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secured in one direction only, it being impracticable to roll a plate with thick edges all round. By a remarkable coincidence, however, the longitudinal strain is half only of the circumferential (71); hence only half the thickness of plate would be required in that direction. Thus, taking the example of the 48-inch boiler, with plates in (71), we found the bursting pressure circumferentially = 350 lbs. per square inch. Now, reducing the thickness of the body of the plate to it inch, then the area of 48%

1838, and of 48 inch 1809; hence the area of the annulus = 1838 1809 = 29 square inches, giving 22400 x 29 = 649600 lbs. total pressure or 649600 = 1809 = 359 lbs. per square inch longitudinally, being practically the same as the other. We thus obtain equality of strength in both directions, and a very considerable economy of material : it would, however, be inexpedient in most cases to carry this out literally for practical reasons; a plate would leave little margin for rust, &c.; moreover, the boiler would probably become deformed by its own weight and that of the water, Perhaps inch in the body of the plate and inch at the margin is the limit safely permissible in such a case.

" Gusset-stays.—The longitudinal pressure in a boiler creates a heavy strain on the ends, and where those ends are flat, as they usually are in ordinary Cornish boilers, they require to be strengthened by gusset or other stays. This is quite a practical question, and may in most cases be left to the judgment of the boiler maker.

STEEL BOILERS.

(73.) “Steam-boiler Joints for Steel Plates.”—To obtain general rules for steel boilers it will be well to take a moderately high pressure, say 100 lbs. per square inch, which will serve for all lower pressures, and sufficiently well for higher ones, say up to 150 lbs.

Taking z-inch plate for 48-inch boiler, the rivets diameter by col. 3 of Table 14, the space between rivet-holes for 100-lb. steam = say 116 by Table 13; hence the pitch = 1 +11 1 inch: the ratio of the metal between holes to the solid part of the plate = 11= 14, or 17 - 28 = .607.

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Table 16.-Of the PROPORTIONS of DOUBLE-RIVETED JOINTS in

ANNEALED STEEL PLATES for STEAM-BOILERS with about 100-lb. Steam.

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The apparent strength of the metal between rivet-holes in steel joints = 91,840 lbs. per square inch by (41); hence we have 91840 X •607 = 55747 lbs. per square inch on the solid part of the plate, and as we have square inch of metal per inch run (or i on each side) we obtain 55747 x * = 41800 lbs. on the whole area, or 41800 - 48 = 871 lbs. per square inch bursting pressure. With 6 for the factor of safety (78) we have 871 : 6 = 145 lbs. per square inch working pressure. Calculating in this way we have obtained Table 16: the mean strain in col. 7 = 57,000 lbs. per square inch. Hence for double-riveted steel boilers with annealed plates we have the general rules : (74.)

P 114000 xt; d. (75.)

p = 19000 xt; d. In which t = the thickness of plate in inches; d = inside diameter in inches; P = the bursting, and p = the safe working pressure in lbs. per square inch. Thus in our case P = 114000 x = 48 = 890 lbs.; and p = 19000 x š = 48 = 148 lbs. per square inch. The general Table 17 has been calculated by these rules, and will apply for all ordinary pressures, not exceeding say 100 to 150 lbs. steam : for higher pressures the case should be specially calculated.

(76.) “Steel Boilers for extreme Pressures.”—As an illustration of an extreme case, say that we require a steam-boiler 27 inches diameter for a working pressure of 450 lbs. per square inch: : we will assume -inch plates and 18 rivets as per col. 2 of Table 16. Then by Table 13 the space between rivet-holes = 1; hence the pitch = 12 + 12 = 1 inch : the ratio of the metal between rivet-holes to the solid part of the plate = :1 or 15 28 = -536; and the apparent strength of metal between holes in a steel joint being 91,840 lbs. per square inch (41), we have 91840 x •536 = 49220 lbs. per square inch on the solid part of the plate. We have 1 square inch of metal per inch run of solid plate (or } inch at each side), hence we obtain 49220 x 1 = 49220 lbs. on the whole of the diameter, or 49220 : 27 = 1823 lbs. per square inch bursting pressure. Taking 4 for the value of the factor of safety (78), we have 1823=4 = 456 lbs. per square inch safe or working pressure, or nearly 450 lbs., as required.

Now, if we had attempted to solve this question by Table 16, which is strictly adapted for 100-lb. steam only, col. 7 gives for l-inch plate 57770 - (27 x 4) = 535 lbs. per square inch working pressure, instead of 456 lbs. Both results, however, are equally correct so far as the strain on the metal is concerned; but then the joint whose pitch, &c., was adapted for 100-lb. steam would most likely leak sooner or later with 450 lbs.

(77.) Limitations."-In applying these rules and tables for very low pressures, it will be found that the thicknesses come out much too light to satisfy practical considerations, although undoubtedly sufficient to resist the internal pressure. For example, with a boiler 6 feet or 78 inches diameter and a pressure of 6 lbs. per square inch, the rule (64) gives a thickness of 6 x 78 - 7466 = .0626, or to inch only, which obviously is excessively too light; in fact, if it were possible to construct the boiler with that thickness it would not be able to sustain its

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TABLE 17.-Of the STRENGTH of STEEL BOILERS with DOUBLE-RIVETED Joints.

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own weight and that of the water contained by it. The rules have, therefore, certain limitations: in the first place, we should not usually make use of plates less than 1 inch thick for steam-boiler work, whatever the pressure or diameter; and, secondly, with thicknesses of 1

를 the diameters should not in ordinary cases exceed 4 5 6 7

8 feet, the corresponding working pressures being 29 31 32 33

34 lbs. per square inch, as per Table 15, which is carried out in accordance with these limitations. Thus for our 6-foot boiler the thickness would be between me and finch; would suffice for such a case, and this, it should be observed, is five times the theoretical thickness necessary for the pressure.

(78.) " Factor of Safety for Boilers.—It is shown in (886) that with ordinary structures of wrought iron and steel the factor of safety for dead loads may be 3, and there appears to be no good reason why that factor should not suffice for new boilers constructed on sound principles. But boilers are subject to great deterioration from corrosion, &c., and for that reason, perhaps, the factor used by Mr. Fairbairn and most practical men is 6, and this value is admitted in Table 15, &c., and should be followed for ordinary cases and moderate pressures of steam. But with Factor 6 the thicknesses for very high pressures come out excessive and almost impracticable, and engineers have been compelled to use a lower factor, and they do so apparently with safety. Thus the L. & N. W. Railway Co. at their Crewe works use best Yorkshire plates }} inch thick for 4-foot locomotive boilers, with single-riveted joints, rivets, 14 pitch, therefore 1 inch between rivets. By Mr. Fairbairn's experiments in col. 3 of Table 5, Yorkshire plates in single-riveted joints break with 42,847 lbs. per square inch of metal between rivetholes ; hence we have 42847 x 33 x 1:14 = 9946 lbs. per inch run of joint, or 19,892 lbs. on the two sides. With a boiler 48 inches diameter we have 19892 = 48 = 414 lbs.

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