94 APPLIED MECHANICS 
When W is to the right of D, the positive shearing force at D is equal 
to R, the reaction at the left-hand support, and this increases the nearer 
‘Wisto D. When W is to the left of D, the shearing force at D is nega- 
tive and equal to R,. Hence the maximum positive shearing foree at D 
occurs when W is at D. Placing W at D, R, -*6 —«x), and the maxi- 
mum positive shearing force at any section D=F= Wa — x), which is the 
equation to a straight line. F,,=W at A where x=0, and F=0 at B 
where x=/. 
It is also evident that the maximum negative shearing force at 
D=F= bit) which is the equation to a straight line. F,,,=W at B where 
x=l, and F=0 at A wherex=0. The complete shearing force diagram 
for the travelling load is shown at (0). 
In designing the section of a plate girder to resist the shearing force, 
it is the maximum numerical value of the shearing force which must be 
known, its sign being of no conse- 2 A 
quence. Hence it is convenient to eye 900000009) 
place the (+) and (—) shearing A ‘Dic BY 
force diagrams on the same side of motes i 1 
the base line, as shown at (c). If a 
| 
however lattice work takes the place we w1 AMOONOOONONO 
of the web plate, the lattice work A Dic BY, 
must be designed so that it will cs >| : 
take either the maximum positive 4 Re 
shearing force or the maximum t 
negative shearing force, but not both (c)i x 
at the same time. . i 1 
Exampie II.—A uniform load 4 H 
of w per unit of length travelling (4) ' ‘ 
along a girder AB (Fig. 124)  y! LRN 
supported at its ends, the length le 
of the load being not less than the i 
span 7. : 
As the load advances over 
the girder it is evident that the (e) 
bending moment at any section 
D will continue to increase until 
the girder is covered by the load, 
because a load placed anywhere on the girder will add to the bending 
moment at D. The bending moment diagram for this case is there- 
fore a parabola having for its axis the vertical through ©, the centre of 
the span as shown at (c), the height of the vertex above the base line 
XX being - : 
The load being in the position shown at (a) or (0), the reaction 
LL, 
Fig. 124. 
Ww 
