MOMENT OF INERTIA OF FORCES 



35 



P 2 R 



FIG. 21. 



Moment of Inertia of Forces. The determination of the moment 

 of inertia of forces and areas by graphics is interesting. There 

 are two methods in common use: (i) Culmann's method, in which 

 the moment of inertia of forces is determined by finding the moment 

 of the moment of forces by means of force and equilibrium polygons , 

 and (2) Mohr's method, in which the moment of inertia of forces is 

 determined from the area of the equilibrium polygon. The moment of 

 inertia of a force about a parallel axis is equal to the force multiplied by 

 the square of the distance between the force and the axis. 



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

 /, of the system of forces P lf P 2 , P 3 , P 4 , Fig. 22, about the axis M N. 

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

 the equilibrium polygon abode, and produce the strings until they 

 intersect the axis M N. Now the moment of P 1 about axis M N equals 

 U D x H; moment of P 2 equals D C x H; moment of P 3 equals C B x 

 H; moment of P 4 equals B A x H; and moment of resultant R equals 

 A x H . With intercepts B D, D C, C B, B A, as forces acting in place 

 of P if P 2J P 3t P, respectively, construct force polygon (b) with pole 

 distance H', and draw equilibrium polygon (c). As before the moments 

 of the forces will be equal to the products of the intercepts and pole 

 distance and the moment of the system of forces represented by the 



