The elasticity and resistance of the materials of engineering
THE ELASTICITY AND RESISTANCE OF THE MATERIALS OF ENGINEERING
BY H. BURR,
NEW YORK; JOHN WILEY & SONS; 1903.
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The elasticity and resistance of the materials of engineering
PREFACE TO SIXTH EDITION.
The present edition of this work constitutes almost a new book, one-half or more of the entire volume being new matter. Much of the latter contains original matter not hitherto published. Portions of those chapters on combined bending and direct stress and on the theory and design of concrete-steel members are of this nature. The effort has been to set forth the treatment of concrete-steel beams and other members with complete fulness to meet the requirements of that rapidly extending field of engineering construction.
It is believed that the value of the book is greatly enhanced by the tables which the author is permitted to include in this volume through the generous courtesy of the Cambria Steel Company. These practical tables, found at the end of the book, are taken directly from the Cambria Steel Company's Handbook, and they will not only enable any instructor to give with the greatest facility extended practical exercises of computations and design in his instruction work, but they will also be found of great value in structural practice.
The advanced analytic matter relating to the general theory of elasticity in amorphous solid bodies, and the exact theories of torsion and flexure, have been placed at the end of the volume in Appendix I. While this matter may not be of immediate use to the ordinary practitioner, every real student of the subject of resistance of materials should be familiar with the treatment of these general problems, special solutions of which only are required in the every-day practice of the engineer.
It is believed that the value of the book is greatly enhanced by the tables which the author is permitted to include in this volume through the generous courtesy of the Cambria Steel Company. These practical tables, found at the end of the book, are taken directly from the Cambria Steel Company's Handbook, and they will not only enable any instructor to give with the greatest facility extended practical exercises of computations and design in his instruction work, but they will also be found of great value in structural practice.
The advanced analytic matter relating to the general theory of elasticity in amorphous solid bodies, and the exact theories of torsion and flexure, have been placed at the end of the volume in Appendix I. While this matter may not be of immediate use to the ordinary practitioner, every real student of the subject of resistance of materials should be familiar with the treatment of these general problems, special solutions of which only are required in the every-day practice of the engineer.
CONTENTS
- ELEMENTARY THEORY OF ELASTICITY IN AMORPHOUS SOLID BODIES
- HOLLOW CYLINDERS AND SPHERES AND TORSION
- FLEXURE
- RESILIENCE
- COMBINED STRSSS CONDITIONS
- TECHNICAL.
- TENSION
- COMPRESSION
- COMPRESSION - LONG COLUMNS
- SHEARING AND TORSION
- BENDING OR FLEXURE
- CONCRETE-STEEL MEMBERS
- ROLLED AND CAST FLANGED BEAMS
- CONNECTIONS
- PLATE GIRDERS
- ROPES AND CHAIN CABLES
- MISCELLANEOUS PROBLEMS
- WORKING STRESSES AND SAFETY FACTORS
- THE FATIGUE OF METALS
- THE FLOW OF SOLIDS
PART I. - ANALYTICAL
ELEMENTARY THEORY OF ELASTICITY IN AMORPHOUS SOLID BODIES.
Art. I. - General Statements
The molecules of all solid bodies known in nature are more or less free to move toward, or from, or among each other. Resistances are offered to such motions, which vary according to the circumstances under which they take place and the nature of the body. This property of resistance is termed the elasticity of the body.
The summation of the displacements of the molecules of a body, for a given point, is called the distortion or strain at the point considered. The force by which the molecules of a body resist a strain, at any point, is called the stress at that point. This distinction between stress and strain is fundamental and important.
Stresses are developed, and strains caused, by the application of force to the exterior surface of the material.
These stresses and strains vary in character according to the method of application of the external forces. Each stress, however, is accompanied by its own characteristic strain and no other. Thus there are shearing stresses and shearing strains, tensile stresses and tensile strains, compressive stresses and compressive strains. Usually a number of different stresses with their corresponding strains are coexistent at any point in a body subjected to the action of external forces.
It is a matter of experience that strains always vary continuously and in the same direction with the corresponding stresses. Consequently the stresses are continuously increasing functions of the strains, and any stress may be represented by a series composed of the ascending powers (commencing with the first) of the strains multiplied by proper coefficients. When, as is usually the case, the displacements are very small, the terms of the series whose indices are greater than unity are exceedingly small compared with the first term, whose index is unity. Those terms, may consequently be omitted without essentially changing the value of the expression. Hence follows what is ordinarily termed Hooke's law:
The ratio between stresses and corresponding strains, for a given material, is constant.
This law is susceptible of very simple algebraic representation. If a piece of material, whose normal cross section is i4, is subjected to either tensile or compressive stress, its length L will be changed by the amount delta L. If P be the external force or loading which produces that deformation or change of length, the amount of force or stress, supposed to be uniformly distributed, acting on I square inch of normal cross-section of the piece, will be found by dividing the total force P by the area of cross section A. This amount of uniformly distributed stress is called the “intensity of stress” and it is a most important quantity. In dealing with the effects of forces or stresses in all engineering work, the amount of such force or stress on a square unit of area, usually a square inch in American practice, and called the intensity, is often the main object sought, for it determines the question whether material is carrying too much or too little load, as well as many other related questions.
Again, the important consideration as to strain is the fractional change in length of the entire piece, and not the total change in length expressed in the unit adopted, ordinarily an inch. This fractional change of length is the same as the amount of actual change of each linear unit of the piece, as is found by dividing AL by L. Inasmuch as that fraction expresses the amount of change in length for each unit, it is frequently called the rate of change of length or rate of deformation. Hooke's law is to the effect that the intensity of stress is proportional to the rate of strain, and its analytic expression may readily be written.
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