. Strength of materials: a practical manual of scientific methods of locating and determining stresses and calculating the required strength and dimensions of building materials . is, if the ratio I ^ r for a steel column with hinged end, for example, isless than 160, we must use the straight-line formula to compute its safe load,factor of safety, etc.; but if the ratio is greater than 100, we must use Eulersformula. For castir^on columns with flat ends, S = 34,(XX1, and in = SS: and sincethey should never be used slender, there is no use of Eulers formula forcast iron columns. The li
. Strength of materials: a practical manual of scientific methods of locating and determining stresses and calculating the required strength and dimensions of building materials . is, if the ratio I ^ r for a steel column with hinged end, for example, isless than 160, we must use the straight-line formula to compute its safe load,factor of safety, etc.; but if the ratio is greater than 100, we must use Eulersformula. For castir^on columns with flat ends, S = 34,(XX1, and in = SS: and sincethey should never be used slender, there is no use of Eulers formula forcast iron columns. The line AB, Fig. 50, represents Johnsons straight-line for-mula; and BC, Eulers forimila. It will be noticed that the twolines are tangent; the point of tangiMUv corresponds to the •lini-iting value / -:- v, as indicated in the table. I. A lO-ponnd Kl-ineh .Ueel 1 beam eoluinn 8 98 STRENGTH OF MATERIALS feet long sustains a load of 100,000 pounds, and the ends are its factor of safety according to the methods of thisarticle. The first thing to do is to compute the ratio I -^ r for thecolumn, to ascertain whether the straight-line formula or Eulers. lOO 200 300 Fig. 50. formula should be used. From Table C, on page 72, we find thatthe moment of inertia of the column about the neutral axis ofits cross-section is 1).50 inches*, and the area of the section square inches. Hence r = Since I 8 feet = 90 inchesI 96 = ; ovr inch. r = 106^ This value of ^ -^ ^ is less than the limiting value (195) indicatedby the table for steel columns with flat ends (Table E, p. 97j, andwe should therefore use the straight-line formula; hence 7 = 52,500 180 X 106-^ or. (52,500- 180 X 106^;:^) == 391,600pounds. This is the breaking load for the column according to the straight-line formula; hence the factor of safety is 391,600 ^ g g 100,000 STKEl^GTH OF MATEEIALS 99 2. Suppose that the length of the colunin desci-ibed in thepreceding
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