= = bursting pressure; with 6 for the Factor of safety (78) we obtain 607 - 6 = say 100 lbs. per square inch, safe or working pressure. From this we have the general rules : (58.) For welded boilers: P = 58200 xt; d. (59.) p = 9700 xt; d. In which t = 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 for the 24-inch boiler we have considered, the rule gives 9700 x = 24 = 101, say 100 lbs. per square inch working pressure, as before. (60.) “Steam-boilers with Riveted Joints.”—Staffordshire plates are now so extensively used for boilers, that it will be expedient to take them as a basis for general rules, although, as shown by Table 5, their strength is inferior to the mean of British plateiron, and still more inferior to Yorkshire iron. We have shown in (44) that the pitch of rivets, and thereby the general proportions of joints in steam-boilers, is governed by the pressure of steam as affecting the tendency to leakage, irrespective of strength to resist bursting. (61.) For the purpose of fixing general proportions, we may take as a “standard” case the working pressure of 50 lbs. per square inch, the proportions due to which will suffice for all lower pressures; and also with sufficient accuracy for practical purposes up to say 70 or 80 lbs. per square inch. The proportions for higher pressures should be found by special calculation (68) (76). We have first to find the space between rivet-holes with the different thicknesses of plate for 50-1b. steam by Table 13; taking the nearest pressures in that Table we obtain col. 6 in Table 14. Thus, for 3-inch plate we have for 50-lb. steam the space 118; Table 14 gives it rivets, as in col. 3 ; hence the pitch = 1 + 11 = 2 inches, col. 4; the ratio of 16 +1 the metal between holes to the solid part of the plate = 11: 2, or 21 ; 32 = .656, as in col. 7. The apparent strength in single-riveted joints of Staffordshire plates being 34,110 lbs. per square inch by col. 7 of Table 5, that on the solid part of the plate 31110 x 656 22380 lbs., as in col. 8 of Table 14. 6 - TABLE 14.-Of the PROPORTIONS of RIVETED JOINTA in WROUGHT-IRON PLATES, for Steam-boilers, with 50-lb. Steam. Double Riveted. Diameter of Strain on Solid Part of Plate', in Los per Square Inch. Thickness. Pitch. Space Working Ratio of to Un. Plate. Single By Practical Sizes. Single Double Lap. Between 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 -inch plate, and for the purposes of calculation say 1 inch long. Now as we have 3 x 1 inch at each side, this is evidently equal to 1 square inch area of metal taken through the solid part of the plate, the reduced resistance of which in a singleriveted joint = 22400 x i = 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 xt; 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 44800 x 3 = 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 i 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 t = d. (66.) p = 9140 xt; d. Thus in our case, P = 54840 x = 48 = 428 lbs. per square inch bursting pressure. case, P 2 TABLE 15.–Of the STRENGTH of CYLINDRICAL BOILERS made of STAFFORDSHIRE PLATES with RIVETED Joints, for internal Pressures in Pounds per Square Inch. .. Bursting Pressure-Single-riveted Joints. 621 466 373 311 266 233 207 186 777 583 466 388 333 292 259 233 212 194 32 699 559 466 400 350 310 280 251 233 215 200 1090 816 652 54 466 408 362 326 297 272 251 233 218 204 932 746 621 533 466 414 373 339 310 287 267 249 233 839 700 600 524 466 419 381 350 322 300 280 262 : : : 15 Bursting Pressure-Double-riveted Joints. 1143 857 686 571 490 428 381 343 312 286 264 245 1112 915 762 653 571 508 457 415 381 352 324 305 286 M 1030 857 734 613 571 514 467 428 396 367 313 321 952 816 714 635 571 519 476 439 408 381 357 898 785 698 628 571 524 483 449 419 393 857 762 685 624 571 527 490 457 428 : : : : : :::: .. (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 = 1 inch, and the diameter of the rivets by col. 3 of Table 14 lit inch: hence the pitch 116 +11o 23; the ratio of the area of the punched plato to that of the solid plate = 14--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 1 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 54810 x id = 27 1397 lbs. per square inch bursting pressure. But by the correct calculation (68) we |