SIMPLE STRUCTURES 



183 



polygon is to pass through both M and N, its closing side must 

 coincide with the line MN, and therefore the pole of the force dia- 

 gram must lie somewhere on a line through H parallel to MN. 



FIG. 121 



Let 0' be any point on this line. Then, if a new force diagram is 

 drawn with 0' as pole, the corresponding equilibrium polygon 

 starting at M will pass through N. 



112. Equilibrium polygon through three given points. Let it be 

 required to pass an equilibrium polygon through three given points, 

 say M, N, and L (Fig. 122). 



A 



Fig. 122 



As in the preceding article, a trial force diagram is first drawn 

 with any point as pole, and the corresponding equilibrium polygon 

 constructed, thus determining the reactions R^ and R 2 as HA and 

 EH respectively. 



