Cyclopedia of architecture, carpentry, and building : a general reference work . d, is, if the ratio l-^ r for a steel column with hinged end, for example, isless than 160, we must use the straight-line formula to campute its safe load,factor of safety, etc.; but if the ratio is greater than 160, we must use Eulersformula. For cast-iron columns with flat ends, S = 34,000, and in = 88; 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 formula. It will be
Cyclopedia of architecture, carpentry, and building : a general reference work . d, is, if the ratio l-^ r for a steel column with hinged end, for example, isless than 160, we must use the straight-line formula to campute its safe load,factor of safety, etc.; but if the ratio is greater than 160, we must use Eulersformula. For cast-iron columns with flat ends, S = 34,000, and in = 88; 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 formula. It will be noticed that the twolines are tangent; the point of tangency corresponds to the lim-iting value Z -^ 7, as indicated in the table. Examples. 1. A 40-pound lO-in-^h steel I-beam column 8 107 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 Z -f- ?• 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 inches*, and the area of the section square inches. Hence 7 = (3 = ; or r = inch. Since 1 = 8 feet = 96 inches,^ _ 96 _ 2106^ This value oi I -^ r 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 jp^ = 52,500 - 180 X 106-^; or, P = (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 391,600 100,000 = 108 STRENGTH OF MATERIALS 99 2. Suppose that the length of the column described in thepreceding example were 16 feet. What would its factor of safety be? Since I := IQ feet = 192 inches; and
Size: 2454px × 1018px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bo, bookcentury1900, booksubjectarchitecture, booksubjectbuilding
