CAMBKIA STEEL. 181 



PROPERTIES OF COMPOUND SHAPES. 



The moments of inertia, section moduli, and radii of gyration 

 of compound sections used as beams or columns, composed of 

 plates and angles, channels, beams, or any combination of these, 

 may be obtained with the aid of the Tables of Properties as 

 follows: 



The first step is to find the center of gravity of the proposed 

 section, which in the case of symmetrical sections is at the center 

 of the figure 



For unsymmetrical sections the position of the center of 

 gravity may be determined by multiplying the areas of the 

 component parts by the distances of their centers of gravity 

 from any convenient line, taken as an axis, and dividing the sum 

 of these products by the sum of the areas, which will give the 

 distance of the center of gravity of the compound section from 

 the assumed axis. 



The position of the center of gravity for all sizes of angles 

 and channels, is given in the Tables of Properties for these 

 shapes, and is given for various geometrical sections on pages 

 168 to 175 inclusive, in connection with their other properties. 



After determining the position of the center of gravity of a 

 compound section, as explained above, the moment of inertia 

 about an axis through its center of gravity may be found by 

 taking the sum of the moments of inertia of each component 

 part about an axis through its own center of gravity, parallel to 

 the axis of the compound section, and adding thereto the sum 

 of products obtained by multiplying the area of each component 

 part by the square of the distance of its center of gravity from 

 the axis of the compound section. 



Having thus obtained the moment of inertia of the compound 

 section, the section modulus may be obtained by dividing this 

 moment of inertia by the distance from the neutral axis to the 

 most remote extremity of the section. 



The square of the radius of gyration for the compound section 

 may be obtained by dividing the moment of inertia by the total 

 area. 



The moment of inertia of a compound section about any axis 

 other than that through its center of gravity may be found in a 

 manner similar to that above described. 



