STRENGTH OF MATERIALS 



(45) J 



Similarly, by taking the origin at C and reckoning backward toward 

 B, it will be found that 



(46) -M; = MC + ^A ~ 

 and 



Equating the values of ( j from equations (45) and (47), and elimi- 

 nating R a and ^ c from the resulting equation by means of equal 

 (44) and (46), 



whence /5 , 



i , r 



which is the required theorem of three moments. 



If the beam extends over n supports, this tln-Mivm fumi>lits n 2 

 equations between the ?i moments at the support-, tin- remaining t w< 

 equations necessary for solution being furnished lv tin- icniiinal con- 

 ditions at the ends of the beam. 



Problem 88. A continuous beam of two equal spans bean a uniform load 

 extending continuously over both spans. Find the bfiulini; moments and reac- 

 tions at the supports. 



Solution. In the present case w\ = to a = to, li It = I, and J/<, = M e = 0. ' 



sequently, the theorem reduces to 



whence 



From equation (44), 



8 2 



whence 



E a = f wl. 



