Variableness in Strength of Materials Agreement of Rules with Experiments Real and Apparent Factor of Safety.. Strength of flat cover to Boiler THERE are five principal strains to which materials may be subjected, namely, the Tensile, Shearing, Crushing, Transverse, and Torsional strains: essentially all strains are modifications or combinations of the Tensile and Crushing ones, but it will be convenient in practice to consider each of them as distinct and specific. (1.) "Central Strain."-When the cross-section of a body is of a regular figure, and the tensile strain is in the centre, it is commonly admitted that the resistance is simply proportional to the area, and that every part of the section is equally strained. This may be practically true in many cases, but where the body is wide or large, the central part is more stretched than the edges, and the strain becomes very unequal. For example, Fig. 1 is a plate of very elastic material whose normal form unloaded is a, b, c, d, and when strained by the central load W it becomes e, f, g, h. Obviously the central part is more stretched and therefore more strained than the edges, and if the load be increased up to the point of rupture, the plate will break first at the centre. (2.) "Strain out of Centre."-When the strain coincides with one edge of a plate as in Fig. 2, the primitive form i, k, l, m, tends to take the form n, o, p, r, and we have this remarkable result, that the maximum extension and corresponding strain at n, o, is progressively reduced towards s, t, where it becomes nil, and between 8, p, and t, r, the plate is compressed, not B stretched, and thus a crushing strain is created by a nominally tensile one. = Say, that we take a spiral spring whose normal length unloaded 10 inches, and its elasticity such that it extends 1 inch per lb.; also let 4 lbs. be the breaking weight, the maximum length being then 14 inches. Let B, C, D, E in Fig. 3 be four such springs attached at equal distances to two rigid crossbars F, G: if now a tensile strain of 16 lbs. be applied at the centre-line H, J, obviously the whole of the springs will be extended to 14 inches, each yielding the 4 lbs. due to it. In Fig. 4, K, L, M, N, are the centre lines of four springs similar to those in Fig. 3, but here the centre line of the strain coincides with L, Q, or the centre of the spring L. Now, it is essential that the forces on the two sides of the centre line should balance one another: they will arrange themselves as in the figure; thus the strain on K being 4, and its distance from the centre 1.0, we have 4 x 1 4, as the effect of the spring K. Then, on the other side, M 2.0, and N = 1 x 2 2.0 also the sum of the two being 4, or the same as K. Then the weight at W, with which the spring K will break, becomes as in the figure, 4 + 3 + 2 + 1 = 10 lbs., whereas with a central strain as in Fig. 3 we obtained 16 lbs., or 60 per cent. more than in Fig. 4. = = == = 2 x 1 = (3.) To show how a compressive strain may be generated by a nominally tensile load, let Fig. 5 be an arrangement similar to the preceding, but one where the tensile strain coincides with the centre line of the spring R, or the extreme edge of the combination. In this case the spring R bears the maximum load of 4 lbs., but S = 2 lbs. only: the spring T is neither extended nor compressed, but retains its normal length of 10 inches; it is therefore useless. The spring U is compressed to the length of 8 inches, and bears a crushing strain of 2 lbs. The tensile load at X from R = 4 lbs., from S 2 x 12 = 1.0; from T 0, and from U = 2 × 1÷2 = the 6 lbs., whereas with a central load as in Fig. 3 we had 16 lbs.; hence the ratio = 616375 to 1.0. Mr. Hodgkinson found by experiment that a cast-iron bar which broke with a central load of 7.65 tons, failed with 2.62 tons only when the force coincided with one side of the bar, the ratio being 2.627-65342 to 1.0, or nearly as we found it by calculation. These illustrations will serve to show the importance of arranging for the tensile strain to coincide with the axis of the body, or the centre line of the section, and that where this is impracticable, due allowance should be made for the fact. (4.) "Experimental Results."-Table 1 gives a general summary of the most important experiments on the tensile strength of materials, from which it appears than the mean breaking weight of: tons per square inch, which is equivalent to :- 16,000 57,500 107,160 35,840 lbs. Table 2 gives the breaking weight of round bars from inch to 3 inches diameter, calculated from these data. (5.) "Effect of Re-melting Cast Iron."-Ordinary cast iron is usually from the 2nd fusion, pig iron being the 1st: it has been found that with some kinds of iron at least, the tensile strength is very much increased by repeated re-melting; thus one set of experiments gave for iron of the lbs. The mean of the two series in tons per square inch 5.6 8.2 .14.65 18.26 = (6.) But Mr. Fairbairn obtained very different results, as given by Table 3, which shows that the transverse and tensile strengths were reduced by re-melting so far as the 3rd, then |