98 APPLIED MECHANICS 
The equation for the maximum positive shearing force is therefore either 
WwW 
¥,= /@-2-a), or Fy=7(l-#+b)-Wy,. 
F, is a maximum when ¢=0, and F, is a maximum when #=0, 
W,l 
F, = 0 when «=1—a, and F,=0 when @=1+b- 
The equations for the positive shearing force at D only apply when 
: W : 
both loads are on the girder. The equation F, = 7 (l-—x-a) applies 
between x=0 and #w=/-—c, and the equation Fy=" (0-2+b)-W, 
applies between a=c and a=/. For the remainder of the beam in each 
case the shearing force is due to one load only. 
The positive shearing force diagram shown at (d), Fig. 125, is fer 
the case where F, is greater than F,. 
The maximum negative shearing force at any section is determined in 
a similar manner. 
106. Travelling Loads—Graphic Method.—The method discussed 
in connection with Example III. of the preceding Article for determining 
| No 
—— oe oe 
D 1 
\ 
Fig. 126. 
the maximum bending moment and maximum shearing force diagrams 
for two travelling loads may be extended to cases where there are more 
than two travelling loads, but for such cases the graphic method now to 
be described is simpler. 
MN (Fig. 126) is a beam, supported at the ends, along which three 
