COLUMNS AND STRUCTURES 247 



but in no case is the maximum stress permitted to exceed that 

 fixed in the ordinance, 14,000 for steel; 10,000 for wrought iron; 

 and 10,000 for cast iron. For steel columns filled with, and en- 

 cased in, concrete extending at least three inches beyond the 

 outer edge of the steel, where the steel is calculated to carry the 

 entire live and dead load, the allowable stress per square inch on 

 the steel is determined by the following formula, 



/ = 18,000 - 70- Z , 



but cannot exceed 16,000 Ibs. 



The student is referred to the following pages in the standard 

 steel handbooks: Carnegie (1913), 251 to 282 incl., 327 to 329 

 inrl. Cambria (1914), 192 to 276 incl., 394-5. Jones & Laugh- 

 lin (1916), 176 to 217 incl., 281 to 283 incl. Lackawanna (1915), 

 205 to 288 incl., Bethlehem (1911), 8, 43 to 55 incl., 70 to 87 incl., 

 97 and 98. In addition to the information contained on the 

 pages mentioned there are tables of the radius of gyration of 

 pieces having different shapes and of pieces in combination, 

 such as angles back to back, etc. 



In Fig. 162 the curves show the allowable fiber stresses per- 

 mitted in the larger American cities and given in various steel 

 handbooks, etc. Some of the curves are for modifications of the 

 original Rankine formula with the theoretically correct curve 

 according to that formula. Others give values according to 

 various straight-line formulas. Speaking generally the first figure 

 in the straight-line formula gives a fair idea of the factor of safety 

 intended by the man responsible for the expression. Assuming 

 a maximum strength of 64,000 Ibs. per sq. in. for structural grade 

 steel, the factor of safety when the formula starts with 16,000 

 Ibs. is 4; for 19,200 Ibs. it is 3.333, etc. This is modified again 

 by the slope of the curve (even straight lines being called curves 

 in graphical work). Notice that there is a top limit when the 

 curve goes horizontally, this being 14,000 Ibs. for Chicago. 



To use the chart determine the ratio of slenderness within 

 which the column length is fixed. Assume a section by trial 

 and determine the radius of gyration in inches. Divide the 

 length in inches by the radius of gyration to obtain the slender- 

 ness ratio which must be within the limit decided upon. If it is 

 past the limit the work must be done over with another assumed 

 section. If the slenderness ratio is within the limit find it at the 



