the beam was a swelling in the tension area, it was much less 
 than the mean, consequently the help derived from the tension in the stirrups in this 
 portion must have been very small. On the other hand, the vertical reinforce- 
 ments have been able to furnish really important tensions in the compression areas, 
 and consequently assist the lateral strength of the concrete. 
 
 When one recalls that it is in the tension area that oblique cracking due to 
 
* \ 
 
 ;/-w 
 
 102 REINFORCED CONCRETE 
 
 shear commences, and that it is the longitudinal reinforcements which resist 
 slipping, one is led to the conclusion that so long as the concrete is not cracked 
 the stirrups hardly act by tension. 
 
 Theoretical considerations indicate that so long as the limit of elasticity is not 
 passed, these stirrups hardly assist the shear, but the action thereafter assumes a 
 great importance ; in fact, well-placed stirrups may prevent the ruin of a structure 
 after the concrete is completely cracked. 
 
 2. Torsion Experiments. 
 
 The experiments above referred to attempted to elucidate directly the role of 
 the transverse reinforcements in bent pieces, but no information was obtainable 
 from them on the characteristic effects of pure shear. To this end M. Mesnager 
 devised the torsion tests described on p. 27. 
 
 It was established that under a moment of torsion equal to one-half the breaking 
 moment the elongation of the reinforcements was only such as produced a stress of 
 about 0'60 ton per square inch, and although it is the case that shearing produces 
 a lateral swelling of the concrete, it is so slight as to merit attention only under 
 very heavy loads. 
 
 The vertical deformations produced by shearing add themselves to those 
 resulting from the swelling of the concrete in the compression areas, and in 
 consequence the reinforcements perpendicular to the axis there give tensions which 
 increase the resistance to shear and to compression. 
 
 In the tension areas the transverse variations in volume produced by shear and 
 by bending oppose each other, the effect of the former predominating at the 
 supports, and of the latter at the places where the bending moment is a maximum. 
 
 D. Resistance of Reinforcements to Shear. 
 
 It is known that in imperfectly supervised work, and there is always some 
 such, the adhesion fails occasionally between the ribs executed at first and the 
 slabs executed later. It should be provided that the reinforcements traversing 
 any such plane of separation should in themselves be sufficient to resist the whole 
 of the horizontal slipping tendency. 
 
 The resistance of these reinforcements is complex, and comprises in the 
 simplest case, which is that of vertical reinforcements, two elements viz., the 
 resistance of the metal to shear and the friction developed between the surfaces 
 in contact. The last element is extremely variable, and in order to keep it as 
 uniform a quantity as possible during the experiments, the sub-Commission has 
 prevented adhesion by interposing sheets of oiled paper. These experiments are 
 described on pp. 25, 26. 
 
 It is observed that whilst the percentages employed are nearly equal in order 
 to equalise the tensions produced by the setting of the concrete, and consequently 
 the friction developed between the surfaces of the concrete, the forms and 
 dimensions of the reinforcements are very various. 
 
 The experiments have established the important fact that the resistances 
 obtained relatively to the section of the metal have been sensibly proportional to 
 the characteristic resistance of the metal ; or, in other words, the shearing resistance 
 was sensibly proportional to the area of the reinforcement and independent of its 
 form. 
 
 The qualities of both elements in the test cube influence the strength of the 
 
ANALYSIS OF BENDING EXPERIMENTS 103 
 
 whole, and one easily grasps the mechanism of this influence in examining the results 
 of experiments. 
 
 The concrete crushed near the surfaces of slipping and the reinforcements 
 took the form indicated in Fig. 29. They resisted thus not by shear alone, but 
 by shear combined with bending to a short radius. 
 
 It is thus possible that the resistance of the reinforcements depends on the 
 extent of the zone of crushing and on the quality of the concrete. The results 
 obtained apply only to concrete containing 6 cwts. of cement to 14*35 cubic 
 feet of sand and 2 8 '7 cubic feet of gravel. 
 
 The graphic representation of the results obtained by measuring carefully the 
 relative displacements of the two surfaces of contact indicates a point analogous 
 to the elastic limit, beyond . which the displacements grow considerably. This 
 point is at a stress of about 8 tons per square inch of the section of the 
 reinforcements, and the maximum load supported varied between 11*5 and 16 '5 
 tons per square inch of the cross 
 section of the reinforcements. j 
 
 These figures indicate the effect 
 of the quality of the concrete. Had 
 the concrete been of sufficient quality 
 to entirely prevent crushing, the 
 reinforcements would have developed 
 the ordinary resistance to shear. It 
 is possible that the percentage of 
 reinforcement used was a little too 
 high for the quality of the concrete. 
 
 It is important to remark that 
 the resistances obtained would not 
 have been so large if the rods had 
 been nearer the surface of the con- 
 crete, as the thin covering would 
 have been more easily burst. 
 
 No experiment has been made on the resistance which proceeds from friction 
 on the surface of slipping. The coefficient of friction of concrete on concrete 
 lies between 0*60 and 0*75, so that the resistance given by friction might attain 
 those proportions of the tension resistance of the reinforcement. It would not be 
 advisable to add the whole or the greater part of this resistance to the bending- 
 shear resistance due to the metal, because it is known that the superposition of 
 different stresses on metal hastens its rupture. 
 
 E. Experiments on Ribbed Slabs. 
 
 The propriety of the application of the hypothesis of the conservation of plane 
 sections during bending and of the exactitude of the formulae which give the 
 position of the neutral axis in rectangular pieces subjected to bending has been 
 discussed on pp. 78, 79. A research was carried out on two ribbed T slabs with 
 a view to finding out whether the same hypothesis and formulae applied in that case. 
 
 Precautions were taken to eliminate, as far as possible, merely local warpings 
 or irregularities, and to obtain a record of the deformations of the structure as a 
 whole. 
 
 The salient feature of the results is their striking regularity, as plotted 
 graphically on p. 47. 
 
