STREET, ALFRED BILLINGS, an American poet, born in Poughkeepsie, N. Y., Dec. 18, 1811. At 14 years of age he removed with his father to Monticello in Sullivan co., where he was admitted to the bar, and for several years practised law. In 1839 he settled in Albany, where he has since resided, and where for a number of years he has held the position of state librarian. He commenced his literary career as a contributor of verses to the magazines, and in 1840 delivered a poem on 66 Euglossian society of Geneva college; and he Nature" before the has since delivered several poems before different colleges in New York, and one before Yale college. In 1842 appeared his first volume of poems, under the title of "The Burning of Schenectady, and other Poems," followed in 1844 by a 2d collection, " "Drawings and Tintings," and in 1846 by a complete collection of his fugitive poems (8vo., New York). In 1849 appeared in London and New York his longest poem, "Frontenac," consisting of 7,000 lines. In 1860 he published two prose volumes: "The Council of Revision" (8vo.), containing the vetoes of the council, a history of the supreme, chancery, and admiralty courts of New York, and biographical sketches of its governors and judges from 1777 to 1821; and "Woods and Waters, or the Saranacs and Racket," a description of a tour in the great wilderness of northern New York. Several of his poems have been translated into German. STRELITZ. See MECKLENburg. STRELITZES. See GUARDS, vol. viii. p. 537. STRENGTH OF MATERIALS, a general expression in the constructive arts for the measure of capacity of resistance, possessed by solid masses or pieces of various kinds, to any cause tending to produce in them a permanent and disabling change of form or positive fracture. (See the articles ARCH, BEAM, BRIDGE, and CARPENTRY.) The present notice will be devoted mainly to the general principles of the subject. The materials employed in construction are chiefly of 4 kinds: 1, timber; 2, rock (or natural stones); 3, bricks, concretes, &c. (artificial stones); 4, metals, especially iron. All these resist fracture in whatever way; but the capability of resistance in a given case varies with many particulars, but chiefly the following: 1, the nature of the material and its quality; 2, the shape and dimensions of the piece used; 3, the manner of support from other parts; 4, the kind and direction of the force tending to produce rupture. Materials of all kinds owe their strength to the action of those forces residing in and about the molecules of bodies (the molecular forces), but mainly as well as most obviously to that one of these known as cohesion, the direct result of the operation of which among the particles and within the fibres of any mass is to impart to it the property of toughness or tenacity. Certain modified results of cohesion, as hardness, stiffness, and elasticity, are also important elements; and the strength is rather in the ratio STRENGTH OF MATERIALS of the toughness and stiffness combined. Since the quality of the same kind of material must vary with a great variety of circumstances, some of them not readily cognizable by the experimenter or the engineer, it will follow that there must be a corresponding variation in the results that the numbers employed to express the as to strength obtained by different observers; strength afford at best but approximations; and that in practice the load or pressure allimits. A timber or piece of other kind may lowed must fall considerably within even these be subjected to strain or fracture in 4 ways: 1. It may be stretched, pulled, or torn asunder, direct pull, tensile strain, or tension; and reas in case of ropes, tie-beams, &c. This is called sistance to it, tensile strength. 2. It may be columns and truss beams. This is direct thrust, crushed in the direction of the length, as in direct pressure, or compression; and resistance to it, the crushing strength. 3. It may be bent oblique to its length, as in common beams and or broken across by a force perpendicular or joists. This is transverse strain, or flexion; It may be twisted or wrenched off, in a direcresistance to it is the transverse strength. 4. tion about its axis, as in case where the shaft rested in its movement. This is torsion; resistor journal of a turning wheel is suddenly arance to it, the torsional strength. A 5th sort is sometimes added, namely, detrusive strength, or that consisting in resistance to the sliding hence, opposing such applications of force as of the particles or fibres upon each other; those made in the operations of punching and shearing. Any bending or breaking pressure is a stress; its effect on the piece, a strain. Briefly, then, the strength of a solid piece or body, in any direction, is the total resistance it can oppose to strain in that direction. I. Tensile Strength. A rod, rope, or any body, being pulled or strained in the direction of its length (the form, in these cases, being usually cylindrical or prismatic), its cohesion posite end being fixed; and the amount of can come into play only by reason of the opcohesion excited is a reaction against the pull follows that, up to the limit of strength, the or strain applied. amount of cohesion excited in the way of reFrom these principles it action is always exactly equal to the amount change following