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National Advisory Committee for Aeronautics, Report - Wing Spar Stress Charts and Wing Truss Proportions

Although the coming of the thick airfoil section has somewhat decreased the number of
airplanes designed with continuous wing spars externally supported at several points, that type
of construct-ion has not by any means disappeared. The truss continuous through two or three
bays is still commonly used, and the calculation of continuous beams is still making heavy
inroads upon the time of the designer. With the objects of reducing the labor involved in such
calculations and of deriving some general conclusions on the properties of continuous beams, the
curves described in this report have been prepared for publication by the National Advisory
Committee for Aeronautics. In presenting them to the public, the writer takes the opportunity
of acknowledging the assistance of Mr. Otto C. Koppen, who has done a very considerable pro-
portion of the work of preparation of the material.

In order to simplify calculation of beams continuous over three supports, a series of charts
have been calculated giving the bending moments at all the critical points and the reactions at
all supports for such members. Using these charts as a basis, calculations of equivalent bending
moments, representing the total stresses acting in two bay wing trusses of proportions varying
over a wide range, have been determined, both with and without allowance for column effect.
This leads finally to the determination of the best proportions for any particular truss or the best
strut locations in any particular machine. The ideal proportions are found to vary with the
thickness of the wing section used, the aspect ratio, and the ratio of gap to chord.

Of all the wing cells built with spars continuous over three or more supports, at least 75
per cent of thetotal number involve calculation for three supports only. If the loading per unit
length of spar be assumed uniform in such a case there are only three variables which affect the
bending moments, reactions, and bending stresses for unit loading. Those quantities are
dependent only on the length of the inner bay, the length of the outer bay, and the length of
the effective overhang, and if all results be reduced to a common total length, as can easily be
done, one of these three variables disappears and curves of moment, reaction, and stress can
be plotted in terms of the remaining two.