104 REINFORCED CONCRETE 
 
 The uniformly distributed load which the first slab could carry without stressing 
 the reinforcements beyond 6'3 tons per square inch was about 6 '4 tons. Up to this 
 load, the deformations were sensibly plane. Beyond it, however, slight deviations 
 were observed. In the second slab the load was applied by means of a balanced 
 platform to the upper surface of the slab immediately over the rib. The defor- 
 mations were perfectly uniform for loads up to 9 tons ; but beyond that load, 
 and largely exceeding the load which would be applied in practice to a similar 
 slab, plane sections showed sensible warpings in the opposite sense to those 
 observed in the first slab. 
 
 Comparing these results with those of the tests made on the floors constructed 
 at the Paris Exhibition, the conclusion may safely be drawn that in ribbed slabs 
 plane sections remain plane during bending, any deviation from the plane being 
 of so slight magnitude as not to merit attention. 
 
 The determination of the position of the neutral axis in any structure is the 
 key to the correct calculation of the stresses in the concrete and moment of 
 resistance of the member. 
 
 The measurements taken on the slab 4 feet wide show that the neutral axis 
 occupied a position 2 '24 inches below the upper surface of the slab. In the slab 
 6 feet 6 inches wide the neutral axis was lower under light loads, but afterwards 
 rose to and retained till the end of the experiment a position sensibly identical 
 to that in the first slab. The ratio x of the distance of the centre of gravity of 
 the tension reinforcements from the neutral axis, to its distance from the upper 
 surface of the slab, is thus 0'70, and assuming the efficient width of the slab to be 
 90 per cent, of its total width, and putting in the known data in the expression 
 given on p. 97 for the value of x the value of m, the ratio of the coefficients 
 of elasticity of steel and concrete is found to be 10'9. From this figure and from 
 the known coefficient of elasticity of the steel used, the modulus of elasticity of the 
 concrete is calculated at 1,270 tons per square inch. 
 
 The modulus of elasticity of this concrete was also obtained experimentally 
 by the compressive tests of two prisms, the mean values up to a stress of 1,420 Ibs. 
 per square inch being 1,274 and 1,175 tons per square inch respectively. 
 
 The experiment in question has thus verified as exactly as possible the formula 
 which determines the position of the neutral axis, and which translates algebraically 
 the hypothesis of the conservation of plane sections and of the constancy of 
 the tension in the area submitted to elongation. 
 
 Participation of Slabs in the Resistance of the Ribs. 
 
 The deformations were measured not only in the ribs, but in the slabs at points 
 removed from the ribs, and it was found that in the slab 4 feet wide the neutral 
 axis rises higher in the slab the further away from the rib the measurement is 
 taken. That is, of course, as is to be expected, since the slab acts in two ways 
 viz., as a part of the compression area of the rib and as an independent beam, and 
 in proportion as the latter action preponderates the neutral axis rises, in order that 
 the necessary tension resistance may be obtained. 
 
 The neutral axis remained sufficiently close to the lower surface of the slab 
 throughout the test that the tension was neglected, and account only taken of the 
 compressions in the calculation of the resistance of slab and rib. Now, what- 
 ever the value of the coefficient of elasticity, these compressions are proportional 
 to the products obtained by multiplying the thickness of the slab situated above 
 the neutral axis by the shortening of the upper fibre of the slab. 
 
STRESSES DUE TO SETTING 
 
 105 
 
 The sections in which the three apparatuses were placed viz., on the axis of 
 the rib, at 13-40 inches and at 22-44 inches from it gave products in the ratio 
 21, 20 and 17'6 respectively. The geometric mean of these figures is 19. 
 
 Consequently in the slab in question, in which the ratio of width of slab to 
 span was 0'42, the slab gave Jy 0'90 of the resistance it would have furnished 
 if in all its width it had been absolutely rigid with the rib. So that to calculate 
 the resistance of this floor one might consider the slab as entirely solid in the 
 deformation of the rib on condition of taking account of only 0'90 of its width. 
 
 In the slab 6 feet wide the ratio of breadth to span attains the exceptional 
 figure of 0'70, and by making the above assumptions which do not apply with so 
 great accuracy in this case as in the former the participation of the slab in the 
 resistance of the rib was 0'55 of what it would have been in the case of absolute 
 solidarity. 
 
 To determine as a function of the span taken as unity the effective widths of 
 the slabs corresponding to spacing of beams of 0'40 and 0*70, it is necessary to 
 multiply these figures respectively by 0'90 and 0*55. The products - 36 and 
 0-385 are thus obtained. These results appear somewhat anomalous, as it is 
 improbable that the useful effect of a slab increases only in the slight proportion 
 of 0*36 to 0'385 when its width grows in the proportion of 0'40 to 0-70, although 
 it should be remarked that the influence of secondary bendings rapidly becomes 
 more important with the increase in width. 
 
 One is led to the conclusion by the consideration of these and of other 
 experiments that, when the width of the slab is 0'40 of the span, its effective 
 width may be taken about 90 per cent, of its total width, and that the help it 
 gives the rib grows more and more slowly as the width of the slab becomes 
 greater. 
 
 F. Variations in Length of Bars of Metal Buried in Concrete during Setting. 
 
 On p. 23 the experiments carried out to throw light on the above question 
 are described. 
 
 Table No. 28 gives the results found. 
 
 TABLE No. 28. 
 
 
 Pieces kept in Water. 
 
 Pieces kept in Air. 
 
 Percentage. 
 
 
 
 
 
 
 Tension in the 
 Metal. 
 
 Compression in 
 the Concrete. 
 
 Compression in 
 the Metal. 
 
 Tension in the 
 Concrete. 
 
