GRAPHICAL METHODS. 



105 



coincides with the first. With this convention, we may say that 

 the conditions of equilibrium of a plane system require the closing 

 of both the force polygon and the funicular polygon. 



176. One of the most important applications of the graphical methods 

 is found in the determination of tJie stresses in the frame-works used for 

 bridges, roofs, cranes, etc. The following example will illustrate the 

 method. 



Fig. 51 represents the skeleton frame of a roof truss subjected to the 



"loads" 



W and the 



reactions of the supports A, B. 

 The members of the frame in 

 connection with the lines of ac- 

 tion of these forces (imagined as 

 drawn from infinity up to the 

 points of application) divide the 

 whole plane into a number of 

 compartments marked in the 

 figure by the letters a, b, c, d, . 

 The external forces as well as 

 the members of the frame (or 

 the stresses acting along them) E 

 can thus be designated by the 

 two letters of the two portions 

 of the plane separated by the 

 force or stress. For instance, 

 the reaction A is denoted ab, 

 and the stresses in the two mem- 

 bers concurring at A are be 

 and ca. The figure just de- 

 scribed may be called the frame 

 diagram ; and we proceed now 

 to construct its stress diagram* 

 Laying off on a vertical line 

 gj = \V\, eg = IV^ be = IV$, and 

 bisecting bj at a, we have the 

 polygon of the external forces which gives the reactions A = ab, B =/#. 



Fig. 51. 



*The student is advised to draw the stress diagram himself step by step as- 

 indicated in the text. 



