Page 295 - Aircraft Stuctures for Engineering Student

9

Bending, shear and torsion

of open and closed,

thin-walled beams

In Chapter 7 we discussed the various types of structural component found in air-
craft construction and the various loads they support. We saw that an aircraft is
basically an assembly of stiffened shell structures ranging from the single cell
closed section fuselage to multicellular wings and tail-surfaces each subjected to
bending, shear, torsional and axial loads. Other, smaller portions of the structure
consist of thin-walled channel, T-, Z-, 'top hat' or I-sections, which are used to
stiffen the thin skins of the cellular components and provide support for internal
loads from floors, engine mountings etc. Structural members such as these are
known as open section beams, while the cellular components are termed closed
section beams; clearly, both types of beam are subjected to axial, bending, shear
and torsional loads.
In this chapter we shall investigate the stresses and displacements in thin-walled
open and single cell closed section beams produced by bending, shear and torsional
loads, and, in addition, we shall examine the effect on the analysis of idealizing
such sections when they have been stiffened by stringers.

We shall show that the value of direct stress at a point in the cross-section of a beam
subjected to bending depends on the position of the point, the applied loading and the
geometric properties of the cross-section. It follows that it is of no consequence
whether or not the cross-section is open or closed. We therefore derive the theory
for a beam of arbitrary cross-section and then discuss its application to thin-walled
open and closed section beams subjected to bending moments.
The basic assumption of the theory is that plane sections of beams remain plane
after displacement produced by the loading. We shall, in addition, make the simplify-
ing assumptions that the material of the beam is homogeneous and linearly elastic.
However, before we derive an expression for the direct stress distribution in a
beam subjected to bending we shall establish sign conventions for moments, forces