CHAPTER IV. 



APPLICATION OF THE LAWS OF EQUILIBRIUM TO THE 

 STRUCTURE AS A WHOLE. 



REACTIONS. 



45. Reactions. Reactions will now be determined both 

 algebraically and graphically for a number of different cases. 



As stated in Art. 42, three unknown quantities may be 

 determined from the three equations of equilibrium. In general 

 there are two unknowns involved in each reaction, its magnitude 

 and direction; therefore, even in the simplest case of a beam 

 with two supports and vertical loads, some other condition must 

 be introduced which will determine one of the four unknowns. 

 The usual assumption is that there is no friction at one of the 

 supports. This determines the direction of that reaction, if 

 there is no friction its direction must be perpendicular to the 

 surface of the support. In practice this condition is - never 

 fully met. 



46. Reactions for a Single Force. Fig. 31 shows a beam 

 carrying a load P and supported at 



its ends A and B. The reactions, 

 R! and R 2 , will be vertical if the 

 support at one end is such that the 

 beam is free longitudinally. 



Since all the forces are ver- 



jf 



tical there are no horizontal com- 

 ponents. Applying the other two 

 equations of equilibrium, we have 3 vert, comps. = 



h-'' U - 



L 



For 2 moments = 0, the center of moments may be taken at any 

 convenient point ; if it is taken at B, the moment of R 2 is zero and 



we have R^ directly from 



h 



= or ^ 



55 



