104 RESISTANCE OF MATERIALS 



Hence the equivalent stress in the column is 



f . = ^J?xl.36 = 3470 lb./in.' 

 Also, the bending stress, produced by the eccentricity of the load, is 



Consequently, by this method, the total stress in the column is 

 found to be 3470 + 292 8 = 6398 lb./in. 2 



If a formula of the Rankine-Gordon type is used, namely, 

 P ' 9 



the equivalent stress p e in the column, due to the given load P, is 



''A 



where u c denotes the ultimate compressive strength of the material, 

 as above. 



APPLICATIONS 



166. A solid, round, cast-iron column with flat ends is 15 ft. long and 6 in. in 

 diameter. What load may be expected to cause rupture ? 



167. A square wooden post 12 ft. long is required to support a load of 15 tons. 

 With a factor of safety of 10, what must be the size of the post ? 



168. Two 8-in. steel I-beams, weighing 25.25 lb./ft., are joined by latticework 

 to form a column 25 ft. long. How far apart must the beams be placed, center to 

 center, in order that the column shall be of equal strength to resist buckling in 

 either axial plane ? 



169. Four medium steel angles, 5 x 3 x | in., have their 3-in. legs riveted to a 

 |-in. plate so as to form an I-shaped built column. How wide must the plate be in 

 order that the column shall be of equal strength to resist buckling in either axial 

 plane ? 



170. A hollow wrought-iron column with flat ends is 20 ft. long, 7 in. internal 

 diameter, and 10 in. external diameter. Calculate its ultimate strength by Rankine's 

 and Johnson's formulas and compare the results. 



171. Compute the ultimate strength of the built column in problem 168 by 

 Rankine's and by Johnson's formulas and compare the results. 



172. Compute the ultimate strength of the column in problem 169 by Rankine's 

 and by Johnson's straight-line formulas and compare the results. 



