Compressive strength

“ Elastic bodies, in the recovery of their forms from a state of compression, after the removal of the compressing force, exert a greater power at first than at last, so that the whole progress of restoration is a retarded motion. ”

“ In all structures the materials have to support their own weight, and therefore their available strength is to be estimated by the excess of their absolute strength above that degree of strength which is just sufficient to support their own weight. ”

“ It is not here necessary to attempt to trace the history of this idea in our minds; but it is certain that such an idea may be distinctly formed, and that upon it the whole science of statics may be built. Pressure, load, weight, are names by which this idea is denoted when the effect tends directly downwards; but we may have pressure without motion, or dead pull, in other cases, as at the critical instant when two nicely-matched wrestlers are balanced by the exertion of the utmost strength of each.
Pressure in any direction may thus exist without any motion whatever. ”

“ As each control of the body is connected with the activity of the muscles, and as each harmonious movement requires constant control, therefore constant exertion of the muscles, it results that strength, perseverance and an elastic dexterity are built up without which strength resembles to brute force. ”

“ In which he takes occasion, among many other weighty particulars, to intimate, That it is principally the business of a Mechanician, to excogitate and make practicable such Engins, to be interposed between the Strength and the Weight, as may so moderate the Celerity of Motion, as to compensate the Greatness of the Weight, by the Slowness of the Motion, or the want of strength, by the length of time. ”

“ According to them, the efficacy of the elastic power of the Air is so prodigious, and its force when compressed so excessive, that it is not possible the other component parts of bodies should be able to confine so much of it, in that state of compression which it must needs undergo, if retaining its elasticity it were pent up among them. ”

“ It is true, that if there are several small weights, manageable by human strength, to be raised to a certain height, it may be full as convenient to elevate them one by one, as to take the advantage of the mechanical powers in raising them all at once ”

“ When the limits of elasticity are not exceeded no injury is done to a material or structure by the action of the forces. The strength or weakness of a material, and the safety or insecurity of a structure, are thus closely related to the elasticity of the material and to the change of size or shape of the structure when subjected to forces. ”

“ Stephenson observed, “one ruling principle appertains, and is common to all of them. Primarily and essentially, the ultimate strength is considered to exist in the top and bottom,—the former being exposed to a compression force by the action of the load, and the latter to a force of tension; therefore, whatever be the class or denomination of girders, they must all be alike in amount of effective material in these members, if their spans and depths are the same, and they have to sustain the same amount of load. ”

“ He was rather above the middle size, of a frame the most muscular and compact I have almost ever seen, and there was a blended mixture of elasticity and firmness in his tread, that to one accustomed, as I had been, to estimate the physical capabilities of men, gave evidence of a union of immense personal strength with great activity. ”

“ While exact data were, therefore, lacking as to stresses and strengths in many of the important parts, yet the models furnished most important illustrations of unusual strength for minimum weight, and a careful study of them showed many ways in which increased strength could be obtained with decreased weight which could hardly have been devised without these concrete examples. ”

“ That, for instance, if two forces start with the relative powers of 10 and 8, the weaker force will be reduced so much more rapidly than the stronger that when it has been reduced to zero the stronger force will have a value of 5.69. The values mentioned indicated the actual fighting strength—strength made up of all the factors—material, physical, and psychic—that constituted it. ”

“ In the first place the rod may be taken by a force at each end and torn asunder by pulling, as a thread may be broken. To do this requires very great power, and the strength of the material with reference to such a mode of destroying it is called its resistance to extension. In the second place, it may be broken by longitudinal pressure at each end, as a pillar may be crushed by the superincumbent weight being too large; the strength that relates to this form of force is called resistance to compression: finally, the rod may be broken by a force applied transversely. ”

“ If, however, w were increased to about 270 lbs., the force on a b would become too great, and fracture would arise from the collapse of this strut.
421. When a structure is loaded up to the breaking point of one part, it is proper for economy that all the other parts should be so designed that they shall be as near as possible to their breaking points. In fact, since nothing is stronger than its weakest part, any additional strength which the remaining parts may possess adds no strength to the whole, and is only so much material wasted. ”

“ B. Since we are not able to increase our natural strength is not any instrument of obvious utility, by means of which we may reduce the resistance or weight of any body, to the level of that strength? This the mechanical powers enable us to accomplish. It is true, as you observe, that it requires a sacrifice of time to attain this end, but you must be sensible how very advantageously it is exchanged for power. If one man by his natural strength could raise one hundred pounds only, it would require five such men to raise five hundred pounds ”

“ Hence it is obvious, that although the strength of a body of small dimensions may greatly exceed its weight, and, therefore, it may be able to support a load many times its own weight; yet by a great increase in the dimensions the weight increasing in a much greater degree the available strength may be much diminished, and such a magnitude may be assigned, that the weight of the body must exceed its strength, and it not only would be unable to support any load, but would actually fall to pieces by its own weight. ”

“ 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. ”

