the ultimate deflection, due to 456 of the breaking weight: three others were all broken when deflected to the ultimate deflection, due to 627 of the breaking weight, with 29, 1282, and 3695 blows respectively. Two others with of the ultimate deflection, due to 78 of the breaking statical weight, broke with 127 and 474 blows respectively.

With 3-inch bars deflected to the ultimate deflection, due to 488 of the breaking weight, one broke with 1085 blows; two others were not broken with 4000 blows each. Two others, with the ultimate deflection, due to 645 of the breaking weight, broke with 127 and 3026 blows respectively.

These bars appear to have been stronger in resisting impact than those experimented upon by Captain James (910), especially considering the nature of the strains; we should have expected that a given deflection produced by a blow, as in Mr. Hodgkinson's experiments, would have been more destructive than the same deflection produced gently by a cam, as in James' experiments. But, in the former, the number of impacts was not carried far enough to exhibit fully the effect of fatigue; one of the bars, however, did fail with of the ulti183 mate deflection, and with 1085 blows; possibly the others would have failed also with a greater number of impacts, such as would occur in practice (911), (919).

(922.) We will therefore retain for cast iron the ratio of the breaking intermittent load at of the statical breaking weight, as found from Captain James' experiments (911); the ratio for Steel and Wrought iron being 3, as in (909).

These probably represent the extremes, steel and wrought iron having the most perfect elasticity of all the materials used in the arts, and cast iron the least perfect. We have no experimental information for other materials, but supposing them to occupy an intermediate position, we may admit for them the ratio for an intermittent load to be the Statical, which will apply to Timber, wrought metals, such as Copper, Brass, &c., also to Slate, York-paving, and other kinds of Stone, &c.

For cast metals, such as Copper, Brass, Lead, &c., we may adopt the ratio as for cast iron.

(923.) "Fatigue from Rolling Load."-The effect of a rolling

load in straining a beam is shown in (832), &c., to depend on the horizontal velocity; at very low speeds the effect is similar to the action of a cam, which quietly deflects the beam; but as the velocity rises the deflection increases until, at a certain velocity varying with the span of the beam and the elasticity of the material, the deflection becomes double that due to the same load acting statically, or as a dead load. We may therefore admit that a rolling load should not exceed the statical or dead load under otherwise similar conditions, and this ratio may be applied for all ordinary cases.

Thus, by Table 66, the Transverse strength of wrought iron is 4000 lbs. breaking-down dead load; with Factor 3 we have 40003 1333 lbs. safe dead working load. Therefore, 1333 × 3 = 888 lbs. intermittent dead working load, and 888 × 444 lbs. rolling or dynamic working load. This last is th of 4000 lbs., the Statical Breaking-down load. Again, with Cast iron, the transverse strength for dead load is 2063 lbs.; with Factor 3 we have 2063 ÷ 3 688 lbs. safe dead load, 688 × 229 lbs. intermittent load, and 229 × = 115 lbs. rolling load, which is th of the statical breaking weight. Again, with English Oak, the transverse strength for dead load is 509 lbs. breaking weight; with Factor 5 we obtain 509 ÷ 5 = 102 lbs. safe dead load, then 102 × 51 lbs. intermittent load, and finally 51 × = 26 lbs. rolling load, which is th of the statical breaking weight.

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=

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(924.) In very many cases the strains on the different parts of machinery are not strictly rolling loads, but acting with a certain amount of shock they may be taken as similar in their action to rolling loads, this being in many cases the best approximation that can be made. Thus, with the rods of single-acting pumps, worked by a 3-throw crank, there is a certain amount of shock in passing the centres, and we may take it as doubling the strain in the same way as a rolling load would act on, say, the vertical rods of a suspension bridge. Then, taking the tensile strength of welded joints, as in our case, at 21 tons per square inch (see Table 1), we have with Factor 3, 21 ÷ 3 = 7 tons safe dead load, 7 × tons intermittent dead load; and finally 4.67 × 1

=

= 4.67

2.33 tons,

or 5220 lbs. per square inch, dynamic or rolling load. This agrees with practice, as shown by col. 10 of Table 30, which shows that rods with 5070 lbs. stand their work, but others with 6600 lbs. fail repeatedly. Those parts of pump-rods which work through the glands or stuffing-boxes are commonly made of wrought copper, principally to avoid rust, to which iron rods would be liable in case of stoppage for a few days. Wrought copper breaks with a tensile strain of 15 tons per square inch; then with Factor 3 we have 15 ÷ 3 = 5 tons safe dead load; 5 × = 2.5 tons intermittent load; and 2·5 1.25 tons, or 2800 lbs. per square inch dynamic load; and this, it should be observed, is the strain at the reduced section, or where the area is reduced by the key or screwthread (210). Table 29 shows that in practice copper rods are much more heavily loaded than we have thus calculated, some having as much as 5670 lbs. per inch, &c.; but, as a matter of fact, these rods are frequently breaking, and in some cases duplicate or spare rods are kept on hand ready for that contingency.

