The first of the classes named above - the characteristics of the materials used in construction - having, in the volume of this "Advanced Series," which embraces construction in stone and brick, been dwelt upon as fully as the space at disposal admitted of, we refer the student to that volume, and proceed to consider the strains or pressures to which these materials are subjected. These we give in the following brief paragraphs or sentences, which, although in most cases have reference to timber beams, apply also directly, with certain modifications which shall be noticed in due course, to those of iron in its two forms of cast and wrought.
57. The strains to which materials are subjected, in the construction of framework, are as follows - (1) "transverse" or "cross strain." When a timber beam is supported at both ends, as the beam a b, fig. 457, and pressed upon by weights at its upper surface, in the direction of the arrow r, it is said to be acted upon by a cross or transverse strain, and this effect or strain is equally produced if the weights act from below, being suspended from the beam. (2) If the beam be acted upon by strains which operate in the direction of the arrows, no, fig. 457, it is said to be subjected to a "tensile strain," and its power to resist this is stated to be its "resistance to tension." (3) If the beam be placed vertically, like a column or pillar d c, and it be placed under a pressure acting in the direction of the arrow k, fig. 457, it is said to be subjected to a "compressive strain" or "force," and its resistance to that is stated as its "resistance to compression." The first (1) of these strains act in the direction of right angles to the fibres of the timber, tending to break them across; the second (2) in the direction of the fibres, with a tendency to tear them asunder; and the third (3) also in the direction of the fibres, but with a tendency to crush them together. Of these three, so far as timber beams are concerned, the two last only are of practical importance, as there is in practice scarcely a limit to the powers of timber to resist having its fibres torn asunder. In the case of wrought-iron its tensile strength is of great importance. When a beam acting as a column is subjected to pressure (3) its resistance, according to Rondelet (Traite L'Art de Batir), does not diminish to any perceptible degree, if its height does not exceed eight times its diameter or base; if it exceeds ten times it begins to bend; if its height is sixteen times the base it is incapable of yielding resistance to pressure. If a beam is subjected to cross pressure (1) it has a tendency to bend or sag in the middle; this is known as its "deflection;" and its tendency or strength to resist this pressure is known as its "elasticity" or "resiliency." The strength of a beam which is rectangular in section is as the square of the depth multiplied by the breadth or the thickness, and divided by the distance between the points of support, as ab, fig. 457, or by the "span." Hence the strength of a beam is more economically increased by increasing the depth than by increasing the breadth; thus, a beam having its depth doubled, the thickness remaining the same, has four times the strength than before; but if its thickness or breadth be doubled, the depth remaining as before, its strength is only doubled. The best proportion of depth to thickness or width, in the face or edge of a beam, "is as the square root of 2 to 1." It is thus seen, as simply stated, that the strength is increased as the square of their depth, and directly as the breadth. A beam therefore, which is rectangular in section, is stronger when laid upon its edge than when laid upon its side, in the proportions as now stated. Ignorance of this simple fact, and of the principle upon which it is based, has led to some strange errors in construction. The strength of beams is also influenced by their length - the longer the weaker; or, stated thus, the strength is inversely as the bearing or span, or distance between the supports. The strength of a beam is also influenced by the way in which the load is distributed over its surface; if it be concentrated in the centre, as at the point c, fig. 457, it will only bear half the weight which it will do if the load be distributed over its surface. As will be presently shown, the strength of a beam increases as the load approaches its points of support, so +that a beam uniformly loaded may be reduced in depth as it approaches the points of support without reducing its strength, if so lessened in depth from the centre to the ends. A parabolic curve is the best outline to give the under side, allowing flat places at the end for the bearings on the wall. A beam or cantalever, projecting from a wall and uniformly loaded, is as strong if the under half be cut away, the outer end being reduced to a point, the inner end of the normal depth of the beam, as the beam would be if kept the full depth from point to bearing. And as in the case of a beam supported at both ends, this cantalever will support twice the weight, if uniformly loaded, which it would do if loaded at the end only. A beam supported at both ends, but not loaded, if of great length, has a tendency to sag or bend in the centre, just as if it was loaded on the surface. In all calculations, therefore, respecting beams, the weight of the beam itself must be taken into account. The fibres of a beam supported at both ends, and subjected to cross pressure, are placed under different kinds of strains. Thus, the upper fibres are subjected to a strain of compression, while the under are under tension. In a beam or cantalever supported at one end, and subjected to a load at one end or distributed over the surface, the upper fibres are under compression and the lower under tension. In the former case the point is pretty well illustrated if the student will suppose the beam, supported at both ends, to be considerably bent; he will then understand how the fibres towards the centre of the upper side g, fig. 458, are crushed together, while those of the lower h side are extended. By taking a piece of thick vulcanised india-rubber and bending it, he will have the point visibly illustrated.