GIRDERS, and the TRANSVERSE and TENSILE STRENGTH of the

60 per cent. over ordinary cast iron, while the tensile test gave 74 per cent., as in col. 5 of Table 143; but when cast in large girders of Mr. Hodgkinson's form, the increase was only 36.6 per cent., as shown by Mr. Owen's experiments in Table 68. In that case, therefore, it is evidently unsafe to calculate the strength of the girders from either the transverse or tensile test-bars. This is the more remarkable because it is the reverse of Mr. Berkley's results with ordinary iron, where the transverse test-bars gave too low a result, the mean of col. 9 in Table 139 being 12.1 per cent. But with Stirling's iron the transverse test-bars gave 60 · 36.6 =

=

23.4, and the 37.4 per cent. too high (940).

tensile 74 - 36.6 (901.) It is evident from all this, that the ordinary test-bar, and tensile tests are unsatisfactory: a more reliable test would be given by the use of "Unit" girders, as in (485), that is to say, by making a model girder to a small scale with precisely the same cross-sectional proportions as the full-sized girders, and calculating the latter from that of the model in the manner explained and illustrated in (483).

(902.) In cols. 12, 13, 14, 15 of Table 139, the effect on the

Girder of a given increase in the Tensile, Crushing, and Transverse strengths of the iron is shown more clearly. Thus with Nos. 8, 9, we find that while the tensile strength is increased 47 per cent., the test-bars are 20, and the girders 22.4 per cent. A further increase in the tensile strength of 95.1 per cent., produces 52 per cent. in the test-bars, and 54·6 per cent. in the girders, &c. The crushing strain in col. 7 was calculated from the experimental tensile and transverse strengths by the Rule (498), in the absence of direct experiment.

CHAPTER XXIII.

FATIGUE OF MATERIALS.

(903.) "General Principles."-Experiments have shown that when materials are subjected to heavy strains of any kind, they manifest distress in several ways. 1st, where the load is constant by the extensions, deflections, &c., increasing with time. 2nd, where the load is progressively increased, by the deflections &c., increasing in a higher ratio than the strains. 3rd, by taking a "Permanent set" (751). 4th, by eventually breaking or giving way with a strain much below the normal strength of the Material, as the result of long-continued and oft-repeated intermittent strains. These results of over-strain may be aptly expressed by the general term "Fatigue.”

This subject may be considered under two heads, 1st, Statical fatigue from a long-continued dead load; 2nd, Dynamic fatigue from a rolling or moving load, which acts more or less with Impact (831).

Statical Fatigue.

1st,

(904.) This case may be divided into two branches. where a heavy and invariable dead load is borne for a long time continuously. 2nd, where the load is intermittent and variable, being alternately and frequently laid on and relieved wholly or partially, but without impact or shock.

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“Constant Load.”—The effect of constant tensile strains on wrought iron is shown by cols. 4, 4, in Tables, 94, 95; thus, by the latter, with 17.86 tons per square inch, fatigue was manifested by the extensions continuing to increase with time, but at a diminishing rate: the 1st hour gave an increase of 14.5 per cent.; the next 15.5-14.5 = 1 per cent.; the next 16.3 15.5 0.8 per cent., &c., up to 7 hours, when it continued constant up to 10 hours. Even with the heavy strain of 22 63 tons per square inch, or about 22·63 ÷ 25·7 = 88, or 88 per cent. of the breaking weight, the extensions increased only '08 per cent. in 7 hours, and then remained stationary up to 12 hours. It would seem from this that fatigue manifests itself with moderate strains even more than with heavy ones, which is very remarkable.

