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press. It would appear from this, that the tensile strength of cast iron in great masses 10 and 11 inches thick is much below the normal strength, or that for small thicknesses, namely, 7 tons per square inch.
(86.) “Tensile Strength of Thick Cast Iron.”—Experiments have shown (933) that the specific transverse strength of cast iron is not the same for castings of all sizes, but that large castings, or rather castings with great thicknesses, are specifically weaker than small ones, so that bars 1 inch, 2 inch, and 3 inch square bave specific transverse strengths in the ratio 1.0, 0.7184, 0.6195, and may be found approximately by the rule (934) or R = 1/t. How far the tensile strength of cast iron is affected by the thickness of the casting is not known experimentally, but admitting the same law as for transverse strength we obtain the ratios given by col. 7 of Table 18, from which we obtain col. 8, also col. 9 from col. 5: thus for 5 inches thick, we get 4.059 X • 497 2.017 tons bursting pressure per square inch, &c.
(87.) By repeated re-melting the tensile strength of cast iron may be greatly increased as shown in (5), where metal of the fourth melting (pig iron being the first) gave as much as 18.26 tons per square inch in small thicknesses; applying to this iron the ratio in col. 7 we obtain the tensile strengths in col. 10, and finally from col. 5 the bursting pressures in col. 11. Thus for 5 inches thick we have 4.059 x 18.26 = 7 X •497 5.265 tous, &c. But we have seen (7) that there is great uncertainty in this method of increasing the strength of cast iron; the safest course where heavy pressures are required, is to test the iron selected by direct experiments on its tensile strength.
(88.) Table 18 seems to show by cols. 9 and 11, that there is no sensible advantage from great thicknesses of metal, the pressure remaining practically constant with all thicknesses from 5 to 10 inches, &c. Of course this rests on the assumption that the tensile strength follows the ratio in col. 7, but as that is derived from limited experiments on transverse strength, where the thickness did not exceed 3 inches, the results are not absolutely reliable, but are the best we can give in the present state of our knowledge.
The great uncertainty as to the important data connected with this subject, should lead to the adoption of large diameters permitting low values for the strain S and pressure p.
For example, in the case of the Britannia press, say that the ram shall be 30 inches diameter
inches area, giving 820 = 707 = 1.16 ton pressure per square inch. The cylinder might be 32 inches internal diameter, and say 5 inches thick, therefore R
21 and r =
16; for strong iron of the fourth melting 5 inches thick S : 9:08 tons by col. 10 of Table 18:
9.08 x (212 – 164) then rule (81) becomes p =
= 2.4 tons
21+ 162 bursting pressure per square inch, or double the working pressure, 1.16 ton; thus leaving a fair margin for contingencies.
(89.) Another advantage of these proportions would be that the weight of the cylinder is reduced nearly to half, despite the increase in diameter; thus with the original sizes, 22 inches diameter 380 area, and 44 inches = 1520 area, hence 1520 – 380 = 1140 square inches, the area of the annulus. With the enlarged cylinder, 32 inches diameter = 804 area, and 42 1385 area, hence the annulus = 1385 – 804 = 581 square inches, or about half.
(90.) “ Cylinders Hooped with Wrought Iron.”—When large diameters are inadmissible and heavy pressures a necessity, the best course is to abandon dependence on the strength of cast iron altogether, and to rely on wrought-iron hoops shrunk hot, on a comparatively thin cast-iron shell, as in Fig. 25. In that case, the cast-iron cylinder may be regarded as a padding adding nothing to the strength of the combination, because when the hoops are shrunk on they exert a powerful compressive strain on the cylinder, which will be partially or perhaps wholly relieved when the internal pressure comes on: if wholly relieved the cylinder will be simply restored to its primitive state, being unstrained either way. It is rather difficult to calculate the strength under these conditions; if we take it as a wrought-iron cylinder 26 inches diameter, 5 inches thick, we have R = 18, r = 13, and the ultimate strength of wrought bar-iron or S being about 25 tons per square inch by Table 1, 25 x (182 – 13) the rule (81) becomes p
= 7.86 tons per
182 + 13° square inch bursting pressure. But we have here taken the pressure as acting on 26 inches diameter, whereas it really acts on 22 inches only: hence 7.86 x 26 = 22 = 9.3 tons per square inch. As applied to the Britannia tube, where the actual pressure due to the weight of the tube was 2.61 tons as shown by (85), we have 9.3 = 2.61 = 3.5 as the “ factor of safety.”
It is shown in (625) that whatever the initial strain on wrought iron may be, the permanent working load with a fixed length cannot exceed 8 or 9 tons per square inch: in our case it is 25 x 2.61 – 9.3 = 7 tons only.
(91.) Care must be taken that the longitudinal pressure does not blow the bottom out: the area of 26 = 531, and of 22 = 380, hence of the annulus 531 - 380 = 151 square inches, giving with 7 tons per square inch of metal, 151 x 7 = 1057 tons, or 1057 = 380 = 2.78 tons per square inch bursting pressure, or about it only of 9.3 tons the bursting pressure circumferentially. This difficulty is easily overcome by the construction shown by Fig. 25; the bottom of the cylinder, supported all over by the sole plate of the press, B, is entirely relieved of the bursting pressure.
