TABLE 137.-Of the RATIOS of the BREAKING WEIGHT, PROOF STRAIN, and WORKING LOAD for different Materials; also the FACTOR of SAFETY: all for DEAD LOADS.

TABLE 138.-Of the RATIOS of the BREAKING PROOF and WORKING LOADS ON BEAMS, according to different Authorities.

with very large structures, the highest possible Factor = 4, being limited by the great weight of the Beam itself.

PROOF STRAIN.

(893.) The great object of testing or proving Materials is to obtain thereby a guarantee that they will safely bear the permanent load assigned to them. To secure that purpose satisfactorily it will not suffice to test up to the working load only: it is necessary to allow an excess of strength to cover the possible contingencies of irregularities in loading, or imperfection in quality. In considering the proper value of the "Proof Strain" there are two different bases to calculate from, 1st, by making the Proof Strain a given fraction of the Breaking Weight, and 2nd, by making it a given multiple of the working load. If the Factor were constant for all materials, the two methods would be identical in their results; but as we have seen, that Factor has a variable value, which alters the case. Thus, say we take the Factor at 3, and allow the Proof Strain to be half the breaking weight; then the Breaking, Proof, and Working Strains would be in the ratio 1,,, the Proof Strain being 1.50, or 50 per cent. in excess of the working load. But with Factor 5, if we made the proof strain half the breaking weight as before, we should evidently have 1,,as the ratios of the three strains, and in that case the proof strain would have been÷} 2.50, or 150 per cent. in excess of the working load.

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(894.) Considering that the special object of testing has direct reference to the safe endurance of the working load, it seems expedient to take that load as the basis, rather than the breaking weight.

The earlier authorities considered that 3rd of the breaking weight was the "limit of elasticity," and that materials would be permanently injured by heavier strains. Although that conclusion has been proved to be incorrect (883), the notion still lingers in the minds of practical men, some of whom, such as Brunel, object to the testing of materials beyond the permanent working load which they are intended to carry. This would, however, be an obviously unsafe practice, for there might be

some latent defect in design or quality, such that the structure would break with a strain very little in excess of the working load, and if in practice that load should from some unexpected cause be a little greater than was assigned to it, utter failure might result. It is therefore highly necessary that the Proof Strain should be considerably in excess of the working load, so as to leave a margin for contingencies. On the other hand, it is not prudent to overstrain the material:—Mr. Fairbairn says, “ I am not an advocate for testing girders much beyond their permanent load"; however, he takes the working load at or of the breaking weight, and the proof strain ator of the breaking weight. Hence the proof strain would be in one case } = 1.33, or 33 per cent., and in the other case÷ 1.50, or 50 per cent. in excess of the working load.

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(895.) Most of the Engineers whose opinions are given in Table 138, consider half the breaking weight to be the extreme limit to which materials should be tested. If we admit that the Proof Strain should be 50 per cent. in excess of the working load, then with Factor 3 we should have 1÷3 × 1·50 =·5, or half the breaking weight, which agrees with the opinion of the eminent Engineers in that Table. Moreover, the various Diagrams and Tables show that with a strain of half the breaking weight there is no excessive deflection or permanent set, which proves that the materials are not overstrained. With Factor 4 we should have for the proof strain 1÷ 4 × 1·50 = 375, or 3ths; and with Factor 5, 1÷5 × 1·50 =·3, or ths of the breaking weight respectively; being in both cases less than half.

We may therefore admit that the Proof Strain should be 50 per cent. in excess of the permanent or working load, giving thus a good margin for contingencies, without unduly straining the material.

ON TEST-BARS, ETC.

(896.) "Factor determined by Test-bars."-In large contracts for cast-iron girders, sleepers, &c., for Railway and other purposes, it is usual, in order to secure a high standard of strength, and uniformity therein, to have test-bars cast from the same

iron as that used for the Girders, usually two or three times a day at given intervals. These sample test-bars are then subjected to transverse strain, and the breaking weights are required to come up to a certain standard load fixed by the Engineers, the Girders being rejected if the test-bars fail to come up to that standard. Thus the "Factor of Safety" is determined by Test-bars.

Another test-standard is to give a certain minimum tensile strength for the iron, in which case the iron used for the girders is cast at intervals as before in forms suitable for being torn asunder, and is required to bear a given strain per square inch.

(897.) It has been doubted, however, whether the strength of girders of ordinary sections will be simply proportional to the transverse strength of such "Test-Bars," or to the tensile strength of the iron as thus taken. Mr. Berkley made some valuable experiments for the purpose of settling this question, the reduced results of which are given by Table 139. The girders were all of the ordinary double-flanged type recommended by Mr. Hodgkinson and used in his experiments, the depth being 5 inches and the length 4 feet between bearings, the other dimensions are given by Figs. 197, 198, 199. Thus No. 4 broke with 16,730 lbs., or 3346 lbs. per square inch of sectional area, when the test-bar (cast from the same iron), 2 inches deep, 1 inch wide, broke with 25 cwt. in the centre, and the tensile strength 7.142 tons per square inch.

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(898.) By judicious mixture a stronger iron was obtained which gave 36 cwt. for the transverse strength of test-bar, and a tensile strength of 13 3 tons per square inch, as in No. 6; and the question was whether the girders would be stronger in the ratio of the transverse strengths 36 to 25, or in that of the tensile strengths 13.3 to 7.142. By the test-bar ratio the girder in the strong iron should break with 3346 × 36 ÷ 25 = 4818 lbs. per square inch of section, but the actual breaking weight was 5309 lbs., hence 48185309 = 908, showing a deficit by the test-bar Ratio of 1·0 — ·908 =·092, or 9.2 per cent.

Again by the tensile ratio we obtain 3346 x 13.37.142

= 6231 lbs. per square inch of section, but the actual breaking weight was 5309 lbs. only, hence 6231 5309 1·174 or 17.4 per cent. in excess by the tensile Ratio.

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(899.) The cols. 8, 9, 10, 11 in Table 139 have been calculated in this way, and show that the strength of the girders do not follow precisely or even very nearly the ratio of the transverse strength of the iron as indicated by test-bars, neither does it follow the ratio of the tensile strength of the iron. The testbars or beams give the best results, and the safest, being always less than the experimental strength of the girders, varying from - 1.7 to 23.8 per cent., as in col. 9. The calculations from the tensile strength give in four cases out of six, errors in excess, in one case to the extent of 26 per cent., as in col. 11. We should have expected that with girders of such a section failure would ensue from the rupture of the bottom flange under tensile strain, and that the strength would be dominated by the tensile rather than by the transverse strength of the iron, but experiment shows that this is not the case.

(900.) With Mr. Stirling's toughened cast iron (938) the mean transverse strength of test-bars showed an increase of