In applying either equation (43) or equation (44) care must be taken
to give each stress and its corresponding strain (lengthening or
shortening) the proper sign. As the formulæ have been written and
used, a tensile stress and its resulting stretch must each be written
positive, while a compressive stress must be written negative. This
holds true for both the stresses _Z_ and _S_ (or _z_ and _s_). The
magnitude of the assumed load _P_ is a matter of indifference, since
the stress _Z_ will always be proportional to it and the ratio _P ÷ Z_
will therefore be constant. _P_ is frequently taken as unity; or, as in
the case just given, it may have any value that the conditions of the
problem make most convenient.
=112. Application of Method for Deflection to Truss.=—In making
application of the deflection formulæ to any steel railroad truss
similar to that shown in Fig. 29, it will first be necessary to
determine the stresses in all its members due to the dead and moving
loads, since the deflection under the moving load is sought. These
loads will be considered uniform, and that is sufficiently accurate for
any railroad bridge. The moving train-load will be taken as covering
the entire span, assumed, for a single-track railroad, 240 feet in
length between centres of end pins. There are eight panels of 30
feet each, and the depth of truss at centre is 40 feet. Other truss
dimensions are as shown in Fig. 29. The dead loads, or own weight, are
taken at 400 pounds per linear foot of span for the rails and other
pieces that constitute the track; at 400 pounds per linear foot for
the steel floor-beams and stringers, and 1600 pounds per linear foot
for the weight of trusses and bracing. The moving train-load will be
taken at 4000 pounds per linear foot. This will make the panel-loads
for each truss as follows:
Lower-chord dead load, 30 × 800 = 24,000 pounds per panel.
Lower-chord moving load, 30 × 2000 = 60,000 ” ” ”
------
Total load on lower chord = 84,000 ” ” ”
Upper-chord dead load, 30 × 400 = 12,000 ” ” ”
The structure is a “through” bridge, hence all moving loads rest on the
lower chord.
[Illustration: FIG. 30.]
The stresses in the truss members due to the combined uniform dead and
moving load are best found by the graphical method. One diagram only is
needed to determine all the stresses, and it is shown in Fig. 30. This
diagram is drawn accurately to scale, and the stresses measured from it
are shown in the table on page 136.
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