Shear (mechanics)

“ Their inclination shows that the metal prefers to elongate by shearing on a section where p t the shearing stress is not at its maximum, because pn the normal component—which is a pull—is greater there, and this can only mean that the presence of a normal component of the nature of a pull at any section reduces the resistance to yielding under the shearing stress which acts at that section, while similarly the presence of a normal component of the nature of a push increases the resistance to shear. ”

“ A stretched rope is in a state of stress, because at any cross section the part on each side is pulling the part on the other side with a force in the direction of the rope's length. A plate of metal that is being cut in a shearing machine is in a state of stress, because at the place where it is about to give way the portion of metal on either side of the plane of shear is tending to drag the portion on the other side with a force in that plane. ”

“ 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. ”

“ Successive half-turns about two skew axes a, b are equivalent to a twist about a screw whose axis is the common perpendicular to a, b, the translation being double the shortest distance, and the angle of rotation being twice the acute angle between a, b, in the direction from a to b. It is easily shown that any displacement whatever is equivalent to two half-turns and therefore to a screw.
In mechanics we are specially concerned with the theory of infinitesimal displacements. ”

“ Bulletin No. 29 of the University of Illinois Experiment Station shows by numerous experiments, and reiterates again and again, that shear rods do not act until the beam has cracked and partly failed. This being the case, a shear rod is an illogical element of design. Any element of a structure, which cannot act until failure has started, is not a proper element of design. In a steel structure a bent plate which would straighten out under a small stress and then resist final rupture, would be a menace to the rigidity and stability of the structure. ”

“ Hodgkinson’s experiments on the compression of cast iron give surfaces of shear whose normal is inclined at about 55° to the axis of stress, and Kirkaldy’s, on the tension of steel, show that when rupture of a rod under tension takes place by shear the normal to the surface is inclined at about 25° to the axis. ”

“ Next let the girder carry a uniform load w per ft. run (fig. 40) . The total load is wl; the reactions at abutments, R1 = R2 = 1/2wl. The distribution of shear on vertical sections is given by the ordinates of a sloping line. The greatest bending moment is at the centre and = Mc = 1/8wl2. At any point x from the abutment, the bending moment is M = 1/2wx (l−x) , an equation to a parabola.
23. Shear due to Travelling Loads.—Let a uniform train weighing w per ft. run advance over a girder of span 2c, from the left abutment. ”

“ However, it is undoubtedly true that actual shear in reinforcing steel is sometimes figured and relied on. Under some conditions it is good practice, and under others it is not. Transverse rods, properly placed, can surely act in transmitting stress from the stem to the flange of a T-beam, and could properly be so used. There are other conditions under which the concrete may hold the rods so rigidly that their shearing strength may be utilized; where such conditions do not obtain, it is not ordinarily necessary to count on the shearing strength of the rods. ”

“ Then exy = s, and the remaining components of strain vanish. The nature of the strain (called “simple shear”) is simply appreciated by imagining the body to consist of a series of thin sheets, like the leaves of a book, which lie one over another and are all parallel to a plane (that of x, z) ; and the displacement is seen to consist in the shifting of each sheet relative to the sheet below in a direction (that of x) which is the same for all the sheets. The displacement of any sheet is proportional to its distance y from a particular sheet, which remains undisplaced. ”

“ The steel which has been thus hammered is much denser and more uniform in composition; its tenacity, malleability, and ductibility are greatly increased, and it is fitted for the manufacture of shears, files, and other tools. It is commonly known as shear steel.1561 Double shear steel is obtained by breaking the tilted bars in two, and welding these into a compound bar. The best variety of steel, however, which is perfectly homogeneous in composition, is that known as cast steel, to obtain which about 30 lbs. ”

“ Fourth Point.—In bridge pins, bending and bearing usually govern, but, in case a wide bar pulled on a pin between the supports close to the bar, as happens in bolsters and post-caps of combination bridges and in other locations, shear would govern. Shear rods in concrete-steel beams are proportioned to take the vertical and diagonal shearing stresses. If proportioned for less stress per square inch than is used in the bottom bars, this cannot be considered dangerous practice. ”

“ 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. ”

“ The use of the screw bolt is to unite certain parts of machinery in close and firm contact. It is peculiarly adapted for this purpose by the compact form in which it possesses the necessary strength and mechanical power. The extreme familiarity of the object tends to prevent the observation of its peculiar fitness. Yet, among all the applications of mechanics, there is, perhaps, no instance of adaptation more remarkable. ”

“ Thirty to fifty tons of metal are sometimes melted in such furnaces.
Among the machine tools used in rolling-mills those called by the general name of "shears" occupy an important place; these tools vary greatly in form and constructive detail, and are designed with especial reference to the work for which each is intended. Fig. 42 is an illustration of a common form of lever shear for cutting bar iron. The cutting knives are located at a b, and when the eccentric d is revolved by the rotation of the shaft on ”

“ The shears of lathes require to be as rigid as possible, because the pressure of the cut, as well as the weight of the carriage, slide rest, and tailstock, and of the work, tends to bend and twist them.
The pressure of the dead centre against the end of the work considered individually, is in a direction to bend the lathe shears upward, but the weight of the work itself acts in an opposite direction. ”