“ Stability, Stiffness and Strength.—A structure may be damaged or destroyed in three ways:—first, by displacement of its pieces from their proper positions relatively to each other or to the earth; secondly by disfigurement of one or more of those pieces, owing to their being unable to preserve their proper shapes under the pressures to which they are subjected; thirdly, by breaking of one or more of those pieces. The power of resisting displacement constitutes stability, the power of each piece to resist disfigurement is its stiffness; and its power to resist breaking, its strength. ”

“ It must be remembered that by the strongest pressure is meant the strongest that one is able to exert upon oneself. Let us take, for example, two persons of widely different physical strength, such as a powerful wrestler and a little girl of about ten years of age. If the wrestler uses the strongest pressure possible for him to exert, that pressure would not be harmful to him (provided, of course, that he has had no recent injuries) , since his body is proportionately strong. ”

“ Determination of the Influence of Internal Stresses on the Strength of Materials.—We call internal stresses those which exist within the mass of any hollow cylinder or other body, when it appears to be in a state of repose, or not under the influence of external forces. When pressure is applied to a hollow cylinder, either externally or internally, the interior layers into which its walls may be conceived to be divided are subjected to a new series of stresses, the magnitude of which is independent of those already existing. ”

“ 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 ”

“ The resistance of a body to compression does not depend upon its hardness. Strike a diamond with a hammer and it flies to pieces, but wood does not. One is brittle and the other is tough.
The machinist can utilize this property by understanding that velocity enables a soft materialp. ”

“ They exist, in fact, in a state of compression, with but little mutual cohesion, and are only held together by the external skin. So long as the skin remains intact the tendency of the inner particles to expand and fill their proper space is checked and resisted by the superior compressive strain of the skin. ”

“ So far, therefore, from it being a fact that animals have strength in proportion to their weight and bulk, the reverse of that statement seems to be the law.
11. Difference in strength of individuals? How caused?
11. Physical Strength.—The difference in strength, as seen in different individuals, is not due to any original difference in their muscles. Nature gives essentially the same kind and amount of muscles to each person, and the power of one, or the weakness of another, arises, in great part, from the manner in which these organs are used or disused. ”

“ During the former the elastic force of the air is found to be greater, and consequently the quantity of motive power produced by the movements of dilatation is more considerable than that consumed to produce the movements of compression. ”

“ Only after many failures has the fact been grasped that a very high degree of strength is inconsistent with a trustworthy degree of elasticity. The reasons were not understood until the researches of Wöhler demonstrated the difference between the effects of merely dead loads and of live loads, and between repetitions of stress of one kind only, and the vastly more destructive effects of both kinds alternating. ”

“ The cases in which a force is apparently increased or diminished, as well as those in which it seems to disappear, are all found, on examination, to be illusive. For example, the apparent increase of a man's power by the use of a lever is really no increase at all. It is true that, by pressing upon the outer arm with his own weight, he can cause the much greater weight of the stone to rise ”

“ The compression of the surface-elements into a quarter or half their known bulk cannot explain the great weight of the interior, for experiments indicate that a limit to the capacity of reduction of volume is soon reached. So far as we know, the reduction of bulk by pressure becomes less and less in proportion to the pressure exerted. ”

“ But as this force has a degree that overpowers, and hence diminishes the space of extension, that is, can be impressed upon the same up to a certain degree, by a given compressive force, but only in such wise that the entire penetration, inasmuch as it would require an endless compressive force, is impossible; [therefore] the filling of space must be regarded only as relative impenetrability. ”

“ For if, while we are applying this force, wind or water or any other agent supplies an additional force just exceeding two tons, the body will be raised; thus proving that the force we applied exerted its full effect, by neutralizing an equivalent portion of the weight which it was insufficient altogether to overcome. ”

“ Each atom of air is a spring of matchless elasticity, which nothing can break, which never wears out, which one can always compress, if one employs force sufficient, and which is always ready to expand indefinitely, in proportion as the compressing power is withdrawn. ”

“ If, instead of human labour, we introduce the work of a weight, and hang to the block a load of 400, and at a, where otherwise the labourer works, a weight of 100 pounds, the block is then in equilibrium, and, without any appreciable exertion of the arm, may be set in motion. The weight of 100 pounds sinks, that of 400 rises. Without any measurable expenditure of force, the heavy weight has been raised by the sinking of the smaller one. But observe that the smaller weight will have sunk through four times the distance that the greater one has risen. ”

“ My difficulty and surprise consist in not being able to see whence and upon what principle is derived the energy and immense force [energia e forza immensa] which makes its appearance in a blow; for instance we see the simple blow of a hammer, weighing not more than 8 or 10 lbs., overcoming resistances which, without a blow, would not yield to the weight of a body producing impetus by pressure alone, even though that body weighed many hundreds of pounds. ”

“ We had, let us say, always seen heavy bodies sink when their support was taken away; we had also seen, perhaps, that the sinking of heavier bodies forced lighter bodies upwards. But now we see a lever in action, and we are suddenly struck with the fact that a lighter body is lifting another of much greater weight. ”