having areas of 6 to 1. His girders were all of the same depth, namely, 5 inches; the ratio of areas were 1 to

The mean Breaking transverse loads per square inch of whole sectional areas were―

lbs. ; hence, taking the equal-flanged girder as = 1.0, the mean increase in strength per cent. becomes

TABLE 92.-Of the COINCIDENCE of EXTENSION and COMPRESSION of

(618.) It would appear, however, that the ratio of the areas of the flanges is not a fixed one for all strains, but should vary with the ratio of the working load to the breaking weight, rising from 1 to 1 with 4th to 6 to 1 with the Breaking weight.

It has been gratuitously assumed that the best form of section for the Breaking Weight must of necessity be the best for lower strains also, say 3rd, which is the ratio commonly used, and thus Mr. Hodgkinson's form, with flanges in the ratio 6 to 1, has been almost universally adopted in supposed deference to authority, although that proportion would not commend itself to the unbiassed mechanical instinct of practical men: Mr. Hodgkinson, however, is not responsible for the erroneous deduction from his experimental results.

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Reasoning seems to show that with Factor 3 the ratio of the flanges should be somewhere between 1 to 1 as for 4th, and 6 to 1 as for the Breaking weight. Fig. 207 gives a section which fulfils the condition that the maximum tensile strain shall not exceed 3rd of the Breaking weight. Thus the area of bottom flange 10 square inches, the strain at T = 2.355 tons per square inch, and the distance from N. A. 4; hence we have 10 × 2·355 × 4 = 94.2. Then, the area of top flange=4.5 square inches, the strain at C =3.5 tons per square inch, and the leverage = 6, giving 4.5 × 3.5 × 6 = 94.5, or practically the same as the resistance to tension, which is a necessity in this case the ratio of the flanges = 104.5 = 2.22 to 1.0.

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But we must see to it, that extension being to the compression in Fig. 207 as 4 to 6, corresponds to 2.355, and 3.5 tons, the respective strains. Table 92 shows that for Tensile strain of 2.355 tons, the extension=00042; then the compression must be 00042 × 6÷4·00063, which is due to 3.5 tons per square inch by Table 89. Fig. 208 is a "UNIT" girder having the same proportions as Fig. 207, from which the dimensions for any load or span may be found, as explained in (485).

Fig. 209 is a Diagram which shows that, admitting equal flanges as the best for 4th of the Breaking weight, and 6 to 1 for the Breaking weight, we have 2.08 to 1.0 for 3rd, which is the ordinary working load, and agrees moderately with 2.22 as found by analysis: 3.08 to 1.0 for ; and 4·08 to 1.0 for

of the Breaking weight. It is probable from (617) that these ratios of strains apply principally to the bottom flange: in Fig. 207 the Factor is 7·142 ÷ 2·355 = 3 for the Tensile, and 433.5 12.3 for the Crushing Strain. See (354) and the Diagram, Fig. 81, &c.

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(619.) The actual and comparative lengthening and shortening of cast iron under different tensile and crushing strains may be shown distinctly by calculating the lengths of bars that would be altered in length 1 inch by different strains. Table 93 gives that length for cast and wrought iron.

(620.) "Extension of Wrought Iron." The elasticity of

wrought iron is very nearly perfect with moderate strains, say up to 8 tons per square inch, differing entirely in this respect from cast iron, as we have seen (604). Mr. Hodgkinson made experiments on two bars 50 feet long of the respective diameters of and inch, the results of which reduced to parts of the length are given by cols. 3, 3 in Tables 94, 95. For the weights in even tons, cols. 1, 1, the extensions were obtained by interpolating between the next greater and lesser experimental numbers as given by cols. 3, 3, without correction, that is to say, without attempting to equalize or eliminate the unavoidable errors and anomalies of experiment; the mean result of the two experiments is given by col. 5 of Table 91. It will be observed that the Modulus of Elasticity, cols. 4, 4 in Tables 94, 95, with which perfect elasticity would have been the same throughout, is practically uniform up to about 8 tons with the 3-inch bar, and about 9 tons with the -inch bar, the departures from uniformity being no doubt due to errors of observation. Defect of elasticity would have been manifested by a regularly progressive reduction of the Modulus; if there were such a reduction it must have been exceedingly small, and being obscured by errors of observation, it does not appear in the experiments.

(621.) "Effect of Time."-One very instructive and important point brought out very clearly by these two experiments is that with heavy loads the extension is not governed by the strain alone, but becomes also a question of time. The falling off in the Modulus with strains greater than 8 or 9 tons, seems to show that the bars were overloaded, and in all probability observations to that end would then have begun to show the effect of time, but such observations were not made until the 3-inch bar was loaded with about 13 tons, and the -inch bar with 14.3 tons per square inch, and then, even five minutes of time had a great effect on the result.

The Table alone gives a very imperfect idea of the relative effects of the gradually increasing strains on the extensions and of the influence of time on the results; the Diagram, Fig. 215, shows both graphically. A careful comparison of the results of the two experiments in Tables 94, 95, will show a