Fuselage Stress Analysis Page: 8 of 16
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ANALYSIS OF FUSELAGE STRESSES.
lower panel points in the proportion correct for the horizontal ones, and such an arrangement
of loads, making the lines of action of all the forces parallel to each other, greatly simplifies the
work. The second method is to balance the horizontal component of ground reaction directly
by a thrust load. This is the condition in taxi-ing, and is illustrated in Case III. The assump-
tion that the thrust is large enough to balance completely the horizontal component while the
dynamic load is a maximum is rather severe, as the thrust would have to be about equal to the
weight of the machine when the dynamic load was 5. The figures obtained on this assumption,
however, at least serve to show in which members the stress is increased by a thrust load.
Case II is intended to relate to the same condition as Case I, but in a simplified form making
it unnecessary to deal with inclined loads. Instead of taking the reactions at the points of
attachment of the chassis strust as passing along the struts, so that their resultant might pass
through the axle, the resultant of the panel-point loads is opposed, in Case II, by a vertical
force passing through the center of gravity. The forces in the chassis struts are then arbi-
trarily replaced by two vertical forces acting at the same points and so proportioned that their
resultant is the line just spoken of. All external forces are then vertical, there are no inertia
forces, and the resultants of the upward and downward forces both pass through the center
of gravity and there is complete equilibrium. This is manifestly an easy case to deal with,
and the stress diagram in Case II is much simpler than that in Case I, where the external forces
can not all be represented on a single straight line. The simplified method has been used by
the airplane engineering department of the Air Service.
It is evident that the entire omission of the horizontal components of the chassis strut
forces will have a considerable effect on the stresses in the longerons in the bays between the
points of attachment of the two struts. This is particularly noticeable in a machine like the JlN,
where the upper ends of the chassis struts are widely separated and their slope is small. An
inspection of the tabulation of the results of the analyses shows that the stresses in the top
longeron near the rear of the body are greater for Case II, those in the bottom longeron for Case I.
This is natural, as the inertia components of the loads, acting from the free end toward the
supporting reactions, tend to increase the compression in the lower longeron and counterbalance
the tension in the upper one. The stresses in the struts and wires are nearly the same for the two
cases except in the bays between the points of attachment of the chassis struts. This, again, is
what might be expected, as, the longerons being nearly parallel and horizontal, the primary
duty of the wires is to carry the shear due to vertical loads, while the strut compressions are
almost exactly equal to the vertical components of the stresses in the adjacent wires. Strut
and wire stresses are therefore substantially unaffected by horizontal components of load at the
panel points. In no case, except in the bays between the chassis struts and in a few other bays
of the top longeron, is the difference of stress in a member for the two cases as much, as 5 per
cent. The percentage difference is large in some of these cases, but only where the magnitude
of the stresses is small and where the factor of safety would be. sure to be very large. The sim-
plified method of Case II leads to an overestimation of the top longeron stresses, as compared
with Case I, by about 100 pounds in one bay. The important differences come in the bays be-
tween chassis struts. The type of loading used in Case II is manifestly wrong for these bays, and
the inclusion of the horizontal components of the strut reactions changes the magnitude of the
stresses very radically. In the case of the lower longeron, the effect of these components is to
change the stress from a large compression to a tension. The difference between the two cases
in the upper longeron is much smaller but the simplified method is not on the safe side. In
the struts, the stress given by the simplified method is too high in the member directly over
the rear chassis strut, and too low in all others. The only pair of wires much affected is that
in the rear bay, where different wires are in tension in the two cases.
Summing up, it is evident that the method of Case II is satisfactory for the rearof thebody,
but that it gives results very badly in error for some of the members in the neighborhood of the
chassis attachment. The simplified loading can well be used for a preliminary analysis to assist
in estimating the sizes of members, but it should not be considered as satisfactorily covering
the landing loads by itself. When it is employed there should be added to the stresses in the
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Warner, Edward P. & Miller, Roy G. Fuselage Stress Analysis, report, 1920; (https://digital.library.unt.edu/ark:/67531/metadc65725/m1/8/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.