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and this would be too near the crippling strain to be admitted safely.

We may therefore allow 3 as the Factor of Safety with all strains on Steel: with a weak bar this would in effect be reduced to 3 × 68 = 2, giving thus the safe load at the ultimate strength, and this, as the diagrams show, may be permitted safely.

(888.) "Timber."-With Timber it is necessary in fixing the value of the Factor of Safety, to provide not only for variableness in the strength common to all materials, but also for deterioration from age and for decay from exposure to the elements, which is quite another matter. To cover all these contingencies it becomes expedient to adopt a higher Factor than would otherwise be necessary: we will take it at 5 as a mean for dead loads.

(889.) "Effect of Age.”—The effect of age may be ascertained approximately from the experiments in Table 1:-Mr. Bevan found as a mean of two experiments the tensile strength of ordinary Oak to be 17,400 lbs. per square inch, while old Oak gave 14,000 lbs., or 80 per cent. By Table 149 the minimum tensile strength is 72, the Factor 5 would therefore in the case of old and weak oak be, in effect, reduced to 5 × 8 × 72 = 2.88, which however is not too low for safety. The transverse strength of young oak or value of M, is 964 lbs., and of old oak 660 lbs., according to the experiments of Tredgold, hence old oak is only 68 per cent. of the strength of young oak, and the minimum transverse strength being 72 by Table 149, Factor 5 is in effect reduced to 5 × 68 ×·72 = 2·45 in the case of old and weak oak, not very different from the result we obtained from the tensile strength, which came out 2.88.

The mean tensile strength of Teak is 15,090 lbs. per square inch, but of old Teak 8200 lbs. only, or 55 per cent.: hence Factor 5 becomes in effect 5 × ·55 × ·97 = 2·67.

We have here taken extreme cases; with ordinary care in selection Timber need never be weaker than we have assumed, and Factor 5 may be taken as sufficient for safety for all strains on timber.

(890.) "Effect of Decay." The effect of decay on the

strength of timber exposed to the destructive action of the elements is very difficult to estimate, there being, in fact, no limit to the extent to which the material may be weakened from that cause. Mr. Bevan found that Oak from an old pile taken out of the bed of a river, had a tensile strength of 4500 lbs. per square inch only, which is 23 per cent. only of the mean strength of sound oak. If it is deemed necessary in any structure exposed to air and water, to provide for the eventuality of decay, the Factor of Safety should not be less than 10 for a dead load, when the mean strength of sound timber is taken as the basis of calculation:-evidently in the case of Mr. Bevan's oak pile that factor would in effect be reduced to 10 × 23. = 2.3.

(891.) "Stone, Slate, Brickwork, &c."-Except for the crushing strain, our experimental knowledge of these materials is limited, and we have little else but judgment to guide us in fixing the value of the Factor of Safety:-they are all weak in resisting Impact, and as in many cases an unexpected blow may have to be borne, it will be well to make the Factor higher than would otherwise be necessary, say 4. Table 149 shows that for brick exposed to transverse strains 4 may become in effect 4 x 75 = 3 with a weak specimen; and that for crushing strains 4 may be reduced to 4 x 5 = 2 in the case of Red Sandstone; and to 4 × 58 = 2·32 in the case of Granite. These reduced numbers show that it is not prudent to adopt a Factor lower than 4 for these materials.

(892.) Collecting these results, we obtain for ordinary cases the series of Ratios and Factors of Safety in Table 137. Special cases, which are very numerous, require special Factors obtained direct from experience, and this is very often the only safe course; the modifying circumstances are in practice so numerous and so complex that satisfactory results are not to be obtained in any other way. Table 138 gives the Ratios of the Breaking, Proof, and Working Loads, with special reference to Railway Bridges, &c., according to the judgment of our most eminent Engineers, as given in Evidence before H.M. Commissioners. Of these, R. Stephenson, W. Fairbairn, J. Hawkshaw, J. Cubitt, and P. W. Barlow, have adopted the Factor 6, as the best for general Railway purposes. It is shown in (491) that

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.

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

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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 ÷ 3 = 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.

(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 at or 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 13 × 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, 15 x 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

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