and d = the internal diameter, and the rest being as before, we have the rules: (157.) (158.) (159.) - It should be clearly understood, that these rules give the breaking load of long flexible pillars, or those whose length is so great in proportion to their diameter, that they will fail by bending simply. Short pillars require correction for "Incipient Crushing," as explained and illustrated more fully in (163). (160.) Tables 35, 36 give the 3.6 and 1.7 powers of numbers to facilitate calculations of the strength of solid and hollow pillars of cast iron, wrought iron, and steel:-Thus, say we TABLE 36. Of the 1·7 PoWER of NUMBERS for CALCULATING the STRENGTH of PILLARS. of CAST IRON, the ends being Flat and well supported by Iron cast on both ends. 12.7 12.7 10.6 10.6 19 419 4 16.2 16.2 28 4 28 4 23.8 23.8 40.0 40.0 33.6 33.6 55.0 55.0 46.0 46.0 42 0.42 0 35.2 35.2 67-062.3 56.0 54.8 ::: ::: Reduced. .. 33.8 33.8 ::: : : : :: ::: ::: 41 341 3 31 631 6 25 325 3 99-084 3 83.0 75.1 60 7.60.7 46.946.9 37.6 37.6 ::: Reduced. ::: ::: :::::: ::: ::: ::: 140 110 181 151 152 118 99.2 87.080.7 66.0 66 0 53 2 53.2 133 112 0 108 86.086 0 68.6 68.6 117 103 89.0 85.8 71.871.8 190 136 159 125 ::: ::: ::: 1224 1654 1551 1427 689 1050 610 802 537 323 255 264 225 222 201 372 296 304 261 253 232 457 371 372 326 310 288 524 380 427 339 356, 303 438 379 608 501 507 446 have a cast-iron pillar 6 inches diameter externally, and 5 inches internally, therefore inch thick, and 14 feet long, with both ends flat. = From Table 34 the value of Mp = 44.19, say 44 tons; from Table 35, col. 4, the value of 63.6 = 633, and of 536 = 328; from Table 36 we obtain 88.8, say 89, for the value of L1 or 147. Then the breaking weight by flexure by rule (157) becomes 44 x (633328)89 151 tons, which being due to flexure only, will require correction for incipient crushing as shown by (168). Table 37 gives the breaking weight of solid and hollow pillars of cast iron from 1 to 12 inches diameter, and from 5 to 20 feet long, calculated in the way we have illustrated, the result being there entered as due to flexure, which is corrected for incipient crushing in the next column when necessary. The breaking weight due to flexure is thus given separately in order to adapt the table to conditions other than those where the pillar is flat at both ends: thus, the pillar which we have found to have a strength of 151 tons when both ends were flat, would bear only 151÷3 = 50 tons with both ends rounded, and 50 × 2 = 100 tons when one end is flat, and the other rounded, &c., correction being made for incipient crushing in all cases where necessary (163). (161.) Table 38 gives a selection of all the more important experiments of Mr. Hodgkinson on solid and hollow pillars of cast iron, and in order to show the correctness of the rules in (151), col. 9 has been calculated by them, the value of Mp being taken from Table 34. In col. 7 these results are corrected where necessary for incipient crushing by the method explained in (163), the value of C, or the crushing strain being taken at 49 tons, or 109,760 lbs. per square inch, this being the strength of the particular iron used by Mr. Hodgkinson, as found by him from direct experiment. The mean crushing strength of British cast-iron is 43 tons, as shown in (132), and this value should be used in ordinary cases. In col. 8 we have given the error or difference between the calculated and experimental results:-the sum of all the + errors is 163, and of all the errors, 141.7; hence we have as a general average result of the forty experiments (163 — 141·7) |