Deformation

“ If we have not been able, as has been said, to determine the surfaces applicable on the sphere, other surfaces of the second degree have been attacked with more success, and, in particular, the paraboloid of revolution.
The systematic study of the deformation of general surfaces of the second degree is already entered upon; it is one of those which will give shortly the most important results.
The theory of infinitesimal deformation constitutes to-day one of the most finished chapters of geometry. ”

“ 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. ”

“ The strain produced by bending stress in a bar or beam is, as regards any imaginary filament taken along the length of the piece, sensibly the same as if that filament were directly pulled or compressed by itself. The resulting deformation of the piece consists, in the first place and chiefly, of curvature in the direction of the length, due to the longitudinal extension and compression of the filaments, and, in the second place, of transverse flexure, due to the lateral com- pression and extension which go along with the longitudinal extension and compression. ”

“ In other countries, and over considerable areas, the corresponding strata are raised up, bent, and contorted in different ways, having been subjected to dislocations through enormous thicknesses. Such lifts and foldings can not have taken place in solid masses without being accompanied by many and important fractures. The principal classes of such fractures, which are nearly vertical, are called faults. They crop out and cut the surface of the ground, sometimes for tens and hundreds of miles, and are of indefinite depth, or descend to below where it is possible for man to penetrate ”

“ Imagine forces of some kind, acting laterally, to compress those layers. There will be corrugations, sometimes actual fractures, the two sides of which, sliding one against the other, will be either raised or depressed. Faults is the name which we give to the fractures that penetrate the terrestrial shell and separate two masses of rock, one of which slides over the plane of fracture. The fault, therefore, reveals an edge, a lower lip produced by the subsidence of the soil, and an upper lip produced by an elevation. ”

“ Oftentimes a great line of fault has been repeated, or the movements have been continued through successive periods, so that, newer deposits having covered the old line of displacement, the strata both newer and older have given way along the old line of fracture. ”

“ In the case of a fault, for example, with a displacement of, say, one mile, where no indication of it is seen at the surface of the ground, we know that on one side of the fault a thickness of rock equal to one mile must have been denuded, but we do not know how much more than that may have been removed. For anything which we know to the contrary, hundreds of feet of rock may have been removed before the dislocation took place, and as many more hundreds after all indications of dislocation had been effaced at the surface. ”

“ The lines of fracture which are marked by mountain-chains are ever, after the first disruption, lines of weakness, where the resistance to lateral pressure is diminished, and where the strain of large unbroken areas is relieved from time to time by displacements, necessarily attended by earthquakes. ”

“ Look at a heap of broken stones and débris, which in detail may contain all sorts of varieties of form, as we find them tumbled down a steep place, as the rocky bed of a mountain stream, a heap of boulders upon a hillside, or the débris from a quarry or mine; in each case the law of gravity and the persistence of force working together arrange the diverse forms in masses controlled by the lines, which express the direction and degree of descent, and the pressure of force. ”

“ FAULTS. In Figure 184 the rocks have been both broken and dislocated along the plane ff'. One side must have been moved up or down past the other. Such a dislocation is called a fault. The amount of the displacement, as measured by the vertical distance between the ends of a parted layer, is the throw. The angle which the fault plane makes with the vertical is the HADE. In Figure 184 the right side has gone down relatively to the left; the right is the side of the downthrow, while the left is the side of the upthrow. ”

“ The simple Fracture is that whereby the Bone is broken, without any other Accident; and the complicated Fracture is that which is follow'd by some Accident; as that in which there is a splitting of the Bone in pieces, or {189}where the Bone is broken in two several places, or else when the Fracture is accompany'd with a Luxation, a Wound, an Inflammation, or other Circumstances of the like Nature.
Are old Men or Children most subject to these Fractures of the Bones? ”

“ The most satisfactory evidence of a fault is the discovery of a rock bed which may be easily identified, and which is actually seen displaced on a plane of fracture which intersects it (Fig. 42, p. 59) . When such an easily recognizable layer is not to be found, the plane of displacement may perhaps be discovered as a narrow zone composed of angular fragments of the rock cemented together by minerals which form out of solution in water. Such a fractured rock zone which follows a plane of faulting is a fault breccia. ”

“ In older persons the bones more readily break than bend. The diagnostic signs of the accident are, pain and deformity at the seat of the injury, loss of power in the limb, want of displacement of fragments, and absence of crepitation. The deformity consists in an unnatural curvature, which can be made to disappear under pressure and extension, but recurs, to a certain extent, when the limb is liberated. When attended with partial fracture, the symptoms are the same, excepting that, instead of a curvature, there is angular deformity opposite the seat of the accident. ”

“ There are certain fallacies to be guarded against. For example, a fracture may exist and yet unnatural mobility may not be present, because the bones are impacted into one another, or because the fracture is an incomplete one. Again, the extreme tension of the swollen tissues overlying the fracture may prevent the recognition of movement between the fragments. Deformity also may be absent—as, for instance, when there is no displacement of the fragments, or when only one of two parallel bones is broken, as in the leg or forearm. ”

“ In this contribution is recorded an element which became an important object in all his subsequent experiments, namely ‘set,’ or the difference between the original position of a strained body and the position it assumes when the strain is removed. He fixed the exact position of the ‘neutral line’ in the section of rupture or fracture, and made it subservient to the computation of the strength of a beam of given dimensions. His conception of the true mechanical principle by which the position of the line could be determined has long obtained general acceptance. ”

