GRAPHIC STATICS 



M 



Culmanris Method 

 !_, I of Forces a bout 

 axis M-N 



FIG. 22. 



intercepts will be equal to the intercept G F multiplied by pole distance 

 H'. But the intercepts D, D C, C B, B A, multiplied by the pole 

 distance H equal moments of the forces P lf P 2 , P z , P 4 , respectively, 

 about the axis M N, and the moment of inertia of the system of forces 

 P lf P 2 , P 3 , P 4 , about the axis M N will be equal to the intercept G F 

 multiplied by the product of the two pole distances H and H', and 



I = F G xH x H' 



Mohr's Method. It is required to find the moment of inertia, 

 I, of the system of forces P lf P 2 , P B , P 4 , Fig. 23, about the axis M N. 

 Construct the force polygon (a) with a pole distance H, and draw the 

 equilibrium polygon (b). Now the moment of P x about the axis M N 

 equals intercept F G multiplied by the pole distance H, and the moment 

 of inertia of P^ about the axis M N equals the moment of the moment of 

 P! about the axis, = F G x H x d. But F G x d equals twice the area 

 of the triangle F G A, and we have the moment of inertia of P equal to 

 the area of the triangle F G A x 2 H. In like manner the moment of 

 inertia of P 2 may be shown equal to area of the triangle G H B x 2 H; 

 moment of inertia of P 3 equal to area of the triangle H I G x 2 H; 

 and moment of inertia of P 4 equal to area of the triangle I J D x 2 H. 

 Summing up these values we have the moment of inertia of the sys- 



