'TABLE IV. Experiments on Pieces of Timler 7.462 inches square, supposing the absolute Strength 57.85. 220:32 2.931 ? 28,2427 8.528 134 59.82 54.88 (28,026 217.62 2.664 28,243 52.92 26,927 245.16 3.286 27,599 9:594 153 58.59 53:04 24,260 5174 23,656 249.00 3.109 123,652 $ 274:32 2.753 21,2221 10.660 174 57.60 51.43 s 18,144 12.792 204 58.80 51:41 | 16,794 325.08 3:553 17,633 50:49 17,318 379.08 4:441 14,688 14.924 57.85 49.21 13,878 379.08 3.997 14,472 | 19:21 14,470 438.48 5.152 s 11,988 17.056 27 56.94 47.07 435.24 12,098 47.98 12,343 5:596 | 11,772 491.32 5.863 s 10,106 19:188 309 56.69 45:49 491.32 10,424 46.76 10,693 6.218 110,152 545.40 8.350 Š 8,914 21•320 343 57.09 44.74 9,208 45:51 9,207 540.00 9.060 8,640 (20,944 } 21,169 51-68 21,246 24 TABLE V. Experiments on Picccs of Timber 8.528 inches square, supposing the absolute Strength 55.08. s 30,024 30,148 49*68 30,363 129,916 428.76 3•198 12.792 18 s 25,812 56:35 49.87 | 427.14 3.109 25,540 | 48.60 24,883 24,840 497.88 4.0861 s 21,6541 14.924 21 56.78 49.23 | 495.72 3.375 21,605 | 47.52 20,854 21,060 570-24 5.107 s 18,1441 17.056 24 55:42 46.78 | 565.92 6:129 17,117 17,968 : 46-4 17,833 | 641.52 4.797 19.188 14,580 27 52:42 42.70 639.64 4.352 13,932 14,577 45:36 115,482 1717:12 7.995 $ 11,717 21.320 30 54.10 43.30 1712.80 | 6:396 13,303 44.28 13,593 | 13,176 ] 1614. The five preceding tables give a view of the results of experiments by Buffon upon beams 4.264,5.330, 6.396, 7:462, and 8·528 inches square, of different lengths, as compared with those found by the modified rule above given (1660.). 1615. The first column shows the length of the pieces in English feet. The second, the proportion of their depth to their length. The third, the weight of each piece in pounds aroirdupois. The fourth, the curvature before breaking. The fifth, the absolute or primitive strengtlı, that is, independent of the length. The sixth, that strength reduced in the ratio of the proportion of the depth to the length of the pieces given in the second column. The seventh column gives the weight borne before breaking, independent of their own weight. The eighth, the mean effort with which the pieces broke, including half their weight, the other half acting on the points of support. The ninth shows the reduced strength of the pieces in respect of the proportions of the depth to the length, supposing the primitive strength equal for all the pieces in the same table. The tenth column gives the result of the calculation according to the rule above given. 1616. In order to give an idea of the method of representing the strength of wood of the same scantling, but of different lengths, by the ordinates of a curve, we annex fig. 613. to explain by it the result of the experiments of Buffon, given in the second table. The ordinates of the polygon N, 0, P, Q, &c. represent the results of the experiments made upon beams 5.330 in. square, of different lengths, whose primitive strength varied in each piece. 1617. The ordinates of the regular curve, m, l, i, h, g, f, e, d, c, b, Z, show the results of the cal. culation according to the rule, taking the same primitive strength for each piece. 1618. After what has been said in a preceding page, it is easy to conceive that the primitive unequal strengths would forin an irregular polygon, whereof each point would answer to a different curve; whilst, supposing the same primitive strength to belong to each piece, there should be an agreement between the strengths and scantlings which constitute a regular curve. 1619. Thus it is to be observed that the points 0 and P of the regular polygon only vary from the regular curve, m, l, k, i, &c., because the ordinate LO is the product of a primitive strength diminished by the mean primitive strength which produced the ordinate of the curve KP. Hence the point P is above the properly correspondent point k. 1620. For the same reason, the point c is above its corresponding point X, because the relative ordinate Cc is the product of a primitive strength greater than the mean which produced the point X. Fig. 613 1621. Referring to the second table, we find that the primitive strength answering to the point O is but 60-76, and the value of the ordinate LO 2502, whilst that of the point P is 68.34, and the value of the ordinate KP 3364; and as the