THEORIES OF THE STRENGTH OF MATERIALS, ROOFS, WITH NUMEROUS EXAMPLES. BY STEPHEN FENWICK, F.R.A.S. OF THE ROYAL MILITARY ACADEMY, WOOLWICH. LONDON: BELL AND DALDY, 186, FLEET STREET. 1861. PREFACE. THE special science which forms the subject of this volume has, during the last few years, made very considerable progress. Not more than a quarter of a century has elapsed since the celebrated French philosopher and mathematician, Auguste Comte, remarked that "the theory of the fracture of solid bodies, a theory barely sketched by Galileo, Huyghens, and Leibnitz,—was in a very imperfect and precarious state, notwithstanding the labours of several recent geometricians." But the theory thus characterised by Comte has, since the first appearance of his Cours de Philosophie Positive, made a rapid and satisfactory advance, through the researches of Poncelet, Morin, and others, whose works I have diligently consulted in the course of my undertaking. The conditions of mechanical constructions have now been divested, in a great measure, of empiricism, and systematic theories have been raised on the foundations of demonstrative evidence. Numerous practical mechanicians, aided by sufficient mathematical knowledge, have tabulated and recorded the results of careful experiments touching the strength and tenacity of various mechanical and architectural organisations. Theory and practice have thus formed an alliance from which the best consequences have already ensued. I have divided my subject into two Parts: The First Part includes the theory and some of the applications of the STRENGTH AND RESISTANCE OF MATERIALS. The Second Part contains the theory and the construction of ROOFS and ARCHES. The straining forces which act upon a structure having been determined by simple Statical considerations, formulæ of solution are thence deduced by the theory established in Part I., with the ultimate view of estimating the strength of each particular construction. These formulæ are the result of exact mathematical reasoning. The various experimental data which have been adopted, are placed in convenient juxtaposition with each corresponding theoretical section. Throughout the whole work the method of determining the dimensions of the different parts of a structure, in order to fulfil certain conditions, has been attentively kept in view. This important feature constitutes a distinguishing characteristic of the present publication. In no other English work is this method adopted with respect to TORSION, SOLIDS OF EQUAL RESISTANCE, ROOFS and ARCHES.* With the desire of rendering my labours more easily available, I have divided the work into small Chapters, and in some cases each Chapter is subdivided into sections. Chapter I., Part I., contains some necessary introductory remarks, and the first principles of the RESISTANCE OF MATERIALS. This part of the subject is developed at considerable length. In the preliminary observations the practical man is cautioned against trusting implicitly to the formulæ established in Part I., when the straining * In the new edition of the Encyclopædia Britannica just completed, in the article on the Strength of Materials, we are told that the writer has not been able to deduce the formula for the Resistance to Torsion of a cylindrical body when the length of the cylinder is taken into account. This formula is given in the present Treatise, and according to Morin, the truth of the formula has been verified by the experiments of MM. Duleau and Savart. forces which act upon a body pass certain limits. It is a remarkable fact, noticed by all experimentalists on the STRENGTH OF MATERIALS, that after a certain point has been reached, any addition of strain increases the dilatation of a body in a much higher proportion than before this limit is passed. This, it is conjectured, arises from the disunion of the particles of the body, whose joint action contributed to the whole effect. Hence I have taken the utmost care to cite from the best authorities the necessary constants for those limits, which are usually denominated coefficients of safety. In the remarks immediately preceding the chapters on ROOFS and ARCHES, it is shown that a structure may yield and give way either by the sliding of certain of its surfaces of contact upon one another, or by their turning upon one another, and that the stability of the structure must be studied with reference to each of these suppositions. On this point the Rev. Canon Moseley's elaborate and excellent work on the MECHANICAL PRINCIPLES OF ENGINEERING has been consulted with great advantage. In the determination of the stability of the ARCH, it may be observed, the main elements of investigation are the horizontal thrust, the point of application of this thrust, and the weakest joint of the arch; and on this part of my work I have bestowed the utmost attention. The immense progress of railways in this country during years recently past, has greatly modified the theory and practice of BRIDGE BUILDING. I have, in consequence, thought it proper to diverge considerably from the ordinary track that has been pursued in the elementary works on this subject that have hitherto appeared. Numerous examples (with their answers) have been proposed for solution in this department of the building art. The London and Waterloo bridges in the metropolis, which rank among the finest structures of the elliptical arch, and |