Stress (mechanics)

“ Professor James Thomson 4 pointed out that the effect of any externally applied load depends, to a very material extent, on whether there is or is not initial internal stress, or, in other words, whether the loaded piece is initially in what Professor Karl Pearson has called a state of ease. Internal stress existing without the application of force from without the piece must satisfy the condition that its resultant vanishes over any complete cross-section. ”

“ This gives an ideal solid, which may be called the stress figure, whose height shows the distribution of stress over the surface which forms its base. A line drawn from g, the centre of gravity of the stress figure, parallel to the ordinates Aa, &c, determines the point c, which is called the centre of stress, and is the point through which the resultant of the distributed stress acts. ”

“ The existence of initial stress has been correlated above with the existence of body forces such as the force of gravity, but it is not necessarily dependent upon such forces. A sheet of metal rolled into a cylinder, and soldered to maintain the tubular shape, must be in a state of considerable initial stress quite apart from the action of gravity. ”

“ Normal and Tangential Stress.—In a solid body which is in a state of stress the direction of stress at an imaginary surface of division may be normal, oblique or tangential to the surface. When oblique it is conveniently treated as consisting of a normal and a tangential component. Normal stress may be either push (compressive stress) or pull (tensile stress) . Stress which is tangential to the surface is called shearing stress. ”

“ The strain-components contemplated in experiments upon which the law is founded are measured from a zero of reckoning which corresponds to the state of the body subjected to experiment before the experiment is made, and the stress-components referred to in the statement of the law are those which are called into action by the forces applied to the body in the course of the experiment. No account is taken of the stress which must already exist in the body owing to the force of gravity and the forces by which the body is supported. ”

“ It is in fact the elastic limit rather than the ultimate strength of the material on which the question mainly depends of how high the working stress may safely be allowed to rise in any particular conditions as to mode of loading, and accordingly it becomes a matter of much practical importance to determine by tests the amount of stress which can be borne without permanent strain. ”

“ We must suppose that there is a pressure in the direction of the lines of force, combined with a tension in all directions at right angles to the lines of force. Such a state of stress would, no doubt, account for the observed effects of gravitation. ”

“ Compound Stress.—A more complex state of stress occurs if the block is compressed or extended by forces applied to a pair of opposite sides, as well as by forces applied to its ends—that is to say, if two simple longitudinal stresses in different directions act together. A still more complex state occurs if a third stress be applied to the remaining pair of sides. ”

“ If, however, instead of an intense overwhelming activation, the kinetic system is continuously or intermittently overstimulated through a considerable period of time, as long as each of the links in the kinetic chain takes the strain equally the result will be excessive energy conversion, excessive work done; but usually, under stress, some one link in the chain is unable to take the strain and then the evenly balanced work of the several organs of the kinetic system is disturbed. ”

“ A body which has been strained beyond the limit of linear elasticity is often said to have suffered an “over-strain.” When the load is removed, the set which can be observed is not entirely permanent; but it gradually diminishes with lapse of time. This phenomenon is named “elastic after-working.” If, on the other hand, the load is maintained constant, the strain is gradually increased. This effect indicates a gradual flowing of solid bodies under great stress ”

“ Since the equable concrete is the natural colorless expression of unimpassioned thought, force applied to any part of it changes its character, and gives it a more or less significant emphasis. The three most usual forms of stress are the radical, the median, and the final; these may be effected in any of the degrees of force. Compound stress and thorough stress admit of but little variation. ”

“ When external forces act upon a bar in a direction away from its ends or a direct pull, the stress is a tensile stress; when toward the ends or a direct push, compressive stress. In the first instance the strain is an elongation; in the second a shortening. Whenever the forces tend to cause one portion of the material to slide upon another adjacent to it the action is called a shear. ”

“ If the applied load is not strictly axial, if the strut is not initially straight, if it is subject to any deflexion by transverse forces, or if the modulus of elasticity is not uniform over each cross- section — then loads smaller than the limit which causes instability will produce a certain deflexion which increases with increase of load, and will give rise to a uniformly varying stress of the kind illustrated in figs. ”

“ Permissible Working Stress.—In applying a knowledge of the strength of materials to determine the proper sizes of parts in an engineering structure we have to estimate a permissible working stress. This is based partly on special tests and partly on experience of the behaviour of the material when used in similar structures. The working stress is rarely so much as one-third of the ultimate strength ”

“ Elastic limit as measured in tests and used in design may be defined as that unit stress at which the deformation begins to increase in a faster ratio than the applied load. In practice the elastic limit of a material under test is determined from the stress-strain diagram. It is that point in the line where the diagram begins perceptibly to curve.2 (See Fig. 1.)
Resilience is the amount of work done upon a body in deforming it. ”

“ Before we leave this subject of mechanical adaptation, let us dwell once more for a moment upon the con­si­de­ra­tions which arise from our conception of a field of force, or field of stress, in which tension and compression (for instance) are inevitably combined, and are met by the materials naturally fitted to resist them. It has been remarked over and over again how harmoniously the whole organism hangs together, and how throughout its fabric one part is related and fitted to another in strictly functional correlation. ”

“ The stresses which occur in engineering practice are, or ought to be, in all cases within the limits of elasticity, and within these limits the change of cross-section caused by longitudinal pull or push is so small that it may be neglected in reckoning the intensity of stress.
Ultimate tensile strength and ultimate shearing strength are well defined, since these modes of stress (simple pull and simple shearing stress) lead to distinct fracture if the stress is sufficiently increased. ”

