t. 47. REACTIONS FOB ANY NUMBER OF LOADS. 



63 



the horizontal and vertical components of the reactions, and it is 

 assumed that the horizontal components are equal (46). 



The direction in which V 2 will act depends upon the rela- 

 tive magnitudes of the horizontal and vertical loads. If it acts 

 downward as shown, the structure must be anchored. 



From 2 hor. comps. = 0, we get, 



from 2 vert, comps. = 0, we get, 



from 2 moms. = 0, with center at A, we get, 



-y 2 bP w -V a b = Q. (c) 



The moments of the other forces (H and VJ are zero. Equa- 

 tion (a) gives the value of H- equation (c), that of V 2 - and 

 equation (6), that of F . As a check a moment equation for B 

 may be written. 



Fig. 45. 



A problem quite similar to this is solved graphically in Fig. 

 45. The force polygon is abcdefna and the string polygon is 

 ABCDEFGA. 



The reactions R and R 2 act in opposite directions. 

 48. Reactions for Uniform Loads. A uniformly distributed 

 load may be conceived to be a series of equal infinitely small con- 

 centrated loads infinitely small and equal distances apart. In 



^ : Fig. 46, the resultant of these loads 



would equal W and act at the middle of 

 *tv./r f \ t ne beam, so that, ~by symmetry, each re- 

 Fig. 46. action is %W. 



