100 APPLIED MECHANICS 
The shearing force diagram for each position of the beam in relation 
to the loads will be a stepped diagram, the levels of the steps being the 
levels of the points a, b, c, and d (Fig. 127) on the line of loads, and the 
zero line zz’ being level with a point 4 obtained by drawing through 0 a 
line oh parallel to the closing line of the funicular polygon. 
Horizontal lines are drawn on the tracing paper through the points 
a, b, ec, and d, and the right-hand top corners of the steps above the zero 
line, and the left-hand 
bottom corners of the 
steps below the zero line, 
are marked on the tracing 
paper, as shown by the Z ? 
prominent dots in Fig. 127, (+) S.F.D. 
z and 2’, the extremities Bo SR areas 
of the zero line, are also Z } tyme 
marked on the tracing 4 “QQ \4 
paper. The tracing paper \ 
is then transferred so that (—) S.F.D. 
zé coincides with a base 
line ZZ’ (Fig. 128) on the 
drawing paper, and the 
points marked on _ the 
tracing paper are pricked 
Ginstigh oh to the draw- Fig. 128. 
ing paper. This is repeated for each position into which the tracing 
paper was placed in determining the bending moments, It will be found 
that the outside points lie on a series of straight lines. 
107. Reversal of Shearing Stress due to Addition of Travelling 
Load.—Referring to the upper part of Fig. 129, AEO and BFO are the 
diagrams of positive and negative shearing forces respectively due to the 
dead or constant load on a girder of span AB, and AHB and BKA are 
the diagrams of maximum positive and maximum negative shearing forces 
respectively due to the travelling load. The lower part of the same 
figure shows all the diagrams, drawn for 
convenience on the same side of the base 
AB, the lines of the negative shearing 
force diagrams being dotted. 
An inspection of the lower part of 
Fig. 129 shows that with the dead load 
only the shearing force over the portion 
CO of the girder is positive, but when the 
travelling load is going over the girder 
there will be between C and O, for certain 
positions of the travelling load, a negative 
shear greater than the positive shear. 
Hence during a part of the time that the 
travelling load is moving over the girder 
the shear on the portion CO will change from positive to negative. 
Also between O and D the negative shear due to the dead load will 
change to a positive shear due to the travelling load, Hence the portion 
of the girder between C and D must be capable of resisting either 
ZY 
LLAALLL, 