“ So far, dealing wholly with the stresses and strains due to tension and compression, we have altogether omitted to speak of a third very important factor in the engineer’s calculations, namely what is known as “shearing stress.” A shearing force is one which produces “angular distortion” in a figure, or (what comes to the same thing) which tends to cause its particles to {685} slide over one another. A shearing stress is a somewhat complicated thing, and we must try to illustrate it (however imperfectly) in the simplest possible way. ”

“ Tests of Strength.—Ordinary tests of strength are made by submitting the piece to direct pull, direct compression, bending or torsion. Testing machines are frequently arranged so that they may apply any of these four modes of stress; tests by direct tension are the most common, and next to them come tests by bending. When the samples to be tested for tensile strength are mere wires, the stress may be applied directly by weights ”

“ Now, as all movement must take place in the presence of or against resistance, a body which moves in the line of the greatest stress necessarily moves in the direction of the least stress, and it is this movement in the direction of the least stress which we mean when we speak of movement in the direction of the least resistance. ”

“ The strength of every part of the machine should be made proportional to the stress it is to bear: and therefore let every lever be made so much stronger, as its length and the weight it is to support are greater; and let its strength diminish proportionally from the fulcrum, or point where the greatest stress is to each end. The axles of wheels and pullies must be so much stronger as they are to bear greater weight. The teeth of wheels, and the wheels themselves, which act with greater force, must be proportionally stronger ”

“ If the applied stress is less than a certain limit, the strain is in general small in amount, and disappears wholly, or almost wholly when the stress is removed. If the applied stress exceeds this limit, the strain is, in general, much greater than before, and most of it is found, when the stress is removed, to consist of permanent set. The limits of stress within which strain is wholly or almost wholly elastic are called limits of elasticity. ”

“ If we assume that there is no other stress, then the magnitude of the traction in question is Ey/R, where E is Young’s modulus, and it is tension on the side where the filaments are extended and pressure on the side where they are contracted. ”

“ There is danger in such high speeds; the stresses in the machine are increased several times merely by the increased resistance, and if the angle of incidence should be suddenly brought up to a large value at this high speed the stress would again be increased so that the total stress increase theoretically might be as high as fourteen times the normal value, thus exceeding the factor of safety. ”

“ In what has been said above it is assumed that the stress is within the limit of elasticity. When the twisting couple is increased so that this limit is passed, plastic yielding begins in the outermost layer, and a larger proportion of the whole stress falls to be borne by layers nearer the centre. ”

“ Relations between the Strains and the Stresses.—When the strains are known, the stresses can be found from a generalized Hooke's law, which can be deduced from the principle of energy, combined with consideration of symmetry. If the solid is isotropic, i.e. is symmetrical in its elastic properties in all directions round a point, the relations between stress and strain are of the form
the values of the other four components of strain can be written down from symmetry. ”

“ Yielding under Compound Stress.—A question of much theoretical interest and also of some practical importance is, what determines the yielding of a piece when it is subjected not to a simple pull or push alone but to a stress combined of two or of three principal stresses? ”

“ The definite mathematical relations which have been found to connect the components of stress with each other, and with other quantities, result necessarily from the formation of a clear conception of the nature of stress. They do not admit of experimental verification, because the stress within a body does not admit of direct measurement. ”

“ It is not considered good practice to stress a material, especially a brittle material, repeatedly to a point half-way to its elastic limit. (The elastic limit is that stress that may be given to a body without producing a permanent set; below which it will return to its original shape upon the removal of the stress.) ”

“ Work is rigidly bound to fixed hours, uniform standards, stints and piece-products, and instead of a finished article, each individual now achieves a part of a single process, and knows little of those that precede or follow. Machinery has relieved the large basal muscles and laid more stress upon fine and exact movements that involve nerve strain.... ”

“ It is further evident that the internal stresses will obey a definite but very simple law, namely, there will be in the hollow cylinder a layer whose radius is √R r0, in which the stress is nil; from this layer the stresses increase toward the external and the internal radii of the cylinder, where they attain a maximum, being in compression in the internal layers and in tension in the external ones. ”

“ Stress is the manner of applying force to a word or accented syllable. Prof. L. B. Monroe, in his book on vocal culture, enumerates six kinds. The marks he uses to represent them exhibit clearly to the eye what the voice is required to do. With radical, terminal, and compound stress, after facility is gained by use of stroke from the shoulder, omit it, and do them forcibly without movement of any part of the body.
1. Radical Stress.—So called, because the stress is on the beginning of the word, and marked thus (>) . Assume standing position with active chest, and take breath ”

“ If, however, for any reason the center of gravity becomes displaced forward, the strain on the posterior musculature necessarily becomes increased throughout, because the vertical stress at each level is determined by the horizontal distance of that point from a perpendicu­lar dropped from the center of gravity, and, if this moves forward, the strain increases in proportion to the increased horizontal distances. ”

“ In the same way, just as when the brain bears the stress of exertion, the body should be completely relaxed, so when one part of the body, the arms or legs, for instance, are actively employed, and above all when storage of energy may be useful, the rest of the body not wanted should be trained to give no trouble, not to require the usage of energy. ”