(905.) Mr. Fairbairn's experiments on cast-iron bars strained transversely lead to the same conclusion; it was found that in a series of bars subjected to constant dead loads for long periods, those with the lightest loads manifested the most distress from fatigue by increase in deflections; thus when strained to

62

75

88

100 nearly

per cent. of the ultimate or breaking weights for periods of

42

5

5

5

years, the increase in deflection from fatigue in those times was

14.1

11.4

8.6

2.8

per cent. respectively; these were the maximum results in each case. It was found that the deflections increased the most considerably during the first weeks and months up to 12 or 15 months, and then became constant or nearly so. One bar loaded up to the very breaking weight for 5 years, had not any greater deflection than it had taken 3 or 4 years before, and Mr. Hodgkinson concludes that it is probably a law with cast iron that the deflection, &c., will go on increasing with time at first until it becomes a certain quantity, beyond which it will no longer increase, but becomes stationary :-We have seen (904) that wrought iron under tensile strains seems to follow a similar law.

(906.) Mr. Fairbairn made similar experiments on the power of cast-iron pillars to sustain long-continued strains :-they were 1 inch diameter, 6 feet long, with rounded ends, were loaded with

per cent. of the breaking weight, as found by direct experiment on similar pillars. The pillar loaded with 13 cwt. bore the strain for 5 or 6 months and then broke :-the others bore their respective loads for 3 years, and their deflections were then

inch. The deflection of the pillar with 10 cwt. was 230 inch when first taken, and after each successive year it became ⚫380, 380, and 409 inch respectively.

(907.) The general results seem to be :

1st. That the elasticity is affected by fatigue from a dead load, but up to a certain extent only, and within a limited time; that is to say, the extensions, &c., do not go on increasing with time indefinitely, nor to an unlimited extent, terminated only by fracture; but that both are limited.

2nd. That the ultimate strength and deflection are not affected by fatigue, both being the same whether the material is broken suddenly or after a long-sustained and heavy dead load.

3rd. That on emergency materials may be safely strained to a much greater extent than was admitted by Tredgold and other earlier authorities :-they, finding that with loads greater than 3rd of the breaking weight, the extensions, &c., continually increased with a constant load, supposed that this increase would go on indefinitely until rupture ensued, whereas, as we have seen, although it may go on increasing for a long time, even years, it does so in a continually diminishing ratio until in a certain limited time it ceases, or becomes constant.

(908.) "Variable Load."-We have seen that when the load is constant, materials seem to be capable of bearing strains

approximating to the breaking weight for indefinite periods without apparent injury. But where the load is variable, being wholly or partially relieved and laid on again continuously, the case is entirely altered.

This case divides itself into two very different conditions. 1st, where the load is variable, but acts in one direction only as, for instance, with the rods of single-acting pumps; and, 2nd, strains acting alternately in opposite directions, as is the case with double-acting pump-rods, and many of the parts of ordinary steam-engines:-for example, in a piston-rod the strains are alternately tensile on the down-stroke and compressive on the up-stroke, &c.

(909.) "Load in One Direction only."-This case must be subdivided into two different conditions. 1st, " Intermittent Strains," where the load is entirely relieved and laid on again continuously without shock; and, 2nd, “ Differential Strains," where the load is intermittent, but is only partially relieved at each stroke.

1st. Wöhler's experiments have shown that where the load is totally relieved each time, the best fibrous wrought iron breaks with tensile strains of 15 to 18 tons per square inch; the mean is 16.5 tons, and as the mean strength for a constant dead load is 25.7 tons, as shown by Table 1, we have the ratio 16.5÷ 25.764 or nearly.

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Soft steel was found by Wöhler to give under similar conditions of entirely relieved strain, from 22.5 to 25 tons per square inch; the mean is 23.7 tons, and as by Table 1 the mean tensile strength of steel for dead loads is 47.8 tons, we have the ratio 23.7 47.8 5, which, being less than the ratio for wrought iron, seems to indicate less perfect elasticity, and must be incorrect. We will therefore assume that with totally relieved strains the breaking weight of steel is of the statical breaking weight, or the same ratio as for wrought iron.

(910.) For cast iron we have the experiments of Mr. Hodgkinson and Captain James, the leading results of which are given in Table 140. In James' experiments the beams were deflected by cams revolving from 4 to 7 times per minute; one