Manchester Memoirs, Vol. lix. ( 1 9 1 5 ), No. %. 3 



if the spans be equal, or by amounts inversely propor- 

 tional to the spans if the spans be unequal. 1 The 

 characteristic points are obtained by setting up at a 

 distance of one-third of the span from the support a 

 perpendicular equal in length to 



2A1 



Z 2 

 where A = Area of bending moment diagram which would 

 be produced on the span if it were dis- 

 continuous. 

 ;r= Distance of centre of gravity of free ended 

 bending moment diagram from the further 

 support. 



The distances by which the base line passes over or 

 under the characteristic points on either side of a support, 

 when multiplied by the span in which the point lies, can 

 be shown to be proportional to the slope of the beam at 

 the nearer support, and hence since there are two charac- 

 teristic points to each support, the base line must pass 

 over one and under the other by equal or proportional 

 distances. 



The above statements are only accurately true if the 

 supports lie in the same straight line. If any support 

 lies below or above the line of the other props by a 

 known amount the method still holds, but other expres- 

 sions are necessary for the heights of the characteristic 

 points above the free ended base line. 



In order to obtain the complete bending moment 

 diagram for a continuous beam it is necessary then, 

 firstly, to draw upon a horizontal base line the bending 

 moment diagrams for each span assumed discontinuous ; 

 secondly, to determine the position of each pair of char- 



1 " Bridge Construction." Claxton Fidler. 