 
 Tons per square 
 
 Lbs. per square 
 
 Tons per square 
 
 Lbs. per square 
 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 0-23 
 
 1-40 
 
 7-1 
 
 2-51 
 
 12-8 
 
 0-49 
 
 1-40 
 
 15-2 
 
 1-95 
 
 21-3 
 
 1-00 
 
 1-27 
 
 28-5 
 
 1-68 
 
 37-5 
 
 1-44 
 
 1-12 
 
 36-0 
 
 1-68 
 
 54-0 
 
 1-96 
 
 1-12 
 
 49-0 
 
 1-68 
 
 73-0 
 
 2-96 
 
 1-12 
 
 57-0 
 
 1-68 
 
 111-0 
 
 4-00 
 
 1-27 
 
 114-0 
 
 
 
 
 
 4-93 
 
 1-12 
 
 123-0 
 
 1-68 
 
 185-0 
 
 9-00 
 
 1-27 
 
 256-0 
 
 1-40 
 
 282-0 
 
106 REINFORCED CONCRETE 
 
 It is seen that for cylinders kept in air there were found compressions in the 
 metal Avhich attained in the length of 19*68 inches a value of 2-51 tons per 
 square inch for a percentage of 0*23, 1*95 tons per square inch for a percentage 
 of 0-49, and which starting from TO per cent, up to 9 per cent, remained sensibly 
 constant and in the neighbourhood of 1*68 tons per square inch. The tension in 
 the concrete balancing the above has varied almost proportionately to the per- 
 centage from 12 to 280 Ibs. per square inch. 
 
 In the prisms kept in water the reinforcements took tensions almost independent 
 of the percentage of reinforcement and of about 1*2 tons per square inch, whilst the 
 opposing compression in the concrete varied from 7 to 256 Ibs. per square inch. 
 
 The experiments appear to establish the surprising fact that when the per- 
 centage of metal exceeds 1 per cent, an increase in percentage has no sensible 
 effect on the stresses set up in the reinforcement as a result of the setting of the 
 concrete, and that the corresponding stresses in the concrete are quasi proportional 
 to the percentage, whatever its value. 
 
 The experiments just described cannot be considered applicable to large pieces. 
 Since the production of the stresses depends on the adhesion, their values are 
 necessarily zero at the extremities, and so much the greater on the average, as the 
 pieces are longer in relation to the transverse dimensions of the reinforcements up 
 to a certain limit far removed. 
 
 Experimental proof of this can be had by referring to the internal stresses 
 measured in other pieces e.g., in the tension prisms 6*56 feet X 3*94 inches X 3'94 
 inches, the compression of the reinforcements was about 2 -92 tons per square inch. 
 In the beams of 13*12 feet X 15*75 inches X 7 '8 7 inches, when the concrete 
 had set freely and unloaded in air the compression was about 5'1 tons per square 
 inch, and was very much more in the compression reinforcements when the concrete 
 of the beam set under a heavy load. 
 
 The incontestable result of this series of experiments is to demonstrate that 
 to obtain figures applicable to structures concerning the effects of the 
 variations in volume of concretes or mortars, the surest method is from the results 
 of similar pieces. If smaller pieces are employed, it would be necessary to establish 
 between the transverse and longitudinal dimensions of the reinforcements 
 proportions analagous to those met with in structures. 
 
 G. The Influence of the Proportion of Gauging Water on the Strength and 
 
 Elasticity of Concrete. 
 
 It is known from experiments made elsewhere that the marked inferiority of 
 very wet mortars and concretes diminishes with time, but the experiments of the 
 Commission show even after ninety days' setting that the resistance and elasticity 
 vary with the proportion of gauging water. 
 
 Compression tests after ninety days on similar prisms 14*2 inches X 2*85 
 inches X 2*75 inches, composed of 6 cwts. of Portland cement, 14*35 cubic feet of 
 sand and 28*7 cubic feet of gravel were made. 
 
 The first series were gauged with 8*8 per cent, by weight of water. There 
 was obtained a resistance to crushing of 1,850 Ibs. per square inch, and a coefficient 
 of elasticity of 2,000 tons per sq. in. between stresses of 280 to 850 Ibs. per square 
 inch, and 1,160 tons per sq. in. between 1,280 and 1,700 Ibs. per square inch. 
 
 The second series were gauged with 11*0 per cent, of water. A resistance of 
 710 Ibs. per square inch was obtained, whilst the coefficient of elasticity between 
 stresses of from 140 to 280 Ibs. per square inch was 1,040 tons per sq. in., and 
 420 tons per sq. in. between stresses of from 560 to 710 Ibs. per square inch. 
 
EFFECT OF SHOCKS 107 
 
 H. Effects of Direct and Repeated Shocks on the Adhesion and 
 Resistance of Concrete. 
 
 Fears have been expressed regarding the disintegration of reinforced concrete 
 in situations where it is exposed to repeated and violent shocks. 
 
 Several sleepers in reinforced concrete were put into operation in April, 1893, 
 on the main down line from Paris to Granville at the entrance to Dreux Station, 
 and remained there till June, 1898. The road was of 78 Ibs. per yard, double 
 headed rails, and the maximum speed at this place about 40 miles per hour. 
 
 One of the sleepers which had been placed near a rail joint was examined by 
 the second sub-Commission. 
 
 The composition of the concrete was not known, but from its appearance it 
 consisted of a rich mixture very carefully made. 
 
 The two features under special examination were the adhesion of the concrete 
 to the reinforcements and the resistance of the concrete. From both points of 
 view the results were remarkable. 
 
 To measure the resistance of the adhesion parts of the reinforcements were 
 torn from the concrete, and gave very high figures, varying from 820 to 1,310 Ibs. 
 per square inch of the surface of contact. 
 
 This whole resistance was not, of course, due to adhesion properly so called, but 
 even making allowances for the other resistances, such as that due to the 
 straightening of the wires and the purely frictional grip of the concrete, the 
 values are still high. A careful examination of other parts of the reinforcements 
 showed that the adhesion was perfect throughout. 
 
 The resistance of the concrete to compression in 3-inch cubes without reinforce- 
 ment was 8, 410 Ibs. per square inch. 
 
 It is thus shown that a concrete sleeper, without doubt exceptionally good to 
 begin with, suffered no deterioration in five years' use. To appreciate the 
 importance of this demonstration account must be taken of the great rapidity 
 with which the effects of shock diminish as the distance from the point of impact 
 increases if the transmission of the stresses is not made by absolutely rigid and 
 continuous pieces. 
 
