Page 168 - Aircraft Stuctures for Engineering Student

. ..

Structural instability

A large proportion of an aircraft’s structure comprises thin webs stiffened by slender
longerons or stringers. Both are susceptible to failure by buckling at a buckling stress
or critical stress, which is frequently below the limit of proportionality and seldom
appreciably above the yield stress of the material. Clearly, for this type of structure,
buckling is the most critical mode of failure so that the prediction of buckling loads of
columns, thin plates and stiffened panels is extremely important in aircraft design. In
this chapter we consider the buckling failure of all these structural elements and also
the flexural-torsional failure of thin-walled open tubes of low torsional rigidity.
Two types of structural instability arise: primary and secondary. The former
involves the complete element, there being no change in cross-sectional area while
the wavelength of the buckle is of the same order as the length of the element.
Generally, solid and thick-walled columns experience this type of failure. In the
latter mode, changes in cross-sectional area occur and the wavelength of the buckle
is of the order of the cross-sectional dimensions of the element. Thin-walled columns
and stiffened plates may fail in this manner.

The first significant contribution to the theory of the buckling of columns was made as
early as 1744 by Euler. His classical approach is still valid, and likely to remain so, for
slender columns possessing a variety of end restraints. Our initial discussion is
therefore a presentation of the Euler theory for the small elastic deflection of perfect
columns. However, we investigate first the nature of buckling and the difference
between theory and practice.
It is common experience that if an increasing axial compressive load is applied to a
slender column there is a value of the load at which the column will suddenly bow or
buckle in some unpredetermined direction. This load is patently the buckling load of
the column or something very close to the buckling load. Clearly this displacement
implies a degree of asymmetry in the plane of the buckle caused by geometrical
and/or material imperfections of the column and its load. However, in our theoretical
stipulation of a perfect column in which the load is applied precisely along the
perfectly straight centroidal axis, there is perfect symmetry so that, theoretically,