138 CONTINUOUS GIKDEBS. [CHAP. TCI. 



A = 9)? -, and join the points thus obtained by two lines cross- 



A> 



ing each other. These cross-lines are the lines OP O E of the 

 force polygon. If now we make U U' and V V equal to the 

 ordinates of the cross-lines vertically under U and V, then the 

 sides of the equilibrium polygon U S and V $ prolonged, pass 

 through U' and V'. This will at once appear from an inspec- 

 tion of Fig. 53. 



In this form the equilibrium polygon was first repre- 

 sented by Mohr. (Zeitschrift des Arch, wnd Ing. Ver. zu 

 Hannover, 1868.) 



S9. Determination of the moments over the Supports. 

 If we draw in the force polygon, lines parallel to the four 

 sides of the second equilibrium polygon, then the segments of 

 the force line between the lines parallel to A U, BV [PI. 15, 

 Fig. 53] and those parallel to S U, S V, are respectively F G = 



\ HI! 1 - and E H = \ M" \. If we prolong S U and S V to 



A A. 2i \ 



intersections M and N with verticals through the supports, and 

 represent A M and B N by y' and y", we have from the simi- 

 larity of the triangles U A M and V B N with O G P and O H E 



hence 



M'? M 



The segments A M and B N are, therefore, proportional to 

 the, moments at the supports M' and M". 



These moments themselves can now be determined in vari- 

 ous ways. 



\st. It is in general best to choose the second pole distance 



b = - \. "We have then 

 6 



M' = y' M" = y" (Art. 70). 



If, then, at a distance from U and V either way equal to 

 we draw verticals, the segments A 4 Mj. and 



O I 



B, Nj cut off from these verticals will evidently be equal to 

 the moments required, viz., M' and M". 



