If _z′_ is placed equal to 0 and _p_ successively, then will equation
(_k_) become identical with equations (_f_) and (_h_) in succession.
The shears at points 4 and 5 will therefore take the same values as if
the loads were applied directly to the beam. For the reasons stated in
connection with the consideration of bending moments, loads in other
panels than that containing the section for which the influence line
is drawn will have the same effect on that section as if they were
applied directly to the beam or truss. Hence _AKLB_ is the complete
influence line for this case.
It is evident that there must be as many influence lines drawn as there
are sections to be discussed. Also, if _g_ is taken as some convenient
unit, i.e., 1000 or 10,000 pounds, it is clear that the labors of
computation will be much reduced.
=102. Application of Influence-line Method to Trusses.=—In considering
both the bending moments and shears when the loads are applied at
panel-points, it has been assumed, as would be the case in an ordinary
beam, that the bending moments as well as the shears may vary in the
panel; but this latter condition does not hold in a bridge-truss.
Neither bending moment nor shear varies in any one panel. Yet the
influence lines for moments and shears are to be drawn precisely as
shown in Figs. 25 and 25_a_. The section _X_ will always be found at
a panel-point, and no intercept drawn within the limits of the panel
adjacent to that section carrying the load _g_ is to be used. This
method will be illustrated by the aid of Fig. 25_b_.
The employment of influence lines may be illustrated by determining
the moment and shear in a single section of the truss shown in Fig.
24, which is reproduced in Fig. 25_c_, when carrying the moving load
exhibited in Fig. 25_b_, although its use may be much extended beyond
this simple procedure.
The moving load shown in Fig. 25_b_ is that of a railroad train
consisting of a uniform train-load of 4000 pounds per linear foot
drawn by two locomotives with the wheel concentrations shown; it is
a train-load frequently used in the design of the heaviest class of
railroad structures. If the criterion of equation (27) be applied to
this moving load, passing along the truss shown in Fig. 25_c_, from
left to right, it will be found that the greatest bending moment is
produced at the section _Q_ when the second driving-axle of the second
locomotive is placed at the truss section in question, as shown in Fig.
25_c_.
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