Mechanics of materials

This book is intended to serve as an introduction to the study of the mechanical aspects of construction. Such a study must inevitably deal with both fact and theory. In conducting their classes in the theory of construction, the authors have felt that the student should acquire his facts as a natural accretion around a core of theory and that empirical and experimental methods should form as small a part as possible of his early training. Therefore, little of an empirical nature appears in this book. Likewise no emphasis has been placed on the study of the physical properties of materials, for this subject should be developed in a separate course which includes some actual contact with the materials themselves and with the methods used in making scientific determinations of their properties.

It has not seemed advisable to present very much in the way of tabulated data though a few tables are included in the Appendix. Many good handbooks are available and it has been assumed that this book will be supplemented by a reference book substantially equivalent to those published by the steel manufacturers.

For reasons more fully explained in 84, no attempt has been made to select topics and problems from the very latest developments in structural practice. The attempt has rather been to select such examples as afford a good opportunity for the study of some general principle. For example the flitched beam (208) is well nigh obsolete, but the principle involved in its design leads directly to the study of reinforced concrete. Again it is quite possible that, with the development of welding, riveted joints may become more or less rare, but as an illustration of certain principles well worthy of study the riveted joint will remain the more important form.

The student is assumed to have an elementary knowledge of physics and of mathematics, including the integral calculus. The attempt has been to present each idea as required by the nature of the subject itself rather than to fit the treatment to students who are insufficiently prepared, on the one hand, or on the other, to make the whole field an exercising ground for the higher mathematics.

Since structural work makes severe demands on the imagination and the ability to "see" solutions, the visual appeal has been emphasized whenever possible. Also physical concepts have been given preference over mathematical processes, graphical methods being used quite freely. Nevertheless, in the treatment of such subjects as the deformations of beams and unsymmetrical bending, well known graphical or partly graphical methods have been omitted and attention has been confined to developing the fundamental concepts on which such methods are based.

In preparing the illustrations the attempt has been made to keep them in scale wherever possible. In the study of such a subject as deformation, some exaggeration is positively necessary; but in other cases, notably in shear and moment diagrams, the actual scales have been followed closely in order to cultivate the sense of proportion and a keenness of observation that comes from a careful training in this respect.

In Chapters XX to XXV several subjects have been touched upon in a most rudimentary fashion. Each subject might well be the basis of a whole book. The idea has been to rouse interest and excite curiosity rather than to offer solutions.

In presenting such a subject, material is necessarily gathered from many sources. Among the books most used for reference are: “The Mechanics of Engineering" by Professor I. P. Church, "Mechanics of Materials" by Professor Mansfield Merriman and "Applied Mechanics" by Professors C. E. Fuller and W. A. Johnson. Members of the various Faculties of the University have been generously helpful with suggestions, advice and encouragement. Special acknowledgment is due to Professor C. F. Craig of the Department of Mathematics for constructive criticism of the most helpful sort. The illustrations of materials tested to destruction were taken from test made in the laboratories of the College of Engineering under the direction of Professors E. N. Burrows, A. C. Davis, and H. H. Schofield. Other acknowledgments are made throughout the text.

Elements of Structural Engineering. The elements which enter into the problem of structural engineering are (1) the loads which a structure or any part of it is to carry, (2) the materials of which it is to be made, and (3) the size, shape, and disposition of the various members.

The determination of the loads will be taken up only in its most rudimentary form. In practice it is a very simple subject, but it depends mainly on experience, statistics, and local conditions. This book will deal more especially with the principles of statics, and with the mechanics of materials, leaving the other questions mentioned above to be taken up in a later course in structural design.

The selection of materials which will be appropriate and economical for use in a given structure involves a detailed knowledge of the physical characteristics and properties of each possible material as well as a broad general acquaintance with market conditions. This is a lifelong study, since the sources of supply, the processes of manufacture, and the comparative costs are constantly changing.

The study of the characteristics of materials has been conducted intensively in the past few decades. There is now a vast amount of literature, both standard and periodical. The testing of materials can fairly be classed as a separate science which is well established and is being carried forward in numerous laboratories.

While the sources of information regarding materials are plentiful, it is probably impossible for a satisfactory knowledge of materials to be acquired merely through reading. Some direct contact with materials, both in the laboratory and in the field, should form part of the training of every person intrusted with their selection. The subject of materials will be discussed in this book only in so far as it is necessary to give point to the problems discussed.

When the loading of a structure has been determined and the material to be used has been selected, it remains to fix the size, shape, and disposition of its parts. It is this problem that is to be investigated in the following chapters. The results of experimental engineering on the one hand and the principles of mechanics on the other are brought to bear on the problem through processes which are chiefly mathematical.

Methods of Structural Engineering. Principles may be combined, elaborated, or even evolved by purely mental processes. Facts are established through the senses, by observation and by experiment. The methods of structural engineering spring from the above considerations.

A. The rational method consists in obtaining results by purely mental processes, reasoning from established facts to their logical conclusions. This is what is done in each of the branches of mathematics, which is a wholly rational science.

B. The experimental method is the one by which most of the facts of science are established. It consists in the observation of actual happenings and the classification of the determined results. Thus the acceleration due to gravity can be established only by experiment; but once the law is thus established, it may be extended and applied to wholly new cases by the rational method.

C. The empirical method consists in the study of precedents, and in following traditions with only such slight and cautious departures as may be dictated by time and circumstance.

The solution of any important structural problem will involve, to some extent, each of these methods. Applied sciences have, in general, grown from the empirical, through the experimental, to a rational stage. The great structures of antiquity were built with a very meagre scientific knowledge concerning the mechanical and structural principles involved. Therefore progress was slow and halting. The developments during the Middle Ages and the Renaissance were, in essence, slow and cautious experiments. It is only in comparatively recent times that rational methods have been made possible by the body of fact and experience accumulated in the past and by the development of science in general. The rapid progress and dependable conclusions of the present day are due solely to the application of the rational method to the problem in hand.

Where the necessary facts are well established, the rational method is far the best and most reliable. But when the facts are at all obscure or confused, it is necessary to check the results of the rational method by experimental determinations. Some important structural problems, notably the design of columns, still are, and will perhaps remain, dependent on experimental data for their solution. Other problems, particularly those involved in masonry construction, depend largely, if not wholly, on empirical solutions. However, most of the important structural problems admit of solutions which are largely rational.

It is important that the student keep these methods and the distinction between them clearly in mind. Empirical methods are to be avoided whenever possible, but often rational and empirical methods must be combined. It is wise to keep clearly in mind which processes rest on a solid rational basis and which depend on the less trustworthy empirical knowledge.