Page 192 - Aircraft Stuctures for Engineering Student

176 Structural instability

load is supported by the plate. Frequently, both methods of stiffening are combined to
form a grid-stiffened structure.
Stiffeners in earlier types of stiffened panel possessed a relatively high degree of
strength compared with the thin skin resulting in the skin buckling at a much lower
stress level than the stiffeners. Such panels may be analysed by assuming that the
stiffeners provide simply supported edge conditions to a series of flat plates.
A more efficient structure is obtained by adjusting the stiffener sections so that
buckling occurs in both stiffeners and skin at about the same stress. This is achieved
by a construction involving closely spaced stiffeners of comparable thickness to the
skin. Since their critical stresses are nearly the same there is an appreciable interaction
at buckling between skin and stiffeners so that the complete panel must be considered
as a unit. However, caution must be exercised since it is possible for the two
simultaneous critical loads to interact and reduce the actual critical load of the
structure3 (see Example 6.2). Various modes of buckling are possible, including
primary buckling where the wavelength is of the order of the panel length and
local buckling with wavelengths of the order of the width of the plate elements of
the skin or stiffeners. A discussion of the various buckling modes of panels having
Z-section stiffeners has been given by Argyris and Dunne4.
The prediction of critical stresses for panels with a large number of longitudinal
stiffeners is difficult and relies heavily on approximate (energy) and semi-empirical
methods. Bleich’ and Timoshenko’ give energy solutions for plates with one and
two longitudinal stiffeners and also consider plates having a large number of
stiffeners. Gerard and Becker6 have summarized much of the work on stiffened
plates and a large amount of theoretical and empirical data is presented by Argyris
and Dunne in the Handbook of Aeronautics4.
For detailed work on stiffened panels, reference should be made to as much as
possible of the above work. The literature is, however, extensive so that here we
present a relatively simple approach suggested by Gerard’. Figure 6.18 represents a
panel of width w stiffened by longitudinal members which may be flats (as shown),
Z-, I-, channel or ‘top hat’ sections. It is possible for the panel to behave as an
Euler column, its cross-section being that shown in Fig. 6.18. If the equivalent
length of the panel acting as a column is I, then the Euler critical stress is

as in Eq. (6.8). In addition to the column buckling mode, individual plate elements
comprising the panel cross-section may buckle as long plates. The buckling stress is

. I W

Fig. 6.18 Stiffened panel.