190 RESISTANCE OF MATERIALS 



to AJ and BJ, they will represent the stresses in these members 

 to the same scale as that to which R^ was laid off (Fig. 127, /). 



Proceeding to the next joint, BJIC, w^e have four forces meeting 

 at a point, one of which, BJ, has just been determined, and another, 

 BC, is known. Hence the other two are found by drawing a force 

 polygon, bjic, giving the stresses in C/and IJ (Fig. 127, //). 



Similarly, passing to the next joint, AJIH, the stresses in AJ and 

 JI having been found, those in IH and AH may be determined from 

 the force polygon ajih (Fig. 127, ///), and finally for the joint If CD 

 the remaining stresses are determined from the force polygon ghicd 

 (Fig. 127, IV). 



Since each force polygon contains one side of each of the others, 

 by placing these sides together they may all be combined into 



one figure, as shown in 



7 Tons flOTons 9 Tons 15 Tons Fig. 127, V. Ill the preS- 



I 

 A |Q \ 



11 i i eiit case separate diagrams 



were drawn for each joint 

 to illustrate the method. 

 In practice, however, but 

 one diagram, the combined 

 one, is drawn, as it affords a 



F 12g saving in time and space and 



produces a neater and more 



compact appearance. Such a figure is called a Maxwell diagram. 

 117. Structures : method of sections. If a section is passed 

 through a structure, cutting not more than two members whose 

 stresses are unknown, the single condition that the force polygon, 

 drawn for the forces acting upon the portion of the structure on 

 one side of the section, must close, will enable the stresses in these 

 members to be found. Commencing at one end of a structure and 

 passing a section cutting but two members, the stresses in these 

 can thus be determined. Then, passing a section cutting three 

 members, one of which has already been treated, the stresses in the 

 other two can be found, etc. Thus, by means of successive sections, 

 all of the stresses can be determined by simple force polygons. 



1. Analytical method. To illustrate the analytical application of 

 this method, consider a Warren truss used as a deck bridge, as 



