188 



KESISTANCE OF MATERIALS 



116. Structures : joint reactions. Since all parts of a structure 

 at rest are in equilibrium, the conditions of equilibrium may evi- 

 dently be applied to the forces acting upon any portion of the 

 structure. This portion may be a single joint, a single member or 

 part of a member, or it may include several joints and members. 

 The forces acting upon the part considered may be partly external 

 forces and partly internal forces, or stresses, or they may be wholly 

 stresses. 



As in finding external reactions, the conditions of equilibrium 

 may be applied either analytically or graphically. 



FIG. 126 



1. Analytical method. To illustrate this method, as applied to the 

 joints of a structure, let it be required to find the stresses in the 

 members of the shear legs, shown in Fig. 126. 



Starting with the joint A, the forces acting at this point are the 

 weight W, the tension P in the guy AC, and the reaction of the 

 legs of the A frame. To simplify the solution the latter may be 

 assumed for the present equivalent to a single force R acting along 

 the center line A'C between the legs of the A frame. The condi- 

 tions of equilibrium applied to this joint are then 



vertical forces = 0, W + P cos (0 + <) R cos 6 = 0, 



horizontal forces = 0, P sin (0 + 0) - R sin 6 =0, 

 giving two simultaneous equations for R and P, 



