Text book on the strength of materials

PREFACE

Five years of extensive use of this book, since the appearance of the first edition, have brought to the authors from various sources numerous suggestions relating to its improvement. In particular the authors wish to acknowledge their indebtedness to Professor Irving P. Church of Cornell University and to Professor George R Chatburn of the University of Nebraska for their unfailing interest and frequent valuable suggestions.

To utilize the material so obtained, the text has been thoroughly revised. In making this revision the aim of the authors has been twofold: first, to keep the text abreast of the most recent practical developments of the subject; and second, to simplify the method of presentation so as to make the subject easily intelligible to the average technical student of junior grade, as well as to lessen the work of instruction.

Besides correcting the errors inevitable to a first edition, special attention has been given to amplifying the explanation wherever experience in using the book as a text has indicated it to be desirable. This applies especially to the articles on Poisson's ratio, the theorem of three moments, the calculation of the stress in curved members, the relation of Guest's and Sankine's formulas to the design of shafts subjected to combined stresses, etc.

Considerable new material has also been added. In Part I a set of tables has been placed at the beginning of the volume to facilitate numerical calculations. Other important additions are articles on the design of reinforced concrete beams, shrinkage and forced fits, the design of eccentrically loaded columns, the design and efficiency of riveted joints, the general theory of the torsion of springs, practical formulas for the collapse of tubes, and an extension of the method of least work to a wide variety of practical problems. This last includes the derivation and application of the Fraenkel formula for the bending deflection of beams, and also a simple general formula for the shearing deflection of beams, never before published.

Nearly one hundred and fifty original problems have also been added to Part L These problems are designed not merely to provide numerical exercises on the text, but have been selected throughout with the specific purpose of emphasizing the practical importance of the subject and extending the range of its application as widely as possible. Many of them are practical shop problems brought up by students in the cooperative engineering course at the University of Cincinnati

In Part II the recent advances in the manufacture of steel have been given special attention, including the properties of vanadium steel, manganese steel, and high-speed steel Reinforced concrete has also received a more adequate treatment, and the chapter on this subject has been thoroughly revised and modernized. The chapter on timber has also received an equally thorough revision, and considerable material on preservative processes has been added.
 

Classification of materials.

Materials ordinarily used in engineering construction may be divided into three classes, plastic, supple, and elastic.

Plastic materials are characterized by their inability to resist stress without receiving permanent deformation. Examples of such materials are lead, wet clay, mortar before setting, etc.

Supple bodies are characterized by their lack of stiffness. In other words, supple bodies are capable of undergoing large amounts of elastic deformation without receiving any plastic deformation. In this respect plastic and supple bodies exhibit the two extremes of physical behavior. Examples of supple bodies are rubber, copper, rope, cables, textile fabrics, etc.

Elastic bodies comprise all the hard and rigid substances, such as iron, steel, wood, glass, stone, etc. For such bodies the plastic deformation for any stress within the elastic limit is so small as to be negligible; but when the stress surpasses this limit the plastic deformation becomes measurable and gradually increases until rupture occurs. This permanent deformation is the outward manifestation of a change in the molecular arrangement of the body. For a stress within the elastic limit the forces of attraction between the molecules are sufficiently great to hold the molecules in equilibrium; but when the stress surpasses the elastic limit, the molecular forces can no longer maintain equilibrium and a change in the relation between the molecules of the body takes place, which results in the body taking a permanent set.

Rigid bodies have the character of supple bodies when one of their dimensions is very small as compared with the others. An instance of this is the flexibility of an iron or steel wire whose length is very great as compared with its diameter. Furthermore, rigid bodies behave like plastic bodies when their temperature is raised to a certain point. For example, when iron and steel are heated to a cherry redness- they become plastic and acquire the property of uniting by contact.

Time effect.

It has been found by experiment that elastic deformation is manifested simultaneously with the application of a stress, but that plastic deformation does not appear until much later. Thus if a constant load acts for a considerable time, the deformation gradually increases; and when the load is removed the return of the body to its original configuration is also gradual. This phenomenon of the deformation lagging behind the stress which produces it is called hysteresis. The gradual increase in the deformation under constant stress is also called the flow of the material; and the gradual return of the body to its original shape upon removal of the stress is known as elastic after work. This gradual flow which occurs under constant stress approaches a limit if the stress lies below the elastic limit, but continues up to fracture if the stress is sufficiently great.

Fatigue of metals.

If a stress lies well within the elastic limit, it can be removed and repeated as often as desired without causing rupture. If, however, a metal is stressed beyond the elastic limit, and this stress is removed and repeated, or alternates between tension and compression, a sufficient number of times, it will eventually cause rupture. This phenomenon is known as the fatigue of metals, and has been made the subject of laborious experiment by Wohler, Bauschinger, and others. The results of their experiments show that the less the range of variation of stress, the greater the number of repetitions or reversals of stress necessary to produce rupture. From this we conclude that the elastic limit of a material is much more important than its ultimate strength in determining the stability of an engineering structure of which it forms a part.

The fatigue of metals indicates that dislocation of matter begins to be produced as soon as the elastic limit is passed, and continues under the action of relatively small forces. This is confirmed by the well-known fact that if, as the result of a blow, a fissure or crack is started in a piece of glass or cast iron, this fissure will spread without any apparent cause until the piece breaks in two, the only way of stopping this tendency to spread being by boring a small hole at either end of the fissure.

The explanation of the above is that for stresses within the elastic limit the temperature of the body is not raised, and consequently all the work of deformation is stored up in the body to be given out again in the form of mechanical energy upon removal of the stress. If, however, the elastic limit is surpassed, the friction of the molecules sliding on each other generates a certain amount of heat, and the energy thus transformed into heat is not available for restoring the body to its original configuration.

Hardening effects of overstraining

When such materials as iron and steel are stressed beyond the elastic limit, it is found upon removal of the stress that the effect of this overstrain is a hardening of the material, and that this hardening increases indefinitely with time. For example, if a plate of soft steel is cold punched, the material surrounding the hole is severely strained. After an interval of rest the effects of this overstrain is manifested in a hardening of the material which continues to increase for months. If the plate is subsequently stressed, the inability of the portion .overstrained to yield with the rest of the plate causes the stress to be concentrated on these portions, and results in a serious weakening of the plate.

Other practical instances of hardening due to overstrain are found in plates subjected to shearing and planing, armor plates pierced by cannon balls, plates and bars rolled, hammered, or bent when cold, wire cold drawn, etc.


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