“ It is evident that the solid envelope of the globe has undergone dislocations at many epochs in its history. The manifestations of gigantic force thus plainly registered are the effects of ancient back-foldings and of lateral or horizontal pressures. It is as if the crust of the earth had become too large for the supporting nucleus, and had, to keep in contact with it, to shrink up and bend upon itself. These foldings and fractures have given origin to chains of mountains. ”

“ Fig. 46.—A series of parallel faults indicated by successive offsets in the course of an easily recognizable rock formation.
There are in addition many indications rather than proofs of the presence of faults, which must be taken account of in every general study of the geology of a district. Thus the outcrops of all neighboring formations may terminate abruptly upon a straight line which intersects all alike. Deep-seated fissure springs may be aligned in a striking manner, and so indicate the course of a prominent fracture, though not necessarily of a fault. ”

“ A dislocation or luxation is a persistent displacement of the opposing ends of the bones forming a joint. We are here concerned only with such dislocations as immediately follow upon injury. Those that are congenital or that result from disease will be studied later.
Causes.—The majority of dislocations are the result of indirect violence, the more movable bone acting as a lever, on a fulcrum furnished by the natural check to movement in the form of ligament, bone, or muscle. It is in this way that most dislocations of the shoulder, hip, and elbow are produced. ”

“ Thus, I urged, when a man falls from a ladder because (as is commonly said) of the breaking of the rung on which his foot was resting, the real or dynamical cause of his fall is the force of gravity, or attraction of the earth, which pulls him to the ground when his foot is no longer supported; the loss of support being only the material condition or collocation, which allowed the force previously acting as pressure on the rung to produce the downward motion of the man who stood upon it. ”

“ The event of highest generalization or universality, in the form of those mineral veins, is fracture and dislocation. It is not, like that of the veins of strata, simple separation and measured contraction; it is violent fracture and unlimited dislocation. In the one case, the forming cause is in the body which is separated; for, after the body had been actuated by heat, it is by the reaction of the proper matter of the body, that the chasm which constitutes the vein is formed. ”

“ For instance, the line of gravity of the body is, by some cause, removed behind it; the anterior muscles contract themselves to bring it forward again; the extensors act on the rotula; it is broken, and a fall ensues. Again, the leg is suddenly thrown into a state of violent extension; the extensors act with great force; a fracture is the consequence, and the patient falls. A soldier once fractured his rotula in kicking at his serjeant; thus the olecranon, in like manner, has been broken by throwing a stone. ”

“ The displacement here is, in general, inconsiderable, because, being drawn in contrary directions, by the muscles of the arm and fore-arm, the condyls separated from the bone remain stationary between these two forces. A fall, a percussion, or some other external cause, can alone produce a displacement, by communicating some degree of motion to the fragments. ”

“ A Dislocation is the forcible displacement of a bone from its socket. It is, generally, the result of a fall or a violent blow. The tissues of the joint are often ruptured, while the contraction of the muscles prevents the easy return of the bone to its place. A dislocation should be reduced as soon as possible after the injury, before inflammation supervenes.
PRACTICAL QUESTIONS. 1. Why does not a fall hurt a child as much as it does a grown person? ”

“ Every species of fracture, and every degree of dislocation and contortion, may be perceived in the form of mineral veins; and there is no other general principle to be observed in examining their form. ”

“ Let us imagine a solid prism ABCD fastened into a wall at the end AB, and supporting a weight E at the other end; understand also that the wall is vertical and that the prism or cylinder is fastened at right angles to the wall. It is clear that, if the cylinder breaks, fracture will occur at the point B where the edge of the mortise acts as a fulcrum for the lever BC, to which the force is applied; the thickness of the solid BA is the other arm of the lever along which is located the resistance. ”

“ In regions where movements along great faults have long since ceased, the original steep slopes may be completely obliterated by erosion.
Fig. 10.—Vertical sections through strata illustrating common kinds of faults: a, “normal faults” where one mass simply sinks below another; b, a “thrust fault” where one mass is shoved over another. (After U. S. Geological Survey.)
How does the geologist determine the actual amount of displacement, especially in the case of a large fault in stratified rocks? ”

“ The result indicates that, when forces which produce any kind of strain are applied to a solid body and are gradually increased, the strain at any instant increases proportionally to the forces up to a stage beyond that at which, if the forces were removed, the body would completely recover its original size and shape, but that the increase of strain ceases to be proportional to the increase of load when the load surpasses a certain limit. There would thus be, for any type of strain, a limit of linear elasticity, which exceeds the limit of perfect elasticity. ”

“ An original horizontal rock layer may be upfolded into anticlines, downfolded into synclines, and broken by either reverse or normal faults. A fault is a fracture or a zone of fractures within the earth’s crust along which movement has taken place. ”

“ The second kind of displacement, that which we constantly find in practice, and which the laws of muscular action render almost inevitable, takes place in such a manner that the shoulder appears to obey the impulse of two powers, one of which draws it downwards, and along with it the external fragment of the clavicle, which is displaced by this power in the direction of its transverse diameter, or thickness. ”

“ It follows from the above considerations, that if there be only one or only two lines of fracture they must gradually diminish and end somewhere, and that the dislocated ground must have at least one place of maximum disturbance towards which it bends down either in one or several directions. ”

“ THE HELICOIDAL OR WIRE STONE SAW.
The sides of solid bodies, whatever be the degree of hardness, and however fine the texture, possess surfaces formed of a succession of projections and depressions. When two bodies are in contact, these projections and indentations fit into one another, and the adherence that results is proportional to the degree of roughness of the surfaces. If, by a more or less energetic mechanical action, we move one of the bodies with respect to the other, we shall produce, according as the action overcomes cohesion, more or less disintegration of the bodies. ”