With double-riveted joints, the apparent strength of metal between rivet-holes = 41,800 lbs. by col. 7 of Table 5, hence the strain on the solid part of the plate = 41800 x :656 = 27420 lbs. per square inch; col. 9. Calculating in this manner, we have obtained the general proportions in Table 14. (62.) The mean strain on the solid part of the plate, when the metal between the rivet-holes is breaking, is with singleriveted joints 22,380 lbs., or say 10 tons, as in col. 8, and for double-riveted joints = 27,420 lbs. : col. 9. “ General Rules.”—We may now apply these results to practice, and may take for illustration a 48-inch boiler with 3-inch plate, and for the purposes of calculation say 1 inch long. Now as we have š x 1 inch at each side, this is evidently equal to # square inch area of metal taken through the solid part of the plate, the reduced resistance of which in a singleriveted joint 22400 x 1 = 16800 lbs : this is the total strain on the whole surface with which the boiler would burst, which being spread over the diameter (56), or 48 inches, gives 16800 = 48 = 350 lbs. per square inch bursting pressure. Hence we have the rules : (63.) For single-riveted joints : P = 44800 x t = d. (64.) p = 7466 x t = d. In which t = the thickness of plate in inches; d = inside diameter in inches; P the bursting pressure, and p = the safe working pressure in lbs. per square inch :thus in our case, P = 44800 x š = 48 = 350 lbs. per square inch as before. With double-riveted joints, the mean reduced strain on the solid part of the plate = 27,420 lbs. per square inch, col. 9 of Table 14, or in our case 27420 x * = 20565 lbs. total bursting pressure on a circle 48 inches diameter, or 20565 ; 48 = 428 lbs. per square inch : hence we have the rules : (65.) For double-riveted joints : P = 54840 xt; d. (66.) P 9140 x t = d. Thus in our case, P = 54840 x = 48 = 428 lbs. per square inch bursting pressure. TABLE 15.-Of the STRENGTH of CYLINDRICAL BOILERS made of STAFFORDSHIRE Plates with RIVETED Joints, for internal Pressures in Pounds per Square Inch. (67.) By these rules, Table 15 has been calculated for the bursting and safe working pressures : the former will enable the engineer to select a factor of safety to suit his case and to satisfy his judgment. For ordinary cases and moderate pressures Factor 6 should be used as in Table 15; but for very high pressures that factor would lead to excessive and almost impracticable thicknesses, and it becomes necessary to use a lower one, the risk being of course proportionally increased (78). (68.) “ Boilers for very high Pressures.”—Tables 14, 15 are strictly adapted for 50-lb. steam only, but may be used for higher pressures up to say 80 lbs. For higher pressures the proportions of the joints should be specially calculated in the manner illustrated in (61). Say that we take the case of a boiler 27 inches internal diameter, for 300-lb. steam, this being the working pressure : for so high a pressure we may take the factor of safety at 4 (78). We will assume that the thickness shall be it and double-riveted : then, by Table 13, the space between rivets = 116 inch, and the diameter of the rivets by col. 3 of Table 14 = 116 inch: hence the pitch = 12 +11€ = 23; the ratio of the area of the punched plate to that of the solid plate 11:23, or 21 : 38 = -553. The apparent strength of the metal between rivet-holes in a double-riveted joint of Staffordshire iron 41,800 lbs. by col. 7 of Table 5, hence we have 41800 X •533 = 23115 lbs. per square inch on the solid part of the plate, and as we have 13 square inch of metal per inch run (or id at each side) we obtain 23115 x 13 31783 lbs. bursting strain, or that on the whole of the internal surface of the 27-inch boiler, or 31783 = 27 = 1177 lbs. per square inch; then with Factor 4, we have 1177 : 4 = 294 lbs. safe working pressure per square inch, which is very nearly the actual pressure required, or 300 lbs. (69.) We may now show the effect of erroneously calculating this boiler by the general Table 15, or rather by the rule (65) on which that Table is based, that rule and table being strictly correct for pressures of about 50 lbs. only (61). In our case the rule becomes 54840 x il • 27 = 1397 lbs. per square inch bursting pressure. But by the correct calculation (68) we obtained 1177 lbs. only, the difference being 1397 - 1177 = 1.19, or 