as soon as the latter has passof the acting strain, rupture or permanent ed the limit named; and also, that at every moment the strain and reaction are equal throughout the whole length of the piece acted upon; hence again, that where weight does not (as it must in any hanging rope or piece) when the limit of strength is exceeded, always come in to modify the result, the piece must, part or yield at its weakest portion; and that the tensile strength can never exceed that of such weakest portion. Two fibres of like character, equally stretched, must exhibit double the strength of one. Generalizing this result, we say that the tensile strength of rods, beams, ropes, wires, or other pieces is, for each mate- increases, for a given thickness, with the fine- of its elasticity; and this effect is not permanent, at least its whole amount is not so; the piece shortens again, when the strain is removed, by quite or nearly the amount of this lengthening. Thirdly, if the body, in addition to these two properties, possess that of ductility, when the limit of its extensibility and elasticity is reached, the particles upon the surface at the weakest point begin to slip upon each other; the body is by this action both permanently and sensibly lengthened, or drawn out; and as this extension does not, as in wiredrawing proper, take place under circumstances favorable to increase of toughness, the strength is with the first yielding impaired; while, if the load be not then diminished, the yielding portion must be drawn rapidly smaller until it parts completely. Thus, for ductile materials, the load beyond which permanent change must occur is the limit of strength. In metallic bars or links, timbers, &c., a considerable proportion of the actual strength is gained by means of the firm hold of the fibres laterally one upon another; as is proved by the fact that, of two ropes of like material and containing in their sections a like number of fibres, in one of which the fibres are twisted and in the other glued together, the strength of the latter is greater by at least one third. In ordinary ropes and cords, the strength is that of so many independent fibres, but made effective by means of the enormous friction between these due to the twist, by which the slipping and parting of the mass are prevented. Cords are weakened by overtwisting; but properly made, their strength Materials. 1.-METALS. Limits of tensile strength. Steel, best tempered 184,000-153,000 shear.. Materials. 118,000 Limits of tensile strength, Iron, ship plates, aver- 44,000 66 cast. 14,000 45,970 cast, mean of 44 66 puddled. 67,200 American... 31,800 Copper, wire... 61,200 96,300 78,700 150,000 24,250 58,000 40,000 "bar, inferior... can... Platinum, wire.. 2.-OTHER MATERIALS. 9,400 | Mortar, of 20 years.... flint. 4,200 Roman cement, to blue stone.... Hemp fibres, glued.... 9,200 Hemp fibres, twisted (rope).. 6,400 Manila rope.... Marble, different species.. Stone, different spe- cies... 46 3,200 Wood, box.... 14,000-24,000 oak.... 10,000-25,000 locust tree..... 20,100 9,000 elm.. 13,200 66 ash. fir 12,000 8,330 4,880 5,200 1,000 850 66 cedar....... The strength of metallic bars is impaired by sudden, frequent, or extreme changes of temperature. The strength of alloys is, in many instances, superior to that of either of the component metals. An alloy of 6 parts Swedish copper with 1 of Malacca tin breaks at 64,000 lbs.; brass, at about 51,000; an alloy of 4 parts tin, 1 of lead, and 1 of zinc, at 13,000. According to Mr. Emerson, the load which may be safely suspended to an inch square is as follows: d3.6 W=f Brass, fine.... wrought. 21.7 3.6 164,000 | Marble, or granite, ..... 10,000 6,000 1,000 rule for the strength of hemp or wire rope is to times the diameter, Hodgkinson finds W=ƒ• allow for each pound weight of the former, per fathom, a strength of 1 ton; of the latter, of 217; and for a like hollow cylindrical column, tons. Of wood, any species of which is subject -; d being the whole diameter to great inequalities, the strongest portion is of the column, and d, the less diameter in case said to be that neither nearest the pith nor of the hollow column. Here, as before, f is the bark, but between the two. The wood the unit or coefficient, varying with the kind from below the springing of the branches is of material; and this, being sought in tables, stronger than that above, and that grown on the south side of the tree than that on the above expressed. The table gives examples is to be multiplied by the ratio of dimensions north side. The strength, per square inch secof crushing strength for short columns, of 1 tion, of any material being known, this besquare inch area: comes for such material the unit or coefficient of strength; and hence, representing this unit for any substance by f, and calling W the breaking weight, and a the area of section in square inches, a general expression for the limit of tensile strength, according to the law found above, will be W=fa. That is, the strength of a piece of any other section is (approximately, of course) found by multiplying the unit for that material by the number of square inches in the transverse section of the piece. But long tie-beams become weaker by having first to do the work of upholding their own weight; and in a long rope, as used in