HISTORY O F STRENGTH O F MATERIALS With a brief account of the history of theory of elasticity and theory of structures STEPHEN P. TIMOSHENKO Professor of Engineering Mechanics Stanford University DOVER PUBLICATIONS, INC., NEW YORK This Dover edition, first published in 1983, is an unabridged and unaltered republication of the work originally published in 1953 by McGraw-Hill Book Company, Inc., N.Y. International Standard Book Number: 0-486-6118 7- 6 Library of Congress Cataloging in Publication Data Timoshenko, Stephen, 1878-1972. History of strength of materials. Reprint. Originally published : New York : McGraw-Hill, 1953. 1. Strength of materials-History. I. Title. TA405.T53 1983 620.1'12 82-17713 Manufactured in the United States by Courier Corporation 61187611 www.doverpublications.com Introduction From the earliest times when people started to build, it was found nec- essary to have information regarding the strength of structural materials so that rules for determining safe dimensions of members could be drawn up. No doubt the Egyptians had some empirical rules of this kind, for without them it would have been impossible to erect their great mon- uments, temples, pyramids, and obelisks, some of which still exist. The Greeks further advanced the art of building. They developed statics, which underlies the mechanics of materials. Archimedes (287-212 B.c.) gave a rigorous proof of the conditions of equilibrium of a lever and out- lined methods of determining centers of gravity of bodies. He used his theory in the construction of various hoisting devices. The methods used by the Greeks in transporting the columns and architraves of the temple of Diana of Ephesus are shown in Figs. 1 to 3. The Romans were great builders. Not only some of their monuments and temples remain, but also roads, bridges, and fortifications. We know something of their building methods from the book by Vitruvius,’ a famous Roman architect and engineer of the time of Emperor Augustus. In this book, their structural materials and types of construction are described. Figure 4 shows a type of hoist used by the Romans for lifting heavy stones. The Romans often used arches in their buildings. Figure 5 shows the arches in the famous Pont du Gard, a bridge which is in service to this day in southern France. A comparison2 of the propor- tions of Roman arches with those of the present time indicates that nowadays much lighter structures are built. The Romans had not the advantages provided by stress analysis. They did not know how to select the proper shape and usually took semicircular arches of compara- tively small span. Most of the knowledge that the Greeks and Romans accumulated in the way of structural engineering was lost during the Middle Ages and only since the Renaissance has it been recovered. Thus when the famous Italian architect Fontana (1543-1607) erected the Vatican obelisk at the order of Pope Sixtus V, (Fig. 6), this work attracted wide attention from 1 Vitruvius, “Architecture,” French translation by De Bioul, Brussels, 1816. 2 For such a comparison, see Alfred Leger, “Les Travaux Publics aux temps dea Romains,” p. 135, Paris, 1875. 2 History of Strength of Materials European engineers. But we know that the Egyptians had raised several such obelisks thousands of years previously, after cutting stone from the quarries of Syene and transporting it on the Nile. Indeed, the Romans had carried some of the Egyptian obelisks from their original sites and erected them in Rome; thus it seems that the engineers of the six- FIGS.1 to 4. Bottom, Greeks’ methods of transporting columns. Top, type of hoist used by the Romans. teenth century were not as well equipped for such difficult tasks as their predecessors. During the Renaissance there was a revival of interest in science, and art leaders appeared in the field of architecture and engineering. Leonard0 da Vinci (1452-1519) was a most outstanding man of that period. He was not only the leading artist of his time but also a great scientist and engineer, He did not write books, but much information Inlroduct ion 3 was found in his notebooks’ regarding his great discoveries in various branches of science. Leonardo da Vinci was greatly interested in mechanirs and in one of his notes he states: “Mechanics is the paradise of mathematiral science because here we come to the fruits of mathematics.” Leonardo da Vinci uses the method of moments to get the corrcct solu- tions of such problems as those shown in Figs. 8a and 8b. He applies the notion of the principle of virtual displacements to analyze various systems of pulleys and levers such as are used in hoisting devices. It seems that FIG.5 . The famous Pont du Gard. Leonardo da Vinci had a correct idea of the thrust produced by an arch. In one of his manuscripts there is a sketch (Fig. 9) of two members on which a vertical load Q is acting and the question is asked: What forces are needed at a and b to have equilibrium? From the dotted-line par- allelogram, in the sketch, it can be concluded that Leonardo da Vinci had the correct answer in this case. Leonardo da Vinci studied the strength of structural materials exper- imentally. In his note “Testing the Strength of Iron Wires of Various Lengths” he gives the sketch shown in Fig. 10, and makes the following remark: “The object of this test is to find the load an iron wire can carry. Attach an iron wire 2 braccia long to something that will firmly support 1 A bibliography of Leonardo da Vinci’s work is given in the Encyclopaedia Britan- nica. Also a selection of passages from the manuscripts will be found in the book by Edward McCurdy, “Leonardo da Vinci’s Note-books.’’ See also the book by W. B. Parsons, ‘‘ Enginecn and Engineering in the Renaissance,” 1939. From the latter book Fig. 10 and the quotations given in this article are taken. 4 H is to r y of S tr e n g th o f M a te r ia ls FIQ.6 . The erection of the Vatican obelisk. Introducl ion 5 it, then attach a basket or any similar container to the wire and feed into the besket some fine sand through a small hole placed at the end of a hopper. A spring is fixed so that it will close the hole as soon as the wire breaks. The basket is not upset while falling, since it falls through a very short distance. The weight of sand and the location of the fracture of the wire are to be recorded. The test is repeated several times to check the results. Then a wire of one-half the previous length is tested and the additional weight it carries is recorded; then a wire of one-fourth length is tested and so forth, noting each time the ultimate strength and the location of the fracture.”’ Leonardo da Vinci also considered the strength of beams and stated a general principle as follows : “ In FIG.7 . Leonardo da Vinci. every article that is supported, but is free to bend, and is of uniform cross section and material, the part that is farthest from the supports will bend the most.’’ He recommends that a series of tests be made, starting with a beam that could carry a definite weight when supported at both ends, and then taking successively longer (a) (b) $J FIG.8 . beams of the same depth and width, and recording what weight these would carry. His conclusion was that the strength of beams supported at both ends varies inversely as the length and directly as the width. He also made some investigation of beams having one end fixed and the other free and states: “If a beam 2 braccia long supports 100 libbre, a beam 1 braccia long will support 200. As many times as the shorter length is See Parsons, “Engineera and Engineering in the Renaissance,” p. 72. 6 History of Strength of Materials contained in the longer, so many times more weight will it support than the longer one.” Regarding the effect of depth upon the strength of a beam there is no definite statement in Leonardo da Vinci’s notes. Apparently Leonardo da Vinci made some investigations of the strength of columns. He states that this varies inversely as their lengths, but directly as some ratio of their cross sections. These briefly discussed accomplish- ments of da Vinci represent perhaps the first attempt to apply statics in finding the forces acting in members of structures and also the first experi- ments for determining the strength FIG.9 . FIG. 10. Tensile test of wire by Leonardo da Vinci. of structural materials. However, these important advances were buried in da Vinci’s notes and engineers of the fifteenth and sixteenth centuries continued, as in the Roman era, to fix the dimensions of structural ele- ments by relying only on experience and judgment. The first attempts to find the safe dimensions of structural elements analytically were made in the seventeenth century. Galileo’s famous book “TWON ew Sciences”’ shows the writer’s efforts to put the methods applicable in stress analysis into a logical sequence. It represents the beginning of the science of strength of materials. 1 See English translation by Henry Crew and Alfonso de Salvio, New York, 1933. Preface This book was written on the basis of lectures on the history of strength of materials which I have given during the last twenty-five years to students in engineering mechanics who already had knowledge of strength of materials and theory of structures. During the preparation of the book for publication, considerable material was added to the initial contents of the lectures, but the general character of the course remained unchanged. In writing the book, I had in mind principally those stu- dents who, after a required course in strength of materials, would like to go deeper into the subject and learn something about the history of the development of strength of materials. Having this in mind, I did not try to prepare a repertorium of elasticity and give a complete bibliography of the subject. Such a bibliography can be found in existing books such as “A History of the Elasticity and Strength of Materials” by Todhunter and Pearson and the articles in volume 44 of the “Encyklopiidie der Mathematischen Wissenschaften,” edited by F. Klein and C. Muller. I wanted rather to follow the example of Saint-Venant’s Historique “ Abr6g6”* and give to a larger circle of readers a historical review of the principal steps in the development of our science without going into too much detail. In doing this, I considered it desirable to include in the history brief biographies of the most prominent workers in this subject and also to discuss the relation of the progress in strength of material to the state of engineering education and to the industrial development in various countries. There is no doubt, for example, that the develop- ment of railroad transportation and the introduction of steel as structural material brought many new problems, dealing with strength of structures, and had a great influence on the development of strength of materials. The development of combustion engines and light airplane structures has had a similar effect in recent times. Progress in strength of materials cannot be satisfactorily discussed without considering the development of the adjacent sciences such as theory of elasticity and theory of structures. There exists a close interrelation in the development of those sciences, and it was necessary to include some of their history in the book. In doing so I have taken * The historical introduction which Saint-Venant added to his edition of Navier’s book: “ R6sum6 des Lepons.” Y vi Preface from the history of theory of elasticity only those portions closely related to the development of strength of materials and omitted all material related to the purely theoretical and mathematical progress of that science. In the same way, in dealing with the development of theory of structures, the portions having only technical interest were not included in this book. In this writing, I have tried to follow the chronological form of presenta- tion and divided the history of the subject into several periods. For each of those periods I have discussed the progress made in strength of mate- rials and in adjacent sciences. This order was not always strictly followed, and in some discussions of the works of a particular author I have found it more expedient to put in the same place the review of all his publications, although some of them did not belong to the period under discussion. In the preparation of the book, the existing publications on the history of sciences were very helpful. In addition to the books already men- tioned I had in my hands the third edition of Navier’s book, “RBsum6 des Lepons . . . ,” edited by Saint-Venant and containing his “His- torique Abr6g6 . . . and his numerous notes which are now of great ” historical interest. I consulted also Saint-Venant’s translation of Clebsch’s book on Elasticity, which in itself contains the history of elasticity in its earlier periods. Among the biographies I found the following very useful: “Histoire des Sciences Mathematiques et Phy- siques” by M. Marie, Geschichte der Technischen Mechanik,” by “ M. Ruhlmann, several biographies in English, and collections of “63oges Academiques” by Franpois Arago and by Joseph Bertrand. For the review of newer publications it was necessary to go through many periodicals in various tongues. This took a considerable amount of time, but the writer will feel completely rewarded if his work will save some labor for other workers in history of strength of materials. I am thankful to my colleagues at Stanford University-to Prof. Alfred S. Niles for his comments on the portions of the manuscript dealing with the early history of trusses and the Maxwell-Mohr method of analyzing statically indeterminate trusses; and to Prof. Donovan H. Young who gave much constructive advice at the time of preparation of the manu- script. I am also very grateful to Dr. R. E. D. Bishop for his reading of the entire manuscript and his numerous important comments, and to our graduate student, James Gere, who checked the proofs. Stephen P. Timoshenko Stanford, Calif. December, 1952