(92.) “Wrought-iron Press-pipe.”—Wrought-iron drawn tubes are commonly used for hydraulic-press work, &c., where the pressures are very heavy; the ordinary sizes are 1 inch diameter outside, -inch bore, therefore 7 inch thick. A series of experiments was made on pipes of this kind with a pressure of 3 tons per circular inch, or 3 = .7854 = 3.82 tons per square inch; the pressure was obtained by a steel plunger 1 inch diameter, loaded with 3 tons of direct weights; there was therefore no uncertainty as to the real pressure. The result was that nearly all the pipes tested in this way bore the strain satisfactorily, the faulty ones alone failing. The maximum strain on the metal by the rule (82), with R = } inch, and r = 1 inch, becomes
3.82 x (1? + +) S=
= 6.37 tons per square inch, which is 12 – 1? abont only of 25•7 tons, the mean tensile strength of wrought iron by Table 1, &c.
Other experiments were made on lighter pipes of the same kind 1 inch external and sinch internal diameter; most of these failed at once under the pressure of 3.82 tons per square inch. In this case, R= 1 inch, r = Pinch, and rule (82)
3.82 x ( + 16) gives S =
= 8.7 tons per square inch of metal, if the pressure had been borne, which it was not. We may take the ultimate or breaking tensile strain of wrought iron in drawn tubes at 7 tons per square inch, which is 7 = 25.7 = 27 or 27 per cent. only of the strength of ordinary bar iron.
(93.) “ Wrought-iron Gas-pipe.”—Ordinary drawn wroughtiron gas tubing is also extensively used for steam-pipes, watermains, &c., where the pressure is considerable and a knowledge of its strength becomes important. Taking 2-inch pipe as an example, the thickness would be about 1 inch: hence R p= 1 inch, and taking S = 7 tons or 15,680 lbs. per square
15680 (12 – 14) inch of metal, rule (81) gives p =
12? + 12 = 2667 lbs. per square inch bursting pressure for constant steady load equivalent by (909) to 2667 x j = 1780 lbs. for intermittent load.
The proper value of the “factor of safety” will depend on circumstances, and must be fixed with judgment; for a waterpipe where the pressure is not only intermittent but where the sudden closing of a cock may create heavy shocks, whose effect cannot be calculated, but must be provided for by the use of a high factor, we may take it at 15, giving in our case 2667 = 15
= 178 lbs. per square inch, or 178 x 2:3 = 410 feet of water, safe working pressure.
(94.) “ Lead Pipe.”—Mr. Jardine made two experiments on ordinary drawn lead pipes, the pressure being obtained by a force pump. One pipe 1} inch internal diameter, } inch thick, bore without apparent alteration a head of 1000 feet of water; with 1200 feet it began to swell, and with 1400 feet, or 1400 ; 2:3 606 lbs. pressure per square inch, it burst. We may find from this the maximum breaking strain on the metal
by the rule (82), which with R = • 95, r = •75, becomes
606 x (-95+ 752) S =
= 2611 lbs. per square inch. .95* - •752 In the other experiment, the pipe 2 inches internal diameter,
inch thick, bore without alteration 800 feet of water, and burst with 1000 feet, or 1000 = 2:3 = 435 lbs. pressure per square inch; then R being 1.2 and p = 1, we obtain
435 x (1.22 + 1) SA
= 2412 lbs. per square inch of metal. 1.22 12 The mean of the two, or 2510 lbs., may be taken as a basis for the strength of lead pipes of all sizes. Table 19 gives the thickness, weights, and safe pressures for standard sizes of lead pipes; they are commonly rated by the weight per 15-foot length up to 1 inch diameter, and per 12-foot length for larger sizes.
The weight per foot being given, the thickness may be calculated by finding the external diameter by the rule :(95.)
(D2 - do) = W: 3.86. In which D = the external, and d = the internal diameter in inches, W = the weight per foot run in lbs. Thus, say we take 4-inch pipe, 32 lbs. per 15 feet, therefore 2.133 lbs. per foot: then 2:133 : 3.86 = •5503, which is D2 - d2; then •5503 +* or ·5503 + •5625 = 1.1128, the square root of which or 1.055 d; hence the thickness = (1.055 – •75) = 2 = 1525 inch, as per col. 2 of Table 19.
Having thus found the thickness, and thereby R, the bursting pressure will be given by the rule:
5800 X (R— 2) (96.)
R2 + go? = the bursting pressure in feet of water, and the rest as in (82): thus with the 3-inch pipe, • 1525 inch thick as in (95)r= .375, R = .375 + •1525 = •5275, and the rule gives 5800 x (52752 – .3752)
5800 x ( 2782 – 1406).
or, •52752 + .3752
• 2782 + .1406 5800 x 1376
= 1906 feet
• 4188 of water, as in col. 5 of Table 19, &c.
In which pw