 There is thus a considerable difference between the sleepers which receive 
 directly the shocks from the chairs and the floor girders, and a fortiori the main 
 girders to which the shocks are transmitted indirectly, at least in large works. 
 Where ballast is used this difference is considerably augmented. 
 
 The experiment of Dreux should remove all apprehension for the duration and 
 conservation of bridges or viaducts carrying roadways or railways. 
 
APPENDIX 
 
 PAKT I 
 
 YEETICALLY IMPOSED LOADS AND .WIND LOADS ON METALLIC BKIDGES 
 AS DEFINED IN THE EEGULATIONS OF AUGUST 29, 1891 l 
 
 VERTICALLY IMPOSED LOADS. 
 Bridges on Railways of Normal Gauge. 
 
 The type train will consist of two engines with their tenders at the head of a train 
 of loaded waggons, and will have the following weights and dimensions : 
 
 
 
 Engine. 
 
 Tender. 
 
 Waggons (Loaded). 
 
 Number of axles . ... 
 
 4 
 
 2 
 
 2 
 
 Load per axle (tons) 
 
 13-88 
 
 11-82 
 
 7-88 
 
 Distance from leading buffer to 
 
 
 
 
 first axle (feet) .... 
 
 8-52 
 
 6-56 
 
 4-92 
 
 Spacing of axles (feet) 
 Distance of rear buffer from last 
 
 > 3-94 
 
 8-20 
 
 9-84 
 
 axle (feet) ..... 
 
 8-52 
 
 6-56 
 
 4-92 
 
 Total weight (tons) .... 
 
 55-52 
 
 23-63 
 
 15-75 
 
 Total length (feet) . 
 
 28-86 
 
 21-32 
 
 19-68 
 
 The engines, with their tenders, will be placed at the head of the train, and the 
 maximum stress in each member will be taken as the maximum stress in it produced by 
 any possible position of the type train on the bridge. For floor members, the stresses 
 due to an isolated axle load of 19'69 tons will be taken as the maxima if they are greater 
 than those produced by the type trains. 
 
 Stresses allowed ; nett area in tension or gross area in compression : 
 
 For mild steel in main girders over 100 feet span = 7 -3 tons per square inch. 
 For other girders . . . . . = 5-4 do. 
 
 For rail bearers and cross girders . = 4-76 do. 
 
 For web bracing exposed to alternating stresses = 3*81 do. 
 
 Bridges on Raihuays of Metre (3*28 Feet] Gauge and Over. 
 
 The weight per engine axle is reduced to 3*00 tons X L, where L is the gauge in 
 feet. The dimensions of the engines and the weights and dimensions of the waggons 
 will be the same as for normal gauge, and the tenders will be supposed to have the same 
 weights and dimensions as the loaded waggons. 
 
 For the calculation of the stresses under a single axle load, a weight of 4*2 tons X L, 
 where L is the gauge in feet, shall be taken. 
 
 1 "K&istance des Materiaux" (Vol. L, p. 
 Publics ; publishers, Dunod et Pinat, Paris. 
 
 595), Bibliotheque du Conducteur de Travaux 
 
110 APPENDIX 
 
 Road Bridges. 
 
 The stresses in each member must not exceed the limits above specified when either 
 (a) a uniformly distributed dead load of 82 Ibs. per square foot occupies the whole 
 
 platform of the bridge, including the footpaths ; or 
 
 (&) as many continuous files of tumbrils as the width of the roadway will hold, the 
 
 footpaths remaining loaded with a dead load of 82 Ibs. per square foot. Each tumbril 
 
 to have one axle and to be drawn by two horses, all of the following weights and 
 
 dimensions : 
 
 Tumbrils. Weight ...... . 5-91 tons. 
 
 Length, not including the shafts . . .9-68 feet. 
 
 Width of roadway occupied . . . .7*26 feet. 
 
 Width of wheel track . . . . .4-98 feet. 
 
 Horses. Weight . . . . . . .0-69 tons. 
 
 Length to each horse, including harness and shafts . 8-20 feet. 
 
 It must be shown that the stress in each member will not exceed by more than 
 0'64 ton per square inch the limits fixed for railway bridges, when a vehicle with one 
 axle weighing 10 '83 tons, and having the same dimensions as the above tumbrils, but 
 drawn by five horses, is substituted for one of the tumbrils, and also in the case where 
 the tumbrils are replaced over the whole platform of the bridge by waggons with two 
 axles drawn by four pairs of horses, having the following weights and dimensions : 
 
 Waggons. Weight on each axle . . . . 7 '88 tons. 
 
 Length of vehicle . . . . 19-68 feet. 
 
 Width of track . . . . . .5-58 feet. 
 
 Spacing of axles . . . . .9-84 feet. 
 
 Distance of front axle to front of waggon . . 4-92 feet. 
 
 Distance of rear axle to back of waggon . . 4 '92 feet. 
 Width of roadway occupied . 7 '38 feet. 
 
 Horses. Weight of a pair ..... 1'38 tons. 
 
 Length of a pair, including harness and shafts . 8 '20 feet. 
 
 Where the roads are steep and the loading defined above is not considered possible, 
 either at present or in the future, the loads to be provided for may, with the consent of 
 the Administration, be modified, but in no case will they be reduced below 62 Ibs. per 
 square foot for the dead load, and half the above live loads. 
 
 Bridges Carrying Canals. 
 
 These must be able to carry the load of water corresponding to the normal water 
 level, increased by 12 inches, without the stress exceeding in any part the above limits. 
 
 WIND PBESSURE. 
 Railway Bridges. 
 
 The stress in the metal under the influence of the highest winds shall not exceed by 
 more than 0*64 ton per square inch the maximum stresses already stated. 
 
 The maximum wind pressure will be taken at 55 Ibs. per square foot ; but it may 
 be assumed that the passage of trains will be suspended when the pressure exceeds 
 35 Ibs. per square foot. 
 
