at F. If this process is repeated
for all positions of the load, we get the influence line AGB for the
bending moment at C. The area AGB is termed the influence area. The
greatest moment CG at C is x(l-x)/l. To use this line to investigate the
maximum moment at C due to a series of travelling loads at fixed distances,
let P_1, P_2, P_3, ... be the loads which at the moment considered are at
distances m_1, m_2, ... from the left abutment. Set off these distances
along AB and let y_1, y_2, ... be the corresponding ordinates of the
influence curve (y = Ff) on the verticals under the loads. Then the moment
at C due to all the loads is

M = P_1y_1+P_2y_2+...

[v.04 p.0553] [Illustration: FIG. 53.]

The position of the loads which gives the greatest moment at C may be
settled by the criterion given above. For a uniform travelling load w per
ft. of span, consider a small interval Fk = [Delta]m on which the load is
w[Delta]m. The moment due to this, at C, is wm(l-x)[Delta]m/l. But
m(l-x)[Delta]m/l is the area of the strip Ffhk, that is y[Delta]m. Hence
the moment of the load on [Delta]m at C is wy[Delta]m, and the moment of a
uniform load over any portion of the girder is w x the area of the
influence curve under that portion. If the scales are so chosen that a inch
represents 1 in. ton of moment, and b inch represents 1 ft. of span, and w
is in tons per ft. run, then ab is the unit of area in measuring the
influence curve.

If the load is carried by a rail girder (stringer) with cross girders at
the intersections of bracing and boom, its effect is distributed to the
bracing intersections D'E' (fig. 53), and the part of the influence line
for that bay (panel) is altered. With unit load in the position shown, the
load at D' is (p-n)/p, and that at E' is n/p. The moment of the load at C
is m(l-x)/l-n(p-n)/p. This is the equation to the dotted line RS (fig. 52).

[Illustration: FIG. 54.]

[Illustration: FIG. 55]

If the unit load is at F', the reaction at B' and the shear at C' is m/l,
positive if the shearing stress resists a tendency of the part of the
girder on the right to move upwards; set up Ff = m/l (fig. 54) on the
vertical under the load. Repeating the process for other positions, we get
the influence line AGHB, for the shear at C due to unit load anywhere on
the girder. GC = x/l and CH = -(l-x)/l. The lines AG, HB are parallel. If
the load is in the bay D'E' and is carried by a rail girder which
distributes it