“ In shallow beams there is little need of provision for taking shear by any other means than the concrete itself. The writer has seen a reinforced slab support a very heavy load by simple friction, for the slab was cracked close to the supports. In slabs, shear is seldom provided for in the steel reinforcement. It is only when beams begin to have a depth approximating one-tenth of the span that the shear in the concrete becomes excessive and provision is necessary in the steel reinforcement. ”

“ For reverse stresses it is advisable to keep the shear stress in any rivet so low, say 3 tons per square inch, that the frictional resistance of the parts gripped by the rivets shall be sufficient to prevent any tendency to slip under the influence of the smaller of the two forces to which the part is liable, to insure that, if brought to a bearing in one direction by the greater force, it shall not go back with reversal of stress. ”

“ A material that is too tough to be cut at the tip ends of the blades may be easily cut if we move it in near the fulcrum or pin that hinges the blades together; for by doing this we shorten the weight arms, because the weight arm is measured not to the end of the blade, but to the point where it is cutting into the material. To cut very tough material, such as heavy tin or sheet steel, we use long-handled short-bladed shears. The cutting pressure depends upon the ratio of the effort arm to the weight arm. ”

“ The shears are of corresponding power.
For dealing with angles and bars there are several interesting tools, in addition to shears and punches. Some of the shears cut 8-in. by 4-in. angles, and are driven by [98] 10 horse-power motors. ”

“ Where great resistances have to be overcome, but where the distance through which the resistance must be urged is short, the lever or the screw is generally found to be the most appropriate means of [Pg 150] increasing power. When, however, the resistance has to be moved a considerable distance, the aid of the pulley, or the wheel and axle, or sometimes of both combined, is called in. The wheel and axle is the form of mechanical power which is generally used when the distance is considerable through which a weight must be raised, or through which some resistance must be overcome. ”

“ Thus we have seen in Art. 291 how the velocity ratio of a screw-jack with an arm attached amounted to 414, while its mechanical efficiency was little more than one-fourth as great. No single wheel and axle could conveniently be made to give a mechanical efficiency of 116; but from Art. 337 we could easily design a combination of wheels and axles to yield an efficiency of quite this amount. The friction in the wheel and axle is very much less than in the screw, and consequently energy is saved by the use of the former machine. ”

“ With cast iron the slope of the plane is such that this simplest mode of fracture can take place only if the height of the block is not less than about 3/2 the width of the base. When the height is less the action is more complex. Shearing must then take place over more than one plane, as in fig. 25, so that cones or wedges are formed by which the surrounding portions of the block are split off. The stress required to crush the block is consequently greater than if the height were sufficient for shearing in a single plane. ”

“ Shear steel is made by breaking up bars of blistered steel into lengths of about 18 inches, and binding four or six of them together with a steel rod, and then heating them to a full welding heat, the surface being covered with fine clay or sand to prevent oxidation. ”

“ This screw does not let the load run down, since less than 50 per cent. of energy is utilised; to lower the weight the lever has actually to be pressed backwards.
294. The details of an experiment on this subject will be instructive, and afford a confirmation of the principles laid down. In experiment 10 we find that 9·0 lbs. suffice to raise 1,120 lbs.; now by moving the pulley to the other side of the lever, and placing the rope perpendicularly to the lever, I find that to produce motion the other way—that is, of course to lower the screw—a force of 3·4 lbs. must be applied. ”

“ If, for example, shear members were spaced half the depth of a beam apart, each would take half the shear by the common method. If shear members take vertical shear, or if they take tension, what is between the two members to take the other half of the shear? There is nothing in the beam but concrete and the tension rod between the two shear members. If the concrete can take the shear, why use steel members? It is not conceivable that an engineer should seriously consider a tension rod in a reinforced concrete beam as carrying the shear from stirrup to stirrup. ”

“ When cordage is engaged in the formation of any part of a machine, it has hitherto been considered as possessing perfect flexibility. This is not the case in practice; and the want of perfect flexibility, which is called rigidity, renders a certain quantity of force necessary to bend a cord or rope over the surface of an axle or the groove of a wheel. During the motion of the rope a different part of it must thus be continually bent, and the force which is expended in producing the necessary flexure must be derived from the moving power, and is thus intercepted on its way to the working point. ”

“ It satisfies the want of every lady, and gives perfect satisfaction. The illustration shows the improvement in the large gauge, which regulates the distance between each hole, and from the edge of the garment. It does away with all measures usually used in making button-holes. The small gauge or screw regulates size of hole. Price $1.25.
TERRY’S FAMILY SHEAR. Given for new subscriptions amounting to $1.50.
It is 8 inches in length, Japanned handle and plated blades. It is the best shear ever made for family use, and is fully warranted. ”

“ It is evident, however, that the distance through which the screw can raise a weight must be limited by the length of the screw itself, and that in the length of lift the screw cannot compete with many of the other contrivances used in raising weights. ”

“ Nor is there any essential difference between the apparatus of Fig. 38 and that of Fig. 20. In Fig. 38 the bar is pulled down by a force at each end, one a weight, the other a spring balance, while it is supported by the upward pressure of the steel edge. In Fig. 20 the bar is being pulled upwards by a force at each end, and downwards by the weight. The two cases are substantially the same. In each of them we find a bar acted upon by a pair of parallel forces applied at its extremities, and retained in equilibrium by a third force. ”