to cross girders at D'E', the part of the influence line
under this bay is altered. Let n (Fig. 55) be the distance of the load from
D', x_1 the distance of D' from the left abutment, and p the length of a
bay. The loads at D', E, due to unit weight on the rail girder are (p-n)/p
and n/p. The reaction at B' is {(p-n)x_1+n(x_1+p)}/pl. The shear at C' is
the reaction at B' less the load at E', that is, {p(x_1+n)-nl}/pl, which is
the equation to the line DH (fig. 54). Clearly, the distribution of the
load by the rail girder considerably alters the distribution of shear due
to a load in the bay in which the section considered lies. The total shear
due to a series of loads P_1, P_2, ... at distances m_1, m_2, ... from the
left abutment, y_1, y_2, ... being the ordinates of the influence curve
under the loads, is S = P_1y_1+P_2y_2+.... Generally, the greatest shear S
at C will occur when the longer of the segments into which C divides the
girder is fully loaded and the other is unloaded, the leading load being at
C. If the loads are very unequal or unequally spaced, a trial or two will
determine which position gives the greatest value of S. The greatest shear
at C' of the opposite sign to that due to the loading of the longer segment
occurs with the shorter segment loaded. For a uniformly distributed load w
per ft. run the shear at C is w x the area of the influence curve under the
segment covered by the load, attention being paid to the sign of the area
of the curve. If the load rests directly on the main girder, the greatest +
and - shears at C will be w x AGC and -w x CHB. But if the load is
distributed to the bracing intersections by rail and cross girders, then
the shear at C' will be greatest when the load extends to N, and will have
the values w x ADN and -w x NEB. An interesting paper by F.C. Lea, dealing
with the determination of stress due to concentrated loads, by the method
of influence lines will be found in _Proc. Inst. C.E._ clxi. p.261.

Influence lines were described by Fraenkel, _Der Civilingenieur_, 1876. See
also _Handbuch der Ingenieur-wissenschaften_, vol. ii. ch. x. (1882), and
Levy, _La Statique graphique_ (1886). There is a useful paper by Prof. G.F.
Swain (_Trans. Am. Soc. C.E._ xvii., 1887), and another by L.M. Hoskins
(_Proc. Am. Soc. C.E._ xxv., 1899).

[Illustration: FIG. 56.]

28. _Eddy's Method._--Another method of investigating the maximum shear at
a section due to any distribution of a trave