 It will be assumed that the maximum pressure will be exercised on the nett surface, 
 after deduction of openings, of each of the main girders ; that it will be applied to the 
 total nett surface of the windward girder of each span ; and that the wind pressure 
 applied to the total "uett surface of the adjacent main girder screened by the first will be 
 reduced in the ratio of the nett surface of the first to the total surface bounded by its 
 contour ; and, further, if there be more than two main girders on each span, the effect on 
 the others will be considered negligible. For metallic piers it will be assumed that the 
 pressure will be exercised to the full extent on the nett surface of all members. 
 
 In considering the hypothesis of a train on the bridge, its vertical nett surface will be 
 reckoned as a rectangle 9*84 feet high, its lower edge T64 feet above the rail and extending 
 
APPENDIX 111 
 
 the full length of the bridge. From the area of this rectangle will be dedacted the nett 
 area of the windward girder, and it will be supposed that the wind action on the girder 
 to leeward of the train is zero. 
 
 It must be shown that the tendency to transverse slipping and the upsetting action 
 of the wind on bridge platforms and piers, assuming the train defined above to consist of 
 empty waggons, and taking into account any special circumstances connected with the 
 structures, cannot attain dangerous values. 
 
 Road Bridge*. 
 
 The above methods of calculation must also be applied to road bridges, with the 
 exception that no account need be taken of the presence of vehicles on the bridge. 
 
 Bridges Carrying C-i-nals. 
 
 A wind pressure of 55 Ibs. per square foot of vertical surface to be applied to the 
 structure. The surface of boats exposed to the wind may be reckoned as a rectangle 
 4-92 feet above the side of the tank, and having the same length as the bridge. 
 
 PAKT II 
 
 KEGULATIONS OF AUGUST 29, 1891, AS TO TESTS OF METALLIC 
 BEIDGES (ABEIDGED) 1 
 
 Railway Bridges. 
 
 EACH metallic span will be subjected to (a] dead load test, (6) rolling load test. These 
 tests will be made by test trains at least equal in weight to the type trains previously 
 defined in these regulations. For tests by dead load the test train will be placed 
 successively in the positions producing the greatest stresses in the principal members 
 of the bridge. 
 
 For separate span bridges the test train will be placed successively on each span, 
 so as to cover it completely, then to cover only one-halt of each span. 
 
 For continuous span bridges each span will be loaded by itself as just described. 
 Then there will be loaded simultaneously the two spans contiguous to each pier, 
 exclusively of all the others. 
 
 For arched bridges the whole span will first be loaded, then each half alone, and 
 finally the middle portion, by placing there the two locomotives head to head. 
 
 For the dead load tests the test train will remain in each of those positions for at least 
 half an hour. 
 
 The live load tests will be two in number viz., at speeds of 12-5 and 25 miles per hour. 
 The latter test may be postponed till the track has somewhat consolidated. 
 
 For double line bridges with both tracks on one platform, the tests will be made 
 on each track separately as explained above, the other track remaining unoccupied ; then 
 on both tracks simultaneously. For the live load tests the trains will travel in the same 
 direction. 
 
 For bridges of exceptional type, special arrangements will be made for the test. 
 
 Road Bridges. 
 
 Metallic spans will be subjected to tests of two kindn viz., (a] dead load, (&) live 
 load. 
 
 For the dead load test the surcharge will be 82 Ibs. per square foot of the platform, 
 including the footpaths. 
 
 For live loads the loads will be arranged as far as possible as to weight and spacing 
 like the type load used in the calculation. They ought to give at least with their yokes 
 a minimum load of 82 Ibs. per square foot, taking 7'38 feet as the width occupied. The 
 number of files of vehicles ought to be equal to the width of the roadway divided by 7*38 ; 
 but in the event of it being difficult to assemble the full number of vehicles, the surplus 
 width might be occupied by a dead weight of 82 Ibs. per square foot distributed on each 
 side of the files. 
 
 For dead load tests of separate spans the load will be extended from one extremity to 
 
 1 " Kesistance des Materiaux " (Vol. I., p. 595), Bibliotheque du Conducteur de Travaux 
 Publics ; publishers, Duuod et Pinat, Paris. 
 
112 APPENDIX 
 
 the other, with a stop of half an hour when the load has reached half span, and the full 
 load shall remain on the bridge for half an hour. 
 
 For continuous bridges each span will be first loaded separately, as described above ; 
 then the two spans contiguous to each pier will be loaded simultaneously, exclusively of 
 the others. 
 
 For arched bridges, each span will be loaded over the whole span ; then on each half, 
 and finally on the middle portion only. 
 
 The live load test will be carried out by causing the files of vehicles to pass at a 
 walking pace from one extremity of the bridge to the other. 
 
 There will also be made to pass over the bridge a vehicle with an axle load of 10'8 tons. 
 
 When a reduction has been allowed in the loads used in calculation, the test loads will 
 be correspondingly reduced. 
 
 Loads notably greater than the test loads will only be allowed to pass over the bridge 
 by special authorisation. 
 
 Bridges Carrying Canals. 
 
 The tests of canal bridges will consist in the measurement of deflections after filling 
 to a depth of 12 inches over normal water-level. 
 
 Measurement of Deflections. 
 
 There will be measured at the time of the test the maximum deflection at the centre 
 of each span, under the influence first of the dead load and then of the live load in 
 movement. 
 
 When there are several bridges of identical construction and of span not exceeding 
 33 feet, the measurement of deflection need only be made for one of them. 
 
 Immediately after the test of each bridge the metallic part shall be examined in all 
 its details. 
 
 For bridges over 33 feet span two permanent bench marks will be fixed clear of every 
 part of the structure. The levels of the lowest parts of the girders or arches at the centre 
 and also at the extremities of each span and of the supports shall be recorded relative to 
 these bench marks. 
 
 The detailed reports of the test made by the engineer in charge, in the form pre- 
 scribed by the Administration, shall contain a description of these bench marks, which 
 will enable them to be found at any subsequent time. 
 
