SIMPLE STRUCTURES 



187 



say, the horizontal reactions ff l and H 2 will never have more than one 

 half the value they would have if the crane was not counterweighted. 

 2. G-raphical method. To illustrate this method, consider the 

 Pratt truss, shown in Fig. 125. Assume the loads in this case to 

 be the weight of the truss 

 W, a uniform load of 

 amount W^ assumed for 

 present purposes to be 

 concentrated at its cen- 

 ter of gravity, and two 

 concentrated loads P^ P y 

 Since the only other ex- 

 ternal forces acting on the 

 truss are the reactions R^ 

 R z , they must hold the 

 loads in equilibrium, and 

 hence the force polygon 

 must close. The force 

 polygon, however, con- 

 sists in the present case 

 simply of a straight line 

 12345, and therefore 



does not suffice to deter- FlG ' 125 



mine the values of R 1 and R^. For this purpose an equilibrium 

 polygon must be drawn. Thus, choose any pole O on the force 

 diagram and draw the rays 1, 02, 03, etc. ; then construct the 

 corresponding equilibrium polygon by starting from any point a in 

 R l and drawing ab parallel to 01, from b drawing be parallel to 

 2, etc. Having found the closing side af of the equilibrium poly- 

 gon, draw through the ray 6 parallel to a/, thereby determining 

 fi l as 56 and R 2 as 61. 



If, for any reason, it is desired to draw the equilibrium polygon 

 through two fixed points, say a and/ in the figure, the reactions 

 are first determined as above. Then a line is drawn through 6 

 parallel to of', and a pole 0' is chosen somewhere on this line. The 

 closing side of the equilibrium polygon will then be parallel to 0'6 

 (or a/), and hence if the polygon starts at a, it must end at/. 