ordinates Ll and Kk corresponding to the curve are calculated upon the same primitive strength of 64.36, which for Ll gives 2726, and for KP 3092: it follows that, in considering all these quantities as equal parts of a similar scale, the point P of the polygon should be (3364–3092=) 272 of these parts above the corresponding point k of the curve, and the point 0 224 of those parts (2726 —2502) below the point l. 1622. To render the researches made, available and useful, the table which follows has been calculated so as to exhibit the greatest strength of beams from pieces 3:198 in. square, up to 19:188 in. by 26 •65 in. The first column contains the length of each piece in English feet. The second column, the proportion of the depth to the length; and The third, the greatest strength of each piece in pounds avoirdupois. The table is for oak; and it is to be recollected that the weight is supposed to be concentred in the middle of the bearing of the beams, and hence double what it would be if distributed over the whole length of each piece. Experience, as well as investigation of the experiments, shows, that in order to resist all the efforts and strains which, in practice, timber has to encounter, the weight with which it is loaded ought to be very much less than its breaking weight, and that it ought not to be more than one tenth of what is given as the breaking weight in the following table, beyond which it would not be safe to trust it. The abstraction of the last figure on the right hand, therefore, gives the practicable strength by simple inspection. In a subscquent page, the reduction of the strength of oak to fir, which is in more general use in this country, will be introduced, so as to make the table of more general utility. TABLE VI. Showing the greatest Strength of Oak Timber lying horizontally, in pounds avoirdupois. Length of Propor: Breaking Length of Propor: Breaking Length of Propor- Breaking each Piece tion of Weight in each Piece tion of Weight in each Piece tion of Weight in In English Depth to lbs. avoir in English Depth to lbs.avoir in English Depth to lbs.avoir Feet. Length, dupois. Feet. Length. dupois. Feet. Length. dupois. 2.132 2.842 3.553 4.264 4.974 5.685 6996 7.106 7.817 8.528 9.238 9.949 10.660 14 16 18 20 16326 3:198 6 8 10 12 14 16 18 20 22 24 26 28 30 24489 3.553 4.441 5.330 6.218 7.106 7.994 8.883 9.771 10.66 11:55 12:44 13.32 8 10 12 14 16 18 20 22 24 26 28 30 16224 12730 10469 8856 7645 6702 5951 5399 4820 4996 4013 3766 22 14.924 2107 15.990 24 26 28 30 5.685 7.106 8:528 9.949 11.37 12.79 14.21 15.63 17 06 18.48 19.90 21:32 8 10 12 14 16 18 20 22242 25460 21942 17713 15291 13410 11902 10677 9562 8772 8026 7480 7.106 8.528 9.949 11:37 12.79 14.21 15.63 17.06 18.48 19.90 21:32 16 18 20 22 24 26 28 90 92225 26174 22141 19106 16757 14877 13338 12057 10965 10053 9225 5.218 7.462 8.705 9.949 11:19 12:44 13.68 14.92 16:17 17.41 1865 14 16 18 20 22 24 26 28 30 33400 27482 23244 20067 17596 15321 13986 12652 11572 10534 9668 22 24 6.396 in. by 8.528 in. 10 12 14 16 18 10 12 14 16 18 20 7.994 9.594 11.19 12.79 14.39 15.99 17:59 19.19 20.78 22:39 23.98 35803 29445 24919 21493 18853 167:37 15002 13556 12336 11287 10378 7:106 8.528 9.949 11.37 12.79 14.21 15.63 17.06 18.48 19.90 21:32 22 24 24 28 30 5.330 inches square. 5.330 in, by S.594 in. 10 12 14 16 4.441 5.330 6.218 7.106 7.99.1 8.863 9.771 10.66 11.55 12.44 13.32 19890 20 38158 28 28 30 Length of Propor. Breaking | Length of Propor. Breaking Length of Propor. Breaking each Piece tion of Weight in cach Piece tion of Weight in each Piece tion of Weight in in English Depth to Ibs.avoir- in English Depth to Ibs.avoir- in English Depth to Ibs.avoir Feet. Length. dupois. Feet. Length. dupois. Feet. Length. dupois. 7.106 8.528 9.949 11:37 12.79 14.21 15.63 17.06 18.48 19.90 21.32 7.462 in. by 10-66 in. 50921 41878 35426 30581 26812 23803 21 342 19280 17345 16051 14760 24 10.66 12.79 14.92 17.06 19:19 21.32 23:45 25.58 27.72 29.85 31.98 10 12 14 16 18 20 22 24 26 28 30 57285 47083 37854 34404 30164 26719 24003 21689 19377 18060 16000 8.983 10.66 19:44 14.21 15.99 17.77 19:54 21.32 23:10 24.97 26.65 10 12 14 16 18 20 22 24 26 29 30 55738 45804 38757 33449 29226 26142 23925 21087 19139 17557 16144 26 28 30 8.528 in. by 9.594 in. 7.994 9.594 11.19 10 12 14 57285 47093 39854 1 |