HOMOGENEOUS BEAMS 



143 



the radius of gyration and the moment of inertia of a sec- 

 tion, and A the area in square inches, then. 



whence f 



The last column of the table entitled Elements of Usual 

 Sections gives radii of gyration corresponding to the mo- 

 ments of inertia given in the fourth column. 



The radius of gyration of a section, or figure, may be found 

 directly from its moment of inertia by means of the formula 

 just given. For example, the radii of gyration for the 

 rectangle and the hollow square in the table just referred to 

 are found as follows: 



For the rectangle, 



Vl2 



For the hollow square, 



12 

 NEUTRAL AXIS 



If, in a cantilever loaded as shown in Fig. 3, any point x 

 on the center line ab is taken as a center of moments, and a 



FIG. 3 



section made by a vertical plane cd through this center is 

 considered, it will be evident that the moment of the force 

 due to the downward thrust of the load tends to turn the 

 end of the beam to the right of cd around the center x. The 



