COLUMNS AND STRUCTURES 245 



The recommended factors of safety were as follows: 10 for 

 timber; 5 for metal under moving load; 4 for metal under quies- 



cent load. The constants were for ratios of - between 20 and 200, 



and are, therefore, not reliable for longer columns. 



The Chicago building ordinance limits the extreme length of 

 cast iron columns to 70 times the least radius of gyration. The 

 length of rolled steel compression members cannot exceed 120 

 times the least radius of gyration, but the limiting ratio of struts 

 for wind bracing may be 150 times the least radius of gyration. 

 See some of the specifications recommended for study and com- 

 pare them with the provisions above quoted. 



Radius of Gyration 



The radius of gyration was once humorously referred to as a 

 happy thought in terminology as it is not a radius and has noth- 

 ing to do with gyration. It is a term used by mathematicians 

 and students of mechanics of materials to describe a factor used 

 in the design of compression members in structures. It is ac- 

 tually the square root of the moment of inertia of a section divided 

 by the area, or, 



in which r = radius of gyration, 

 I = moment of inertia, 

 A = area of section. 



The moment of inertia and the area being in inches, the radius 

 of gyration is in inches. 



The would-be humorist was wrong in his statement, for the 

 radius of gyration may be shown to be a radius and it has actually 

 to do with gyration. 



Each cross section has two radii of gyration, one perpendicular 

 to the axis // and the other perpendicular to the axis x. In using 

 a formula the least radius is chosen, except when it may be safe 

 to use the greater. Assume that the mass rotates (bends) about 

 the given axis. If the column bends, some resistance will be 

 offered by the section, which is assumed to be a mass moved by 

 the rotation (bending) of the column about the axis chosen. 



Assuming the section to be a rotating body, there is some kinetic 

 energy developed, and in order to find the amount it is first neces- 



