68 
When the beam is not prismatic as was assumed in $ 1, but has 
a variable cross-section, the diagrams of bending moment can be 
reduced in the way already indicated by Monk. 
19. Lines of influence. 
By the aid of the construction given in the preceding $$ the lines 
of influence for the moments of transition of a statically indeter- 
minate elastically supported beam can now also be constructed 
graphically. In order to determine for instance the line of influence 
for the moment of transition above the pt point of support, we 
need only construct the elastic line giving the position of the beam 
on being cut above the p'' point of support and charged in the 
arising cross-section by a moment of transition of 1 metreton. For 
each of the pieces into which the beam is divided, the moments of 
transition — hence the diagram of bending moment — can be 
determined as described, after which the elastic line can be drawn in 
the known way. 
