MOHR'S METHOD FOR MOMENT OF INERTIA 

 M 



37 



N 



Mohr's Method 

 I of Forces about axis M-N 

 =Area FABGDfxJ-F x2H 



(b) 



FIG. 23. 



tern of forces equal to the area of the equilibrium polygon multiplied 

 by twice the pole distance, H, and 



/ = area F AB C D B J Fx2 H 



To find the radius of gyration, r, we use the formula 



/ = R r 2 



In Fig. 23 the moment of inertia, 7 r , of the resultant of the sys- 

 tem of forces about the axis M N, can in like manner be shown to be 

 equal to area of the triangle F H J x 2 H. 



If the axis M N is made to coincide with the resultant R the mo- 

 ment of inertia I c g of the system will be equal to the area of equi- 

 librium polygon ABCDEx2H. This furnishes a graphic proof for 

 the proposition that the moment of inertia, I, of any system of parallel 

 forces about an axis parallel to the resultant of the system is equal to 

 the moment of inertia, I c g , of the forces about an axis through their 

 centeroid plus the moment of inertia, I rt of their resultant about the 

 given axis. 



I=I c .e. + Rr* 



= Ic. f . + Ir 



It will be seen from the foregoing discussion that the moment of 

 inertia of a system of forces about an axis through the centeroid of the 

 system is a minimum. 