 PAKT III 
 
 IMPOSED LOADS AND TESTS STIPULATED IN THE REGULATIONS 1 
 OF FEBEUAEY 17, 1903, FOE METALLIC STATION BUILDINGS 
 (ABEIDGED) 
 
 THE snow load used in calculating stresses is to be taken at 12'3 Ibs. per square foot 
 of horizontal surface, and the wind pressure at 31 Ibs. per square foot normal to its 
 direction, which is assumed to be at an angle of 10 degrees to the horizontal downwards 
 towards the earth. 
 
 If a is the angle of inclination of the roof, the action of the wind might be replaced 
 by a vertical surcharge equal to 31 sin 2 (a -f- 10) Ibs. per square foot of surface covered, 
 and a horizontal thrust having the same value 31 sin 2 (a -f 10) Ibs. per square 
 foot of surface in elevation. 
 
 The maximum wind might occur even after a fall of snow, but in that case the weight 
 of snow may be considered as 6'2 Ibs. per square foot of horizontal surf ace. 
 
 After erection one or several of the main trusses are to be submitted, as far as 
 possible, to tests intended to demonstrate their resistance to forces analogous to those 
 which they will be called upon to support. The results obtained by measurements 
 during the tests wjll be compared with those furnished by the calculations. 
 
 For works constructed or contracted for by the concessionaires, the tests are to be made 
 in the presence of the engineer charged with the control of the tests, or of an agent 
 delegated by him. Detailed special reports of the tests are to be sent to the Administration, 
 which reserves the right to make any modification in the regulations to meet exceptional 
 cases. 
 
 1 " Resistance des Materiaux " (Vol. III., p. 506), Bibliotheque du Conducteur de Travaux 
 Publics ; publishers, Dunod et Pinat, Paris. 
 
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 EXPERIMENTAL EESEARCHES ON EEINFORCED CONCRETE. A. CONSIDERE. 
 
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 INSPECTORS' HANDBOOK OF EEINFORCED CONCRETE. W. F. BALLINGER. Hill 
 
 Publishing Co. 4s. net. 
 CONCRETE PLAIN AND EEINFORCED. TRAUTWINE. Chapman and Hall. 8s. Qd. 
 
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 1910. MANUAL OF EEINFORCED CONCRETE. 2nd Edition. MARSH AND DUNN. 
 
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 EXTRACTS ON EEINFORCED CONCRETE DESIGN. TAYLOR AND THOMSON. Chapman 
 
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 CONCRETE AND EEINFORCED CONCRETE CONSTRUCTION. HOMER A. EEID. The 
 
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 EEINFORCED CONCRETE. WEBB GIBSON, Crosby Lockwood & Son. 4s. Qd. net. 
 EEINFORCED CONCRETE THEORY AND PRACTICE: F. EINGS. Batsford. 7s. Qd. 
 
 net. 
 R.c. I 
 
114 BIBLIOGRAPHY 
 
 REINFORCED CONCRETE. Captain J. G. FLEMING, R.E. The Royal Engineers' 
 
 Institute, Chatham. 3s. 6d. net. 
 BRAYTON STANDARDS FOR THE UNIFORM DESIGN OF REINFORCED CONCRETE. 
 
 Louis F. BRAYTON. 2nd Edition. Hill Publishing Co. 12s. Qd. net. 
 DIAGRAMS FOR DESIGNING REINFORCED CONCRETE STRUCTURES. G. F. DODGE. 
 
 Spon. 17s. net. 
 A TECHNICAL DICTIONARY IN Six LANGUAGES OF REINFORCED CONCRETE IN 
 
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 1911. TREATISE ON CONCRETE, PLAIN AND REINFORCED. TAYLOR AND THOMSON. 
 
 2nd Edition. Chapman and Hall. 21s. net. 
 REINFORCED CONCRETE, COMPRESSION MEMBER DIAGRAM. C. F. MARSH. 
 
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 LECTURES ON REINFORCED CONCRETE. WILLIAM DUNN. Hodder and Stoughton. 
 
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 DIAGRAMS FOR SOLUTION OF T-BEAMS IN REINFORCED CONCRETE. WILLIAM 
 
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 REINFORCED CONCRETE IN THEORY AND PRACTICE. ADAMS AND MATTHEWS. 
 
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 PLAIN AND REINFORCED CONCRETE. (Section 5, American Civil Engineers' Pocket 
 
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 REINFORCED CONCRETE CONSTRUCTION. Elementary Course. M. T. CANTELL. 
 
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 REINFORCED CONCRETE BEAMS AND COLUMNS. W. N. TWELVETREES. Whittaker. 
 
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 Tn addition to the a^ove the Proceedings of the Concrete Institute and the Proceedings 
 of the Institution of Civil Engineers contain information regarding Reinforced Concrete. 
 The Preliminary and Interim Report of the Committee of the Institution of Civil 
 Engineers on Reinforced Concrete contains a list of Papers and Abstracts referring to 
 Reinforced Concrete in recent volumes of the Proceedings. 
 
 SOME FRENCH PUBLICATIONS. 
 
 LE BETON ARME ET SES APPLICATIONS. PAUL CHRISTOPHE. Beranger, Paris. 
 
 32*. 
 RESISTANCE DU BE"TON ET DU CIMENT ARME. TEDESCO ET MAUREL. Beranger, 
 
 Paris. 20s. 
 LE BETON FRETTE ET SES APPLICATIONS. A. CONSIDERS. Dunod et Pinat, 
 
 Paris. 2s. 
 LA CONSTRUCTION EN CIMENT ARME. BERGER ET GUILLERME. Dunod et 
 
 Pinat, Paris. 40s. 
 COMMISSION DU CIMENT ARM : EXPERIENCES, RAPPORTS, ETC. Dunod et Pinat, 
 
 Paris. 22s. 
 BETON ARM. VOL. I. PROCEDES GENERAUX DE CONSTRUCTION ET CALCUL DES 
 
 OUTRAGES. VOL. II. APPLICATIONS DU BETON ARME. LIEUT.-COL. M. G. 
 
