82 



THE GRAPHIC METHOD OF SECTIONS. 



Art. 61. 



Fig. 60 shows a case in which R is determined by means of 

 a resultant polygon and Fig. 61, a case in which R is determined 

 by a string polygon, 1-2-6. 



61. Graphical Solution. The flethod of Sections by Ho- 

 ments. In Culmann's method, stresses are determined by means 

 of force polygons, that is, the resolution equations of equilibrium 

 are used. In order to use the moment equation, we resort to the 

 string polygon. 



Fig. 61 shows a simple truss with vertical loads and reac- 

 tions. The force polygon of external forces is abcdena. The 

 shear diagram is drawn opposite it and shows how the shear 

 changes at the panel points and passes through zero at joint 7 

 or at load P s . From any pole draw the rays 1 to 5, and in the 



'Shear 

 Fig. 61. 



space diagram, the corresponding strings; string 6 determines 

 ray 6 and point n. 



To find stress U 2 , for example, take section pq and center of 

 moments at joint 5, then 

 M 6 = or 



The moment of the external forces (7^ and PJ is equal to 

 the moment of their resultant R, which from the force polygon 







(nabn) is equal to nb. R acts at the intersection of strings 2 

 and 6 triangle nbOnand its lever arm is 5 . The above equa- 

 tion becomes 



