CHAPTER VIII. 

 SIMPLE: BEAMS. 



Reactions. The reactions of beams may be found by the use 

 of the force and equilibrium polygon as shown in Chapter V. As a sec- 

 ond example let it be required to find the reactions of the overhanging 

 beam shown in Fig. 36. 



Ri 



>^v a i 



d 



.. b 



P, 

 JH 



I. 



>o 



(W 



X ^ 



\r''C 



(a) I 



FIG. 36. 



Construct a force polygon with pole o, as in (b), and draw an equi- 

 librium polygon, as in (a). The ray o d drawn parallel to the closing 

 line o d in (a) determines the reactions. In this case reaction R^ is 

 negative. It should be noted that the closing line in an equilibrium 

 polygon must have its ends on the two reactions. 



The ordinate to the equilibrium polygon at any point multiplied 

 by the pole distance, H, will give the bending moment in the beam at a 

 point immediately above it. 