towing, especially when wet, this becomes a serious element of weakness. A like result holds for a long rod or rope, pendent, and intended to support other weights; obviously such rod or rope, loaded, must tend to break near its upper end. Again, the safe load of any piece must diminish with increase of length, owing to greater probability of weak parts; and in some instances a like result arises from long continued pull, apart from the known deterioration, from decay, rusting, jar, &c., with age. II. Crushing Strength. This form of strength, or that which bodies can. oppose to direct thrust, or pressure, is important in all materials having the form of blocks for foundations or walls, in columns, beams, &c. Mr. Hodgkinson finds this form of strength to be dependent in a marked degree (of course, after the nature of the material is regarded) on the proportion borne by the height of the piece to its other dimensions. For heights less than the diameter or side of the piece, the strength against crushing increases as the height is less -short, however, of such thinness as, in more fragile materials, would of itself favor fracture. When the altitude exceeded the diameter, fracture commenced by the cleaving off at the sides of pieces leaving a cone or pyramid of the column; the actual limit of strength was nearly the same up to a height of 4 or 5 times the diameter; beyond this altitude bending in flexible bodies was more likely to occur, and the strength rapidly diminished. Other things being equal, however, the strength was proportional to the area of section. Calling b the breadth, t the thickness, and h the height, Eytelwein had found for crushing strength the formula, W=f.b.13 For a solid cylindrical column, the ends flat, the height 30 or more III. Transverse Strength. Suppose a beam stretched horizontally, supported at one or both of its extremities, and having a load placed upon the suspended portion at one or more points. If the beam were either incompressible or inextensible, it could not bend in consequence of the load, but, when the limit of strength was reached, must crush or snap asunder at once. But all materials are susceptible both of compression and of extension-different ones, however, in very different degrees, both as to each of these changes absolutely, and also as to their relative amounts. In fact, a beam supported at the ends or at other points is between any such points of support loaded, first, by its own weight within such length; if any load be then placed upon this portion, the effect is the same in kind, and simply increased in amount. The obvious effect is a deflection or flexure of the beam, under pressure of the sum of the weights its strength must bear. In this deflection the particles and fibres of the under side of the beam are extended, and the actual length of this portion is increased. The fibres are here in a state of tension, cohesion supplying the chief resistance to rupture. The fibres of the upper side of the beam are subjected, on the contrary, to compression; this part of the beam is really shortened; the resistance is that to crushing, and due to action both of repulsion and cohesion. The result is, that in either portion of the bent beam the fibres act by a sort of leverage, one component of their whole pull or pressure being exerted in a direction and amount exactly opposed to the whole transverse strain, at least so long as the piece is not bending, or until it breaks. Between the extended and the compressed portions of the beam there is evidently a continuous film or surface, horizontal when the beam is straight, and correspondingly bent when the beam is so, along which film the material suffers neither extension nor compression. This film, commonly spoken of as a line, is called the neutral line or neutral axis of the beam. Its importance in connection with the strength will presently appear. Since the fibres act by a sort of leverage, in either portion of the beam, most forcibly at the surface, and less and less, down to 0, at the axis, their total action in b x d2 4d The either portion must be determined by the num- area of material, still greater gain of strength ber of them in it, and their average distance is secured by carrying a good part of the mafrom the axis. In stones and cast metals gen- terial out into two lateral extensions, called erally, the resistance to compression is greater; flanges, united by a vertical portion, the web, in woods and wrought metals generally, the thus I. Here a positive gain arises through resistance to extension is greater. The place increased leverage; a negative, through saving of the neutral line, in a general way at about of weight. For the ultimate transverse strength the depth of rectangular beams, is variable of rolled or wrought iron flanged beams, callslightly in unlike beams of the same form and ing the depth d, area of section of lower flange dimensions. But in any case, in rectangular A, and that of the web a, the following forbeams, the mean leverage either of the commula has been obtained: W = ƒ · (4+ ). pressed or extended portion is at its depth. Hence, the entire transverse strength, the fore- For further particulars in respect to flanged going conditions alone considered, will be pro- beams, and the differences required in flanges portional to the product