30 GRAPHIC STATICS 



The imaginary force a o acting in a reverse direction as shown 

 is an equilibrant of R lt and the imaginary force c o acting in a reverse 

 direction is an equilibrant of R 2 . The remaining equilibrant of R 1 and 

 of R 2 must coincide and be equal in amount, but opposite in direction. 

 The string b o is the remaining equilibrant of 7? x and of R 2 and is 

 called the closing line of the equilibrium polygon. The ray b o drawn 

 parallel to the string b o divides P in two parts which are equal to the 

 reactions R^ and R 2 (for reactions of overhanging beam see Chapter 

 VIII). 



Reactions of a Cantilever Truss. In the cantilever truss shown 

 in Fig. 1 6, the direction and point of application B of the reaction Rj^ 



(a) 



(b) 



are known, while the point of application A of the reaction R 2 only 

 is known. The direction of reaction R 2 may be found by applying the 

 principle that if a body is in equilibrium under the action of three 

 external forces which are not parallel, they must all meet in a common 

 point, i. e., the forces must be concurrent. The resultant of all the 

 loads acts through the point c, which is also the point of intersection 

 of the reactions R and R 2 . Having the direction of the reaction R 2 , 

 the values of the reactions may be found by means of a force polygon. 

 The direction of reaction R 2 may be found by means of a force and 

 equilibrium polygon as follows : Construct the force polygon (b) with 

 pole o and draw equilibrium polygon (a) starting with point A, the 