 ESPITALLIER. iWe Speciale des Travaux Publics. 
 
 SOME GERMAN PUBLICATIONS. 
 
 HANDBUCH FUR EISENBETONBAU. Edited by DR. ING. F. v. EMPERGER. 
 Wilhelm Ernst u. Sohn, Berlin. 
 
 DlE ElSENBETONLITERATUR BIS ENDE 1911. Von INGENIEUR R. HOFFMANN. 
 
 Wilhelm Ernst u. Sohn, Berlin. 
 
BIBLIOGRAPHY 115 
 
 DER ElSENBETONBAU EIN LEITFADEN FUR SCIIULE UND PRAXIS. Von C. 
 
 KERSTEN. Wilhelm Ernst u. Sohn, Berlin. 
 BRUCKEN IN EISENBETON. TEIL I. FLATTEN u. BALKENBRUCKEN. TEIL II. 
 
 BOGENBRUCKEN. C. KERSTEN. Wilhelm Ernst u. Sohn. 
 DIE THEORIE DES EISENBETONBAUES. PROF. M. FOERSTER, Dresden. Julius 
 
 Springer, Berlin. 
 TABELLEN FUR DIE BERECHNUNG VON EISENBETONKONSTRUKTIONEN. Von 
 
 INGENIEUR G. FUNKE. Julius Springer, Berlin. 
 
 EISENBETONBRUCKEN. DR. ING. F. KoGLER, Dresden. Julius Springer, Berlin. 
 There are also the publications of the Deutscher Ausschuss f iir Eisenbeton. Published 
 by Wilhelm Ernst u. Sohn. 
 
 PERIODICALS. 
 
 In addition to the articles on Reinforced Concrete in the general engineering 
 periodicals, the following are wholly or largely devoted to that subject : 
 
 CONCRETE AND CONSTRUCTIONAL ENGINEERING. Published at the North British 
 and Mercantile Building, Waterloo Place, London. Monthly, Is. Per 
 annum, 12s. 6rf. 
 
 FERRO-CONCRETE. A Monthly Review of Hennebique Construction. The 
 St. Bride's Press, Ltd., 24, St. Bride's Lane, E.C. Monthly, 6d. 6s. per 
 annum. 
 CEMENT AGE AND CONCRETE ENGINEERING. Cement Age Co., New York. 
 
 $1.50 per annum. 
 
 CEMENT ERA. Chicago. Monthly. $1.00 per annum. 
 
 In addition, Bulletins are issued by the United States Government Departments and 
 the American Universities from time to time. Particulars of these can be had from the 
 Technical Literature Company, 90, West Street, New York, or Messrs. Constable & Co., 
 10, Orange Street, Leicester Square, London. 
 
 The principal French and German periodicals are : 
 
 LE BETON ARME, CIMENT, NOUVELLES ANNALES DE LA CONSTRUCTION, and 
 REVUE DES MATERIAUX DE CONSTRUCTION ET DE TRAVAUX PUBLICS, 
 published in Paris. 
 BETON u. EISEN, ZEMENT u. BETON, and ARMIERTER BETON, published in 
 
 Berlin. 
 
 Particulars of which can be obtained from any of the French or German publishers 
 mentioned above. 
 
INDEX 
 
 ADHESION of the concrete to the reinforcements, 
 
 16, 79, 87 
 
 values of stresses on, 100 
 ARCH ribs, stresses in, 12 
 
 BEAMS, continuous, stresses in, 12 
 
 experiments on bending of, 30 
 notes on bending experiments, 95 
 BENDING, calculation of stress due to, 13 
 combined with thrust, 14 
 effects of transverse reinforcements 
 
 in, 101 
 BRIDGES, live loads on, 109 
 
 tests of, 111 
 
 BUCKLING of compression members, 17 
 BUILDINGS, loads and tests, 112 
 
 CALCULATIONS of resistance, instructions re- 
 garding, 2 
 simplification of, 81 
 CANAL bridges, 110, 111 
 CEMENT, properties of cement used in tests, 
 
 40 
 CENTRE of gravity in reinforced members, 
 
 10 
 COLUMNS, strength of concrete at base and top, 
 
 59, 74 
 
 safe loads on highly spiralled, 84 
 actual conditions of in practice, 85 
 experiments on eccentric loading of 
 
 49, 85 
 long, 83 
 
 limits of working stress in, 84 
 estimation of stability of, 17 
 exposed to lateral pressure, 18 
 tests of, 48 
 tests on axially loaded columns, 50, 
 
 51 
 
 hollow, tests of, 64 
 Stuttgart, experiments on, 20 
 variously reinforced tests of, 57 
 COLUMN reinforcement, most efficient percent- 
 ages, 84 
 COMPRESSION, calculation of simple com- 
 
 pressive resistance, 9 
 with bending, calculation of 
 resistance, 9, 85 
 
 COMPRESSION reinforcements, comparison of 
 
 longitudinals and spirals, 82 
 COMPRESSIVE STRESSES allowed by French 
 
 regulations, 7 
 allowed by Foreign 
 
 regulations, 7 
 
 CONCRETE, reinforced and without reinforce- 
 ment, weight of, 23, 57 
 volume of, from given mixture, 
 
 68 
 
 CONSIDERE, notes by, 91 
 CONTINUOUS beams, stresses in, 12 
 CONTRACTION, during setting of concrete, 22 
 
 measurement of, 22 
 CRACKS, influence on resistance of compression 
 
 areas, 100 
 CRUSHING, resistance of concrete to, 69 
 
 increase due to rein- 
 forcements, 70, 73 
 
 DEFLECTION of beams, measurement of, 31 
 
 curve of, 40, 41 
 
 of slab, load-deflection dia- 
 grams, 42 
 
 characteristics of, 46 
 DEFORMATION of reinforced concrete, 93 
 
 in beams, 98 
 
 of plane sections during bend- 
 ing, 78, 96 
 
 laws of, applied to bending, 79 
 estimation of, 91 
 
 ELASTICITY, modulus of concrete without rein- 
 forcement, 18, 22 
 modulus of reinforced concrete, 
 