of the total number for wrought and for cast iron, see BEAM. It of fibres into the depth of the piece; that is, has been calculated that with web and flanges proportional to the product, area of cross secof proper form the actual strength of wrought tion x depth; and therefore, as the product, iron beams may be doubled, and of cast iron inwidth x depth. The dimensions in any two creased in the ratio 1. In rectangular beams or bars of like material and similar sections, the cases compared must correspond in denomination; it is convenient to express widths and strength will compare as the cubes of like sides; depths in inches, and lengths in feet. Now, in cylinders, roughly, as the cubes of the diamethe strength of beams supported at both ends ters. A difference must be made in estimating the and loaded at the middle point between sup- strength of any beam between cases of simple ports is generally (calling the breadth b, depth support from beneath, and those in which the end or ends are firmly fixed, as in a wall. d, and length 7) in the ratio ; that is, it strength in the latter cases will be to that in is directly as the product above named, and the former in the ratio of about 3 to 2. The inversely as the length between supports. To strength of a cylindrical beam is to that of a find, then, the total strength of a rectangular square beam of like diameter, as 4.71 : 8; that beam of given material and section, it is neces- of a prism whose section is an equilateral trisary to seek its unit or coefficient of strength angle with the edge up, to that of one of square (that of the square inch section) by experiment section and the same area, as 22: 27; of the or in tables; and having introduced this, the prism, equilateral, with the edge down, to a like beam with the edge up, as 38: 23. In rule becomes, W = ƒ• As examples, the certain experiments upon beams having secunit, f, is, for good cast iron (short lengths, tions of different forms, the area being in all supported at both ends), about 2,548 lbs.; mal- uniform, and equal to 1 square inch, fixed at leable iron, 2,050; Canadian oak, 588. Callone end, and the loads applied to the other at ing of this ultimate strength the limit of a a length or distance of 1 foot, the following resafe load, the formula becomes, W = ƒ• 26 d. sults were obtained: a cast iron beam, section When the load is distributed equally along the of the section being vertical, with 568; cylinsquare, broke with 673 lbs.; square, a diagonal beam, the strength is practically doubled. The drical, 573; hollow cylinder, the greater diambeam being supported at one end only, and eter twice the less, 794; rectangular, depth loaded at the other, the strength falls to of 2 inches, breadth inch, 1,456; rectangular, that obtained by supporting at both ends; but 3x inch, 2,392; do., 4x inch, 2,652; equithis is in like manner doubled by uniform dis- lateral triangle, edge up, 560; do. do., edge tribution of load. For some materials, how- down, 958; T form, 2 inches deep x 2 wide ever, the formula gives a theoretical strength x .268 thick, 2,068; same inverted, 555; oak, too great; for cast iron, by about of the to- equilateral triangle, edge up, 114; do. do., edge tal result. Remembering, now, that the total down, 130. The strength of the largest square leverage of the fibres will be as the product of their number into their average distance from the neutral line, it will follow that, for the same quantity and kind of material, the strength can be increased, but within certain limits, by any change in the form of section that carries the fibres further from the neutral axis. When the area of the section is of oblong form, the strength when the beam rests on a narrower side is to the strength when supported on a flat side in the greater ratio of the depth to the thickness. Hence, plain rectangular beams are now seldom made square, but usually as flat prisms, and placed on the narrower side. But with a cross section containing a given total timber that can be cut from a tree is to that of the tree itself, as about 10: 17. But since a beam must bend before breaking, and since a permanent bend is found considerably to reduce the strength for an added load, deflection becomes of itself an element of weakness. Let B denote the amount of deflection, and e the coefficient of elasticity (see MECHANICS) of the given material; then, for given dimensions of the piece and amount of load, the deflection will be expressed by the following formula: Bb.de and a given deflection being found experimentally to reduce the load borne by a certain amount, a corresponding deduction W.13 must be made for flexures greater or less. Sometimes the weight of a long beam so nearly breaks it, that a cut across its under surface (acting somewhat on the principle of the incipient fracture started by the diamond in glass) suffices to occasion complete rupture. Peschel advised to saw down into the upper part of a long beam near the middle, and drive in wedges; and in this way, flexure being more powerfully resisted, the strength is greatly increased. The practice of deepening the middle part of a beam, long between supports, appears to be actually injurious; since the maximum strength, with the load distributed, that can be secured with a given weight of material and length of piece, is