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National Advisory Committee for Aeronautics, Report - Torsional Stiffness of Thin Walled Shells Having Reinforcing Cores and Rectangular, Triangular, or Diamond Cross Section

A theoretical investigation has been made of the Saint-
Venant torsion of certain composite bars. These bars are
composed of two materials—one material in the form of a
thin-walled cylindrical shell and the other material in the form
ofacorewhichfillstheinteriorqftheshellandis bondedtoit.

An approximate boundary-value problem is formulated on
assumptions similar to those of the theory of torsion of hollow
thinwafled shells (Bredt theory). This boundary—value prob-
lem is solved exactly for a rectangular cross section and approri-
mately for slender triangular and slender diamond cross sections.
Results for the torsional stifiness constants are presented
graphically.

Certain airframe components such as wings, stabilizing
fins, control surfaces, and helicopter rotor blades have been
fabricated by employing a high-strength shell bonded to a
core made of some light-weight material. The shell is
formed in the external contour of the component and the
core fills the interior and acts to stabilize the shell against
local buckling. Such a structure has been called a 'foam-
filled sheet' because the core is often a foamed—plastic
material. Metal honeycomb and balsa wood have also been
used for cores

A large amount of literature exists on the problem of
torsion of homogeneous isotropic cylindrical bars, but rela-
tively little work has been done on the torsion of composite
cylinders. A few exact solutions to problems in the torsion
of composite sections are presented in references 1 and 2.
Solutions for other cross-sectional configurations are desir-
able, and the methods used in references 1 and 2 do not
appear to be applicable for sections of the type considered
in the present report.

In this report an approm‘mate boundary—value problem
for the torsion of foam—filled shells, is formulated. The
fact that the thickness of the outer shell is small relative to
overall dimensions of the cross section allows an approximation
similar to that of the theory for the torsion of
hollow thin-walled shells with free warping. (See ref. 3,
pp. 298—302.) For a rectangular cross section, an exact
solution to the approximate boundary-value problem .is
obtained.