 77 
 ratio of the moduli for concrete 
 
 and steel, 8 
 
 modulus of, for steel, 18, 26 
 ELASTIC effect of longitudinal reinforcements, 
 
 77 
 ELONGATION of reinforcements, curve of, 41 
 
 reinforced concrete without 
 
 cracking, 93 
 
 EMPIRICAL formulae, 89 
 EULER'S formula for long columns, 18 
 EXPERIMENTS on actual works, 80 
 
118 
 
 INDEX 
 
 FACTOR of safety, 6, 20, 81 
 FINAL state of stress in a member after un- 
 loading, 95 
 
 GRAVITY, centre of in reinforced members, 10 
 
 HEAT, variations of volume of concrete due to, 
 68 
 
 INERTIA, determination of moment of, 10 
 
 LOADS imposed on structures, 1, 109 
 LOADING and unloading, effects of, 94 
 LONGITUDINALLY reinforced prisms, compres- 
 sion tests of, 57 
 
 LONGITUDINAL reinforcements compared with 
 spirals, 82 
 
 " m," values of, 9, 19, 71 
 
 effect of exaggerating value in members 
 
 subject to bending, 86 
 " m'," values of, 8, 71 
 
 MODULUS of elasticity of non-reinforced con- 
 crete, 18, 22 
 of reinforced concrete, 
 
 77 
 
 MOMENT of inertia of section of reinforced 
 members, 10 
 
 NAVIER'S hypothesis, graphical verifications of, 
 
 39,47 
 NEUTRAL axis, position of, 13, 96 
 
 comparison of actual and cal- 
 culated positions, 97 
 
 PERCENTAGE of reinforcement, influence of on 
 stresses due to setting, 23, 96, 105 
 
 PITCH of spirals in spiral reinforcement, 8, 21, 
 71 
 
 PRISMS without reinforcement, compression 
 tests of, 54-55 
 
 RAILWAY bridges, loads on French bridges, 109 
 RANKINE'S formula for long columns, 17 
 REACTIONS, reciprocal after unloading, 95 
 RECTANGULAR beam, calculation of stresses in, 
 
 13 
 REINFORCEMENTS, slipping of, 16, 27, 99 
 
 effect of pro- 
 jecting over points of 
 support, 87 
 modulus of elasticity of, 18, 
 
 26 
 
 transverse in members sub- 
 ject to bending, 88 
 REPETITION of loading, effects of, 94 
 RESISTANCE of columns, variations through- 
 out the length, 74 
 
 RIBBED slabs, experiments on, 46, 103 
 ROAD bridges, loads on, 110 
 
 SAFETY, factor of, 6, 20, 81 
 SETTING of concrete, stresses due to, 23, 93, 96, 
 105 
 
 cement, variations in volume due 
 
 to, 68 
 
 SHEAR resistance, estimation of, 16 
 SHEAR resistance of reinforcements to, 80, 
 
 102 
 
 SHEAR reinforcements, tests of, 25 
 SHEAR strains in concrete of beam, curve of, 
 
 41 
 
 SHOCKS, effect of, on the resistance of rein- 
 forced concrete, 107 
 
 SLABS, remarks on the calculation of, 15 
 with concentrated loads, 15 
 width of acting with rib, 15, 104 
 supported along four sides, 16 
 transverse reinforcements in, 89 
 experiments on bending of, 42 
 graphical representation of strains in, 
 
 47 
 
 SLEEPER, experiments with a reinforced con- 
 crete sleeper, 107 
 SLIPPING of reinforcements, resistance to, 16, 
 
 99 
 
 experiments on, 27 
 
 SLIPPING of the concrete on itself, 16 
 SNOW loads on roofs, 112 
 SPIRAL reinforcements, analysis of effect of, 82 
 SPIRALLED column, increase of allowable 
 
 stress due to spiralling, 7 
 
 SPIRALLED prisms, compression tests of, 55, 56 
 SPIRALLING, instructions regarding, 1 
 SPIRALS, intertwining, experiments on, 66 
 
 multiple concentric, experiments on, 
 
 64 
 
 pitch of, 8, 21, 71, 77 
 STEEL, modulus of elasticity of. 18, 26 
 STIRRUPS, effects of in bending, 101, 102 
 STRAINS in slab, graphical representation of, 
 
 47 
 
 STRESS, limits of, 1 
 
 STRESSES and deformations of reinforced con- 
 crete, 81 
 
 STRESSES, initial due to setting, 23, 93, 96, 105 
 effects of high compressive stresses 
 
 in concrete, 75 
 allowable in French bridges (steel), 
 
 109 
 SYMBOLS, 5 
 
 T slab, calculation of stresses in, 13 
 TENSION tests on reinforced concrete, 23, 66 
 
 analysis of results of, 91 
 resistance and deformation of con- 
 crete without reinforcement due 
 to, 69 
 
INDEX 
 
 119 
 
 TENSION, effects of on the resistance and elas- 
 ticity of concrete to compression, 
 94 
 in members subject to bending, effect 
 
 of neglecting in calculations, 86 
 TESTS of structures, 3, 90, 111 
 TORSION tests, 27 
 TRANSVERSE reinforcements, notes on effects 
 
 of, 101 
 
 increase of com- 
 pressive stress 
 due to, 7, 71 
 
 TRANSVERSE reinforcements, resistance to 
 slipping of concrete, 17 
 
 TRANSVERSE reinforcements, comparison with 
 longitudinal reinforcements, 82 
 
 VOLUME of concrete resulting from given 
 mixture, 68 
 
 WATER, influence of proportion of water used 
 in gauging, 22, 74, 106 
 
 WEIGHT of concrete with and without rein- 
 forcement, 23, 57 
 
 WIND pressure, 110, 112 
 
 WORKS, instructions regarding execution 
 of, 2 
 
 lADBl'RY, AGNEW, & CO. LD. , PRINTERS, LONDON AND TONBRIDGE. 
 
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