1920-21.] Graphical Treatment of Shear Influence Lines. 69 
771 
hence R = cd x ~ ; 
/ T) r b 
therefore cd represents the reaction R to a scale of 1" — — =n units. 
JL 
If, now, the loads move to the left by a distance l v it is easy to show 
that R is represented by c ± d ± = the depth of the diagram at a distance l x to 
the right of A. 
Again, if the loads move a distance l 2 to the right , the sum of the 
moments at A due to all the loads will be represented by ed 2 , where ce = l 2 . 
But since is now off the beam, the bending moment, ec 2 , due to it is 
ineffective. The true bending moment is now c 2 d 2 ; and, from what has 
v 
gone before, it follows that the new value of R is represented by c 2 d 2 for 
this position of the loading. 
When Wj is at an infinitely small distance to the left of B, R = cd ; but, 
immediately it passes off the beam, R is reduced by W 2 or eg. Similarly, 
just when W 2 leaves the beam at B, the reaction is suddenly reduced by 
W 2 . This reduction is shown by hk( = W 2 ), which is drawn at a distance 
p from A, where p is the spacing between W 1 and W 2 . A similar treatment 
is adopted for the adjustment of the reaction R when W 3 passes B. This 
is not shown on the diagram. 
Generally, the vertical intercept between the lines o x cghht — conveni- 
ently termed the “ control ” line, and the line o x o 2 o z v, which may be 
referred to as the “ moment ” line, at a distance l , where l is the motion 
of the loads, measured horizontally from A in a direction opposite to that 
in which the loads have moved from the position where W x is over B, 
gives the then value of R. 
