The strength of materials - Ewing

In modem schools of Engineering a student acquires his knowledge of the Strength of Materials and of its application in design, partly by hearing lectures, partly by making experiments in the laboratory, and partly by working out examples in the drawing-office. The present treatise is an attempt to set forth briefly a lecture-room treatment of the subject, which to be effective must be supplemented by laboratory and drawing-office work. Indications are also given of some laboratory experiments in elasticity, and a number of pieces of apparatus are described which have proved serviceable at Cambridge.

I am indebted to Messrs A. and C. Black for permission to use the substance of the article "Strength of Materials" which I wrote for the Ninth Edition of the Encyclopedia Britannica. Also to Professor Unwin, and his publishers Messrs Longmans, for the illustrations on page 77, which are taken from his valuable Treatise on the Testing of Materials. To Mr T. Peel of Magdalene College I owe much for his kindness and care in reading the proofs of these sheets.

CHAPTER I - STRESS AND STRAIN

1. Introductory. The term "Strength of Materials" is used in a somewhat wide sense to name that part of the Theory of Engineering which deals with the nature and effects of stresses in the several parts of engineering structures. When a structure is loaded, that is to say, when forces of any kind are applied to it, the applied forces cause the parts of the structure to be stressed in various ways. Unless the parts are severally strong enough and stiff enough to bear these stresses the structure fails. To determine beforehand what loads the structure will bear safely, or conversely to design a structure which will be safe under a given set of loads, requires two things. We must be able to analyse the stresses in the various parts of the structure and by determining their relation to the applied loads to calculate their amounts. And further, we must know by experiment the properties of the materials which form the structure, both as to strength and as to stiffness, in order to judge after the action of the load has been analysed, what dimensions should be given to the parts to make them individually safe, and to prevent the structure as a whole from being unduly strained out of shape.

Hence the subject has two sides. On one hand, it is experimental and deals with the properties which materials are found to possess as to strength and elasticity. On the other, it is mathematical and discusses the kinds of stress to which the pieces of structures are subject, and also the changes of form which occur in consequence of the fact that all materials are more or less elastic.

2. Stress. Stress is the mutual action between two bodies, or between two parts of a body, whereby each of the two exerts a force upon the other.

Thus when a stone lies upon the ground there is at the surface of contact a stress, one aspect of which is the force which the stone exerts upon the ground, pushing the ground downwards, and the other aspect is the equal force directed upwards which the ground exerts upon the stone. Newton's "Third Law," that action and reaction are equal and opposite, may be paraphrased by the statement that every force is one aspect of a stress. A stress may exist between two separate bodies, or between portions of a single body separated only by an imaginary surface of division. In a tie-rod, for instance, which is bearing a pull there is a stress between the two parts into which the rod may be imagined to be divided by any plane of cross-section: each part exerts a pull upon the other part across the plane.

3. State of Stress. A body is said to be in a state of stress when there is stress between the two parts which lie on opposite sides of any imaginary dividing surface. Thus the tie-rod of the last example is a body in a state of stress because there is a pull between the parts into which the rod is cut by any imaginary surface of cross-section.

A pillar or block supporting a weight is in a state of stress because at any cross-section the part above the section pushes down against the part below, and the part below pushes up against the part above. A plate of metal that is being cut in a shearing machine is in a state of stress, because at the plane which is about to give way by shearing the portion of metal on either side is tending to drag the portion on the other side with a force in that plane.

4. Condition of Equilibrium, The kind and amount of stress which exists over any surface within a body at rest is in general to be determined by considering that if the body is conceived to be divided into two parts A and B by the surface in question the force which A exerts upon B across the surface must equilibrate all the other forces which act on B, namely, the loads or external forces which are applied to it, including its weight and any forces which are exerted on it by its supports. Similarly the forces which act on A must when taken together be in equilibrium, and the forces exerted by B upon A must balance the other forces which act on A, Thus the stress between A and B may be investigated by considering the equilibrium of either A or B.

6. Distribution of Stress. Intensity of Stress. A stress acting at a surface is distributed over it, each square inch or other portion of the surface bearing so much. The distribution may or may not be uniform. If it is uniform every square inch or other unit of area in the surface bears the same amount of the stress as every other. The intensity of stress, by which is meant the amount of stress per unit of area, is in that case found by dividing the whole stress by the whole area.

6. Normal and Tangential Stress. When a solid body is in a state of stress the direction of the stress at any imaginary surface of division may have any inclination to the surface; it may be normal to the surface, or tangential to it, or oblique.


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