obtained when the section is slightly less at the middle, and increasing toward the supports. The general principle is that the strength of a beam is increased by whatever contributes to its stiffness. This result is in carpentry secured by increasing or distributing the number of points of support; and also by a special contrivance of several connected pieces of less size, and so adjusted as to secure a continued thrust against or lift upon the middle of the piece to be stiffened. This arrangement, applied either below or above the piece, is called a truss, and the application of it trussing. Since the neutral axis of a beam or of a column contributes nothing to its stiffness or resistance in any way to transverse strain, it may be removed without diminishing the strength. Moreover, the force requisite to sever or bend any bundle of fibres increasing with distance of this from the axis, it follows theoretically that great increase of strength will be secured, with a given weight of material, by giving to this the hollow cylindrical or tubular form. This form more than any other, indeed, augments the strength toward bending or crushing strains. Tredgold finds that in such a cylinder, the inner diameter being to the outer as 7: 10, the strength is doubled; and that it is greatest when the diameters are as 5:11. A rectangular beam, area 1 square inch, length 1 foot, sustained about 2 tons; a hollow cylinder of like area of metal sustained 13 tons; and a rectangular hollow beam, 8 tons. Obvious instances of gain of strength and lightness at the same time by conformity to this principle, are seen in the long bones of the vertebrate animals, especially in those of birds, in the quill part of feathers, and in hollow stems, as the straw of wheat. Applications of the principle in the arts of construction have latterly attained to great importance; among them are the use of hollow iron columns in building; the tubular bridges; the cellular structure, as in the double sides of iron ships, the space intervening being cut up by transverse plates, made both to bind and brace between the two; and fluting or corrugation of metallic sheets or walls, which thus, though light, may have the stiffness and strength of much thicker ones. IV. The torsional strength, being rarely of importance in practice, may be omitted.-It has often been observed that wheels, chains, beams, cranes, and other iron structures, after being long subjected to blows or to distinct jarring during use or in any manner, at length break, and apparently without adequate cause. On the London and Blackwall railway, cars were run by a stationary engine, by means of a wire cable 6 miles long. This, however well made, broke, it was found, after a time, though showing no visible wear or other deterioration. It is known that by continued rolling, hammering, or wire-drawing, metals lose their toughness and become fragile. It is asserted, and, though the question is yet somewhat in dispute, is probably true, that the tough metal is fibrous or laminated in structure, while the fragile or deteriorated pieces have become granular or crystalline. It is probable, therefore, that under continued agitation the molecules of the body undergo a new arrangement, in consequence of which its properties are changed, its tenacity and strength diminished. It has been proposed to call this condition fatigue of the metals. Applications of the principle are seen in the liability of cannon after being fired many times to burst, so that usually, after a certain number of discharges, pieces are now condemned and laid aside; and also in the danger from long use of breakage in car wheels, the chains used in hoisting from mines, in axles, &c. In two like structures of very different sizes, the larger is relatively weaker in consequence of its increased weight. At a certain size a structure would reach its 0 of strength for outside load, and beyond this would fall by its own weight. This result must follow because, while the strength of a structure is in a general way augmented in the ratio of the square of any certain dimension, the weight will increase usually as the cube of the given dimension. Of two like structures, one having its corresponding dimensions 4 times that of the other, the first will hence have a theoretical strength about 16 times that of the second, but a weight about 64 times that of the second. Hence, all unnecessary weight in the parts of a structure is a source of positive weakness; and in all our constructions a practical limit of size must be reached sooner or later. Hence, also, it is that we cannot judge of the effective strength of a structure from the actual ratio of strength afforded by its model. And a like principle furnishes one among the reasons why the smaller animals have relatively to their size a greater available strength than larger ones. For further study of this subject the reader is referred to the works of Barlow, Fairbairn, Hodgkinson, Tredgold, and Emerson (English); to Tate on " Strength of Materials" (London, 1851); to the "Report of the Royal Commissioners on Iron" (London, 1849); and to a series of articles on "Strength of Materials, deduced from the latest Experiments of Barlow, Hodgkinson, &c.," in the "Journal of the Franklin Institute," Philadelphia, commencing in Nov. 1860. |