REACTIONS OF A BEAM 



29 



The imaginary forces represented by the rays in the force poly- 

 gon may be considered as components of the forces and the analysis 

 made on that assumption with equal ease. 



It is immaterial in what order the forces are taken in drawing 

 the force polygon, as long as the forces all act in the same direction 

 around the force polygon, and the strings meeting on the lines of the 

 forces in the equilibrium polygon are parallel to the rays drawn to the 

 ends of the same forces in the force polygon. 



The imaginary forces a o,b o, c o, d o, e o are represented in mag- 

 nitude and indirection by the rays of the force polygon to the same 

 scale as the forces P lt P 2 , P 3 , P. The strings of the equilibrium poly- 

 gon represent the imaginary forces in line of action and direction, but 

 not in magnitude. 



Reactions of a Simple Beam. The equilibrium polygon may 

 be used to obtain the reactions of a beam loaded with a load P as in 

 Fig. 15- 



a 

 TT*. 





it I 



(b) 



FIG. 15. 



The force polygon (b) is drawn with a pole o at any convenient 

 point and rays o a and o c are drawn. Now from the fundamental con- 

 ditions for equilibrium for translation we have P = R + R 2 > At any 

 convenient point in the line of action of P draw the strings o a and o c 

 parallel to the rays o a and o c, respectively, in the force polygon. The 

 imaginary forces a o and o c acting as shown equilibrate the force P. 