19 per cent. ; this difference is due to the circumstance that to avoid leakage with so great a pressure as 300 lbs., the pitch of the rivets was reduced, with the result that the ratio of the metal between holes to the solid plate became •553 with 300-1b. steam, instead of •653 as for 50-lb. steam, by col. 7 of Table 14. It should be observed that both results are equally correct so far as the bursting strains only are concerned ; the danger would be, that the joints having the pitch of rivets, &c., adapted for 50-lb. steam as given by Table 13, would in all probability leak more or less with 300 lbs., and in order to avoid that contingency it is expedient to sacrifice the 19 per cent. of strength involved in the case. (70.) For such very high pressures it would be prudent and perhaps commercially economical to use the best Yorkshire iron, which, as shown by (24), has 25.6 per cent. greater strength than Staffordshire. Say for our 27-inch boiler and 300-1b. strain, we assume the thickness of Yorkshire plate at i inch, for which Table 14 gives z-inch rivets, and Table 13, 11-inch space; hence the pitch : } + 1} 2 inches; the ratio of punched to solid plate 1} = 2, or 9 - 16 = .563. The apparent strength of metal between rivet-holes in double-riveted joints of Yorkshire iron 52,503 lbs. per square inch by col. 3 of Table 5; hence 52503 X •563 29592 lbs. per square inch on the solid part of the plate, and as we have 1-square inch of metal per inch run (namely at each side), we obtain 29592 x 1} = 33291 lbs. the bursting strain, or that on the whole of the internal surface of the 27-inch boiler, or 33291 · 27 = 1233 lbs. per square inch. Then with Factor 4 we have 1233 - 4 = 308 lbs. per square inch safe working pressure : by substituting Yorkshire plates for Staffordshire we have thus reduced the thickness from 11 to 1, and the weight from 1.0 to 9 - 11 = .82, or 100 – 82 = 18 per cent. The effect of substituting steel for wrought-iron plate is shown by (76) (71.) “Longitudinal Strain on Boilers."--There are two distinct strains to which an ordinary cylindrical boiler is subjected, one acting circumferentially and the other longitudinally: the former alone is considered in the various rules and tables we have so far given; we have now to investigate the latter. Say we take a plain cylindrical boiler with either hemispherical or flat ends, but without any internal flue, finch thick, 48 inches internal, therefore 48 inches external diameter. Taking the apparent strength of single-riveted Staffordshire plates at 22,400 lbs. per square inch on the solid part of the plate, as in col. 8 of Table 14 and (62), the bursting pressure circumferentially = 22400 x x 2 = 48 = 350 lbs. per square inch, or the same as given by Table 15. To find the strain on the two ends we have the area of 483 = 1868, and of 48 = 1809; hence the area of the annulus = 1868 – 1809 = 59 square inches, giving a total pressure of 22400 x 59 = 1321600 lbs. on the ends, and the internal area being 1809, we have 1321600 - 1809 = 730 lbs. per square inch bursting pressure longitudinally, or about double the circumferential bursting pressure, which we found to be 350 lbs. Applying this reasoning to other diameters and thicknesses, it will be found that the ratio between the two strains is constant for all sizes ; hence when a boiler is on the point of rupture circumferentially with the pressure given by the rules in this work, the longitudinal strain is only half the breaking weight in that direction. In an ordinary Cornish boiler with one or two internal flues the longitudinal bursting pressure will be still greater, the flues adding greatly to the strength. (72.) It is shown in (62) that with a single-riveted joint the strain on the solid part of the plate, when the joint is breaking through the rivet-holes, is 10 tons only, or half the normal strength of the iron, so that half the strength is lost. In order to avoid this loss, it has been proposed to roll the plates with extra thickness at the edges, as in Fig. 21: for example, if the thickness of the body of the plate at A is half that at the edge B, then when the metal between rivet-holes is breaking, the strain at A would become 20 tons per square inch, and the full strength of the iron would be utilised. Here, however, a difficulty seems to arise : the extra thickness at the edges could be |