IO4 TOWERS AND TANKS fOR WATER-WORKS. 



ing to the applied load, and deflecting laterally ; the longer 

 the column the greater the tendency to this lateral deflection 

 or bending, and the greater the stresses upon the fibres of the 

 concave side. The combined stress is very complex and 

 difficult of demonstration, but it is pretty well established that 

 the stress produced by such deflection increases directly as the 

 square of the length of the beam. 



In the discussion of columns, a quantity called the " radius 

 of gyration " of the cross-section is an important factor in cal- 

 culations, and, in the determination of the strength of a 

 column or strut, represents the effect of the form of the 

 column which is expressed by the square of the radius of 

 gyration, or the moment of inertia of the section divided by its 



I-r* 

 area, or - - - . 



A 



Radius of Gyration. In the discussion of columns, a quantity 

 called the "radius of gyration" is an important factor in the 

 determination of the strength of columns to resist the applied 

 stresses. This quantity has been denned as . " that quantity 

 whose square is equal to the moment of inertia of the cross- 

 section divided by its area, or 



is the expression by which r 2 is to be computed. 



" It should be observed that r has no connection with gyra- 

 tion, as / has no connection with inertia, in the case of sections 

 of beams and columns. 



" Radius of gyration is merely a technical name, which has 

 unfortunately come into use, to denote the square root of the 



quantity -7." 



In the numerous publications by the larger steel manufac- 

 tories, the radius of gyration, the moment of inertia, and the other 

 elements of standard shapes have been conveniently tabulated 



