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National Advisory Committee for Aeronautics, Technical Notes - Working Charts for the Stress Analysis of Elliptic Rings

This report presents charts which reduce the stress
analysis of circular and elliptic rings of uniform cross
section subjected to balanced systems of concentrated
loads from a statically indeterminate problem to a stati+
cally determinate one. The charts are constructed for two
simple loading conditions into which most of the loading
conditions encountered in the design of the main frames of
a monocoqus fuselage may be resolved.

The theoretical calculations required for the con-
struction of the charts employed the "minimum energy meth—
od" but are omitted in the report.

To demonstrate the use of the charts in the stress
analeis of elliptic rings an'illustrative problem is in—
cluded.

The design of main frames for monoc0que fuselages has
been discussed by Roy A. Miller in reference 1, where he
also developed equations for the shear, thrust, and moment
in a circular.ring of uniform cross section subjected to
balanced systems of concentrated loads symmetrical with
respect to a diameter. As the monocoque fuselage is per—
haps more often elliptical than Circular in section, the
author has extended the solutions given in reference 1 to
include the elliptic ring of uniform cross section subject—
ed to balanced systems of concentrated loads symmetrical
with respect to the major axis.

From structural theory and dimensional reasoning it'
developed that for any loading condition the shear, thrust,
and moment at any point in a ring could be reduced to cor
efficient form and presented conVeniently in charts, and
that with a series of these charts the stress analysis of
the ring is reduced from a statically indeterminate prob-
lem to a statically determinate one. The object of this
report is to present a group of these charts for circular
and elliptic rings which will be useful in the stress anal-
ysis of the main frames in monocoque fuselages.