= 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 × ·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 × 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 × = 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.) (64.) In which For single-riveted joints: P = 44800 x t÷d. diameter in inches; P = the bursting pressure, and = Ρ the safe working pressure in lbs. per square inch-thus in our case, P = 44800 × ÷ 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 × 3 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 x td. Thus in our case, P = 54840 × 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. 467 350 280 233 200 175 621 466 373 311 266 233 207 186 777 583 466 388 333 292 259 233 212 194 :: :: ::: ::: 932 699 559 466 400 350 310 280 254 233 215 200 Bursting Pressure-Double-riveted Joints. 1143 857 686 571 490 428 381 343 312 286 264 245 1333 1000 801 666 571 500 444 400, 363 333 308 286 267 250 1142 915 762 653 571 508 457 415 381 352 324 305 286 1030 857, 734 643 571 514 467 428 396 367 343 321 952 816 714 635 571 519 476 439 408 381 357 898 785 698 628 571 524 483 449 419 393 857 762 685 624 571 527 490 457 428 Working Pressure-Single-riveted Joints: Factor 6. 78 58 47 39 33 29 155 117 93 78 67 ::: 104 78 62 52 45 39 35 31 130 97 78 65 56 43 39 140 117 100 32 42 39 36 50 45 42 39 34 39 78 70 64 58 54 50 47 44 182 136 109 91 78 155 124 104 89 78 69 62 57 52 48 45 (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). 16 : 16 = 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 1 and double-riveted: then, by Table 13, the space between rivets 11 inch, and the diameter of the rivets by col. 3 of Table 14 1 inch hence the pitch = 1% +116 = 1% +1% = 23; the ratio of the area of the punched plate to that of the solid plate = 1,424, or 2138553. 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 at each side) we obtain 23115 × 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 × 11÷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-lb. 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. = iron = = 16 (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-lb. strain, we assume the thickness of Yorkshire plate at inch, for which Table 14 gives 3-inch rivets, and Table 13, 14-inch space; hence the pitch } + 12 inches; the ratio of punched to solid plate 12, or 916·563. The apparent strength of metal between rivet-holes in double-riveted joints of Yorkshire 52,503 lbs. per square inch by col. 3 of Table 5; hence 52503 × 563 = 29592 lbs. per square inch on the solid part of the plate, and as we have 11-square inch of metal per inch run (namely at each side), we obtain 29592 × 11 33291 lbs. the bursting strain, or that on the whole of the internal surface of the 27-inch boiler, or 3329127 = 1233 lbs. per square inch. Then with Factor 4 we have 12334 308 lbs. per square inch safe working pressure: by substituting Yorkshire plates for Staffordshire we have thus reduced the thickness from 1 to 1, and the weight from 10 to 911 ·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, inch 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 3 x 248 350 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 × 59 = 1321600 lbs. on the ends, and the internal area being 1809, we have 13216001809 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 |