the reduced breaking weight, as in col. 8, showing an error of 6081060075 = 1·012, or + 1.2 per cent., as in col. 9, &c. (224) The sum of all the + errors in col. 9 is 225 6, and of all the errors, 243.2, giving on the thirty-six experiments an average of (243 2-225 6)36 0.461, or 0.461 per cent. (243·2-225·6) only. It will also be observed that the range of the error plus and minus is nearly equalized, the greatest +30 4, and the greatest = error is 33.0 (959). error being (225.) "Square Pillars of Wrought Iron."-Admitting that for wrought iron, the ratio of the strength of round and square pillars is 1.0 to 1.7, as shown by theory, we obtain the values of Mp given for square pillars by Table 34. The rules in (196) then require a simple modification, and become :— In which S = the side of the square, and the rest as in (196). Say that we have a pillar 14 inch square, 5 feet long, with both ends pointed; then taking Mp from Table 34 at 72.74 tons, and 1436 from Table 35 2.2, the rule becomes 72-74 × 2.2 256.703 tons = F, or the breaking weight by flexure. This result will not require correction for incipient crushing: thus the area is 1.25 x 1.25 crushing strength being 19 tons 1.5625 × 19 29.69 tons, and = 1.5625 square inches, and the per square inch, Cp becomes 7.425 tons, and as F CP = is less than that (169) the correction is not required. For hollow square pillars of wrought iron the rules become : In which S the side of square externally, and 8, internally; the rest being as in (222). Thus for a pillar in which S = = 4 inches, 8 3 inches, L = 11 feet, both ends flat, we have 223 × (436 — 346) ÷ 112, or 223 × (147 - 90·9) ÷ 121 = 103.5 tons F. Correcting for incipient crushing (164), the area of the section being 4.75 square inches, Cp becomes 4.75 x 19 = 90.25 tons, Cp 67.69 tons, hence Pc = (103.5 × 90·25) ÷ (103·5 + 67·69) = 54.56 tons breaking weight. = With thin plates of wrought iron correction is required for incipient "Wrinkling" (249) rather than incipient crushing: in our case, however, the wrinkling strain is (√√25÷÷√√4) × 80, or (52) × 80 20 tons per square inch, which being in excess of 19 tons, the crushing strength of wrought iron in pillars (201), the strength is governed by the latter. = (233.) "Rectangular Pillars of Wrought Iron."-For rectangular sections, other than square, the rules for square pillars are modified, and we have: In which the letters have the same signification as in (177), namely F the breaking weight by flexure in lbs., tons, &c., dependent on the value of Mp as given by Table 34, t = the thickness or least dimension of the rectangular pillar, the 2.6 power of which is given by col. 3 of Table 35; b dimension, and L = length in feet, &c. = the greatest (239.) Table 53 gives the results of twenty-one experiments on solid rectangular pillars of wrought iron by Mr. Hodgkinson; col. 9 has been calculated by the rule (234), the value of Mp for rectangular pillars with both ends flat being taken at 498,500, or say 500,000 lbs., from Table 34. Thus taking No. 9 as an example, to find 6, the logarithm of 995 or 1.9978 × 2.6 = 1.99428, the natural number due to which, or 9869, is the 2.6 power of t, and 7.52 being = 56.25, the rule becomes 500000 = X 9869 x 5.86 56.25 = 51410 lbs. = F, or the breaking weight by flexure, as in col. 9. We shall find that this does not require correction for incipient crushing; the area of the section is 5.86 × ⚫995 = 5.8307 square inches, and the crushing strength being 19 tons or 42,560 lbs. per square inch (201), Cp becomes 42560 × 5·8307 248100 lbs., as in col. 8, therefore Cp 62025, and as F is less that, namely 51,410 lbs., the correction is not required (164). The experimental breaking weight was 54,114 lbs., as in col. 5, hence we have 51410 ÷ 54114 = 95, showing a difference or error of 5 per cent., as in col. 7. TABLE 53.-Of the STRENGTH of RECTANGULAR, SOLID PILLARS of WROUGHT IRON, both ends Flat. |