166 



STRENGTH OF MATERIALS 



a point on this line. Then if a new force diagram is drawn with 0' 

 as pole, the corresponding equilibrium polygon starting at J/ will pass 

 through N. 



134. 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. 123). 



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 E l and R^ as AH and 

 HE respectively. 



Now if the equilibrium polygon is to pass through N, the pole of 

 the force diagram must lie somewhere on a line HK drawn through 



FIG. 123 



H parallel to MN, as explained in the preceding article. The next 

 step, therefore, is to determine the position of the pole on this line 

 HK, so that the equilibrium polygon through M and N shall also pass 

 through L. This is done by drawing a vertical Z/A' thrnu^li L and 

 treating the points M and L exactly as M and N were treated. Thus 

 OABCD is the force diagram for this portion of the original figure, and 

 MA'B'C'S is the corresponding equilibrium polygon, the reactions 

 for this partial figure being AH' and H'D. If, then, the equilibrium 

 polygon is to pass through L, its closing side must be the lino 

 ML, and consequently the pole of the force diagram must lie on a 

 line H'K' drawn through H' parallel to ML. The pole is therefore 

 completely determined as the intersection O 1 of the lines 11 K and 

 H K . If, then, a new force diagram is drawn with 0' as pole, the 



