Preface to Engineering mechanics

The importance of mechanics in the preparation of young engineers for work in specialised fields cannot be overemphasised. The demand from industry is more and more for young men who are soundly grounded in their fundamental subjects than for those with specialised training. There is good reason for this trend: The industrial engineer is continually being confronted by new problems, which do not always yield to routine methods of solution. The man who can successfully cope with such problems must have a sound understanding of the fundamental principles that apply and be familiar with various general methods of attack rather than proficient in the use of any one. It seems evident, then, that university training in such a fundamental subject as mechanics must seek to build a strong foundation, to acquaint the student with as many general methods of attack as possible, to illustrate the application of these methods to practical engineering problems, but to avoid routine drill in the manipulation of standardised methods of solution. Such are the aims of this book.

The content of the book is somewhat wider than can be covered in two courses of three semester hours or five quarter hours each. At the end of the discussion of statics, for example, there is a chapter on the principle of virtual work. The use of this principle results in great simplification in the solution of certain problems of statics, and it seems desirable to acquaint the student with its possibilities. At the end of the discussion of dynamics, there is a short chapter on relative motion, together with applications to engineering problems. These chapters can easily be omitted without introducing any discontinuity if there is insufficient time for them. Where time will not permit their consideration, they at least serve the purpose of indicating to the student that he has not exhausted the possibilities of the subject in his first encounter with it. Also, it is hoped that such material will be of value to those students especially interested in mechanics.

In many of our engineering schools, statics is given during the second semester of the sophomore year, before the student has studied integral calculus. For this reason Part One of this volume has been so written that, except for one or two sections that can easily be omitted, no knowledge of mathematics beyond the differential calculus is required. However, a free use of mathematics is made within these limits. Statics is probably the first course wherein the student has a chance to make practical use of his training in mathematics, and it seems important that he be not only given the opportunity but encouraged to use it to the full extent of its applicability.

The situation is usually quite different with dynamics. In some schools, for instance, this course does not immediately follow statics but is taken after strength of materials. Thus the students are more mature, and it seems justifiable in Part Two to make free use of the calculus and even some use of elementary differential equations. In this latter respect, however, the solutions are discussed in sufficient detail so that the student without special preparation in differential equations need have no difficulty.

Throughout Part Two the equations of motion are presented and handled as differential equations. Dynamics is not a subject to be handled superficially, and a too arduous attempt to simplify its presentation can easily result in the fostering of false notions in the mind of the beginner. Besides helping to forestall such possible misconceptions, the use of the differential equation of motion, as such, possesses several other advantages:

1. It makes it possible, at the outset, to place proper emphasis upon the inherent difference between dynamical problems involving known motion and those involving known acting forces.
2. It makes practicable the discussion of certain problems of dynamics (such as vibration problems) which otherwise could be handled only in a very cumbersome manner, if at all.
3. It gives the student a foundation in dynamics upon which he can successfully build if he desires to pursue advanced study or to read current literature on the subject.

Since the student usually has his greatest difficulty in applying the principles and theorems that he has just learned to specific situations, special attention has been given to the selection and treatment of a series of illustrative examples at the end of each article. The purpose of these examples is twofold:

1. They are sometimes used as a medium of presentation of material not included in the text proper.
2. They are designed to set an example to the student in logical methods of approach to the solution of engineering problems.

The solution of a problem in mechanics usually consists of three steps:

1. the reduction of a complex physical problem to such a state of idealisation that it can be expressed algebraically or geometrically;
2. the solution of this purely mathematical problem; and
3. the interpretation of the results of the solution in terms of the given physical problem.

Many of the illustrative examples are worked out in algebraic form, the answers being given simply as formulas. When numerical data are given, their substitution is made only in the final answer at the end. Such a procedure possesses several advantages, one of which is the training the student gets in reliable methods of checking answers. Two of the most valuable aids in checking the solution of a problem are the `dimensional check' and the consideration of certain limiting cases as logical extremes. The opportunity of making either of these checks is lost when given numerical data are substituted at the beginning of the solution. Another advantage of the algebraic solution is that it greatly enriches the possibilities of the third step in the solution of the problem, namely, significance of results. Finally, the algebraic solution is preferable if proper attention is to be given to numerical calculations, for only by having the result in algebraic form can it be seen with what number of figures any intermediate calculation must be made in order to obtain a desired degree of accuracy in the final result.

Since the first edition of `Engineering mechanics' appeared in 1937, the authors's `Theory of structures' and `Advanced dynamics' have been published, and these later volumes now contain some of the more advanced material that was originally in `Engineering mechanics'. It is hoped that the three volumes taken together represent a fairly complete treatment of engineering mechanics and its applications to problems of modern structures and machines, at the same time leaving the present volume better suited to the undergraduate courses in statics and dynamics as given in our engineering schools today.

In the preparation of this fourth edition, the entire book has been thoroughly revised. In doing this, the authors have had these objectives:

1. simplification of the text proper,
2. improved arrangement of subject matter, and
3. deëmphasis of the algebraic treatment of problems.

Various textbooks have been used in the preparation of this book, particularly in the selection of problems. In this respect, special acknowledgement is due the book `Collection of problems in Mechanics', edited by J. V. Mestscherski (St. Petersburg, 1913), in the preparation of which the senior author took part. The authors also take this opportunity to thank their colleagues at Stanford University for many helpful suggestions in regard to this revision, in particular, Prof. Karl Klotter, who read some portions of the revision and made many valuable suggestions for improvement in this edition.