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(925.) But, wherever possible, the constant, or Factor of Safety, for any particular machinery should be obtained direct from cases working well in practice: the whole matter of the strains in machinery is so complicated and obscure that no other course is likely to be perfectly safe and satisfactory. It is only in those cases where no direct data are attainable that the theoretical methods we have explained and illustrated should be used.

(926.) When a dynamic strain acts in both directions, or is an alternated strain, we must apply the ratio for that circumstance, as explained in (915). Thus, taking the cases in (923), wrought iron becomes 444 × = 222 lbs., orth of the statical breaking weight; cast iron becomes 115 × = 57 lbs., orth of the statical breaking weight; and Oak is reduced 13 lbs., which is th of the statical breaking

=

to 26 × weight, &c. (927.) "Fatigue of Plate-iron Beams."-Mr. Fairbairn made some valuable experiments showing the effect of fatigue from oft-repeated strains on a riveted plate-iron beam, Fig. 133, the

load being completely relieved and laid on again about 8 times per minute by a crank-arrangement. To imitate as nearly as possible the strain to which Railway bridges are subjected by the passage of heavy trains, the apparatus was designed to lower the load quickly, and to produce a considerable amount of vibration, as the large lever with its load was left suspended on the beam at each stroke. The beam was 16 inches deep, and 20 feet between supports; Table 140 gives a compendium of the experimental results.

By (909) with an intermittent dead load, the breaking weight of wrought iron is 3rds of the breaking dead weight; and by (923) half that amount, or 3rd where the load rolls over the beam at a certain velocity, or where it acts in a manner analogous to a rolling load, which is our case; accordingly Mr. Fairbairn found that with 3rd of the statical breaking weight, the beam broke with 313,000 changes of load.

This beam bore first 596,790 changes of the statical breaking weight without apparent injury, or manifesting distress by increasing in deflection, which remained practically the same throughout, namely 16 or 17 inch. It was then loaded with or of the breaking weight and bore 403,210 changes without distress, the deflection remaining constant throughout at 22 or 23 inch. The load was then increased to or of the breaking statical weight, and the beam broke with 5175 changes.

3 2

2.5

The beam was then thoroughly repaired, and with th the breaking weight bore without apparent injury 3,150,000 changes, the deflection remaining constant throughout at 17 or 18 inch, and the permanent set at 01 inch. The load was then increased to rd of the statical breaking weight, with which the beam broke after 313,000 changes, but without manifesting distress by increase of deflection, which remained constantly throughout at 2 inch.

(928.) Mr. Fairbairn concludes from these experiments that with rd of the statical breaking weight, Railway bridges would be decidedly unsafe, but that with th of that weight, a wrought-iron bridge would be perfectly safe for a great number of years. Nevertheless, he allows in practice a larger margin

for safety, namely, or of the breaking weight; many of our leading Railway Engineers, such as R. Stephenson, J. Cubitt, P. W. Barlow, &c., adopt th as the ratio in practice, as shown by (892) and Table 138.

We have shown in (840) that in Railway bridges, the velocity is never high enough to give anything approaching to the maximum effect, or to produce a deflection double of that due to the same load acting statically; moreover, the inertia of the bridge itself gives a considerable resistance. The combined effect of these two circumstances is, that the strain is very little greater than that due to a dead load, which is proved to be the fact by the experiments on the Ewell and other bridges (839). The strains on Railway bridges may therefore practically be regarded as dead loads: they are, however, intermittent, and for wrought iron should be, and for cast iron of the equivalent constant dead loads. Then with Factor 3 as given by Table 137 we finally obtain for wrought-iron Girders the Ratio 3 = 222 or 4, hence the working Factor of Safety 4.5 for Cast-iron girders we obtain ÷ 3 = }} of the statical Breaking weight, the Factor being = 9. As we have seen (928), the leading Railway Engineers, making no distinction between cast and wrought iron, have adopted the ratio or Factor 6, which is intermediate between 4·5 and 9.

(929.) Collecting these results and applying them to the three great Strains, namely, the Tensile, Crushing, and Transverse strains, we obtain for various Materials, the series of equivalent strains for varying conditions of loading given by Table 141, combining which with the Ratios or Factors of Safety in Table 137, we may find the proper load under all ordinary conditions. As the matter is essentially and necessarily a complicated one, we may give examples which will help to make it more clear.

Say, we have a single-acting pump, 18 inches diameter, 150 feet head of water, &c.: the strain being Intermittent and Dynamic, col. 3 of Table 141 gives 8.6 tons per square inch Breaking weight, and Table 137 gives the Factor of Safety

3: hence we obtain 8.6 32.87 tons Working load. Then 18 inches diameter = 254 square inches area, and the pressure due to the water = 150 ÷ 2·3 = 65 lbs. per square