1 66.] JOINTED FRAMES. 99 



3. JOINTED FRAMES. 



165. The equations of equilibrium are derived on the suppo- 

 sitions that all the forces of the given system act on one and 

 the same rigid body and that this body is perfectly free to 

 move. Hence, in applying these equations to determine the 

 equilibrium of an engineering structure, a machine, etc., each 

 rigid body must be considered separately, and the reactions 

 required to make the body free must be introduced. It will be 

 shown in a subsequent section how the principle of work makes 

 it possible to dispense with some of these precautions. 



When two rigid rods are connected by a pin-joint whose axis 

 is perpendicular to the plane of the rods, the action of either rod 

 on the other at the joint is represented by a single force whose 

 direction is in general unknown. Sometimes considerations of 

 symmetry will allow to determine this direction. 



If a rigid rod, in equilibrium, be hinged at both ends and not 

 acted upon by any other forces, the reactions of the hinges 

 must of course be along the rod, and must be equal and 

 opposite. 



166. Two rods AC, BC (Fig. 45) in a vertical plane, hinged together 

 at C, rest with the ends A,J$0na horizontal plane, and carry a weight 

 W suspended from the joint C. If the proper 



weight of the rods be neglected, determine the 

 normal pressures A y , B y and the horizontal 



thrusts A x , B x at A, B. k/a WT ^\B 



Resolving the weight W along C/4, CB into 

 ^A> ^B and considering the rod AC alone it 



appears that the total reaction at A is along A C and = W A ; hence 

 resolving W A in the horizontal and vertical directions, A x and A y are 

 found ; similarly for BC. If a, ft be the angles at A and -5 in the tri- 

 angle ABC, we find 



J p A= _cosg_jfr WB= cos a ^. 



