as in the case of the beam, piston-rod, &c., of ordinary steamengines, double-acting pump-rods, &c.

(882.) "Variableness in Materials."-Besides the variations due to methods of loading, there are at least three others due to the materials themselves, and we have, 5th, the natural variableness in the strength of all materials, even those of apparently the same kind and quality (957); 6th, deterioration from age and decay in such materials as timber, ropes, &c., and from rust in the case of wrought iron, especially when exposed to the weather; and 7th, the effect of thickness or size of casting with cast iron, and probably other cast metals (931).

It will not be necessary, however, to consider each case in detail under these several heads; for practical purposes it will be more convenient to take a Factor so high as to cover many of these contingencies, and we may then reduce the cases to 1st, a dead load; 2nd, a rapidly rolling load; 3rd, an intermittent load; and 4th, an alternating strain in opposite directions. See (960) for Real and apparent 66 Factors of

Safety."

We shall in this Chapter confine ourselves to the simple case of a dead, or statical load; having found the proper value of the Factor of Safety for that case, the modifications necessary for other conditions will be considered in the Chapters on Fatigue (903), Impact (774), &c.

(883.) The earlier writers, Tredgold and others, finding that with 3rd of the breaking weight, beams of cast iron, &c., began to show signs of distress by taking a permanent set (752), assumed that strain to be the limit of elasticity, and therefore that 3 should be the Factor of Safety for cast iron. It was considered that with loads not exceeding that limit materials would be quite uninjured, but that with greater loads a beam would go on increasing in deflection with time, until at a period more or less remote it would finally break. The Factor 3, based on these conclusions, has been almost universally accepted for dead loads by practical men, although Mr. Hodgkinson's experiments have shown long ago that, 1st, with cast iron particularly there is no such point as the limit of elasticity, or any strain, however small, with which there would be no

permanent set (752), and 2nd, that beams and pillars of cast iron will bear not rd only, but ths of the breaking weight safely and without increase of deflection for years (905).

(884.) From this last statement it would appear that the Factor of Safety might be very much less than 3, say 2, the beam, &c., being then loaded to half the breaking weight, and perhaps this might be permitted if we knew perfectly the actual ultimate strength of the particular specimen to be dealt with, but this must always be an unknown quantity, being, in fact, incapable of proof except by loading that specimen up to the breaking point, which of course would not answer the purpose.

:

From the variableness in the qualities of most materials, the assumed Factor 3 becomes often 2, or even 1 in practice :-for example, say we would calculate the transverse strength of a bar of cast iron 3 inches square. It is shown in (933) that the mean specific strength of a 3-inch bar is only 62 per cent. of the strength of 1-inch bars from which the ordinary Multiplier is usually derived moreover, by (957) and Table 149 the minimum transverse strength is shown to be only 79 per cent. of the mean strength, of which that multiplier is the exponent. Now if it should happen that our 3-inch bar is of weak iron, the Factor 3 would really become in effect 3 × ·62 × ·79 = 1.47, or less than half its assumed value. Considering possible but unknown contingencies from mode of loading and otherwise, it is evident that even the Factor 3 would in that case be too low for safety.

(885.)" Cast Iron."-The effect of size or thickness of casting is thus shown to be so influential that it becomes expedient to consider it separately in each particular case, because if we adopted a Factor sufficiently high to cover this and all other contingencies in the case of large castings, that Factor would be higher than necessary for ordinary sizes, and would lead to a costly excess of strength. Adopting that course but allowing for variableness as shown by Table 149, then the Factor 3 for transverse strength becomes in effect, with weak bars 3 × 79 = 2.37; for tensile strength, 3 × 79 = 2·37 also; and for crushing strength, 3 x 67 2.0. These reduced values being admitted as sufficient for safety, we may adopt 3 as the Factor

=

for all strains with ordinary thicknesses of cast iron, applying subsequently the correction for size of casting where necessary (932). For example, with a cast-iron girder whose breaking weight calculated by the ordinary Multiplier (335) is 30 tons, we have 30 ÷ 3 = 10 tons safe load if the thickness of metal differs little from 1 inch; but if the thickness (of the bottom flange more particularly) is about 2 inches, we have 10 x 72 7.2 tons; and if 3 inches thick, then 10 x 62 safe dead load.

=

6.2 tons

(886.) "Wrought Iron."-The Diagram, Fig. 215, shows that under tensile and compressive strains wrought iron practically fails with 12 or 13 tons per square inch, the extensions and compressions becoming excessive and increasing with time. The mean tensile breaking weight is 25.7 tons, as shown by Table 1; evidently, therefore, the iron begins to be crippled with half the breaking weight, and 2 would be too low for the Factor of Safety even if we were sure that the iron was of average quality. Besides, Table 149 shows that if the bar happens to be of weak iron, Factor 2 would really become 2 x 77 = 1.54, and the bar would be very much overstrained. Factor 3 becomes 3 x 77 = 2.3, which as the diagrams show by may be safely permitted.

**

We may therefore admit 3 as the Factor of Safety with all strains on wrought iron :-thus the safe tensile strain becomes say 25.73 = 8.6 tons per square inch with bar iron; and 21.637-2 tons, with plate iron, &c.

(887.) "Steel.". The elasticity of steel under transverse strains is wonderfully perfect as shown by the Diagram, Fig. 211, where a bar of untempered steel shows no appreciable signs of distress with even ths of the ultimate strain, or that with which the bar sinks down completely. In such a case we might admit that the bar might be loaded safely to the ultimate strength, or that the Factor might be = 2. But Table 149 shows that the variableness in the tensile strength of steel is very great, namely 68, the mean strength being 1·0, hence if a weak bar is loaded with the ultimate load due to an average bar it would evidently be strained to ÷ 68 73, or but little less than of its own ultimate strength,

=

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 x 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 x 8 x 72 = 2.88, which however is not too low for safety. The transverse strength of young oak or value of Mr 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 x 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.

T

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 x 55 x ⚫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 × 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