Page 191 - Aircraft Stuctures for Engineering Student

6.10 Instability of stiffened panels 175

(a) (b) (C) (d)
Fig. 6.17 (a) Extruded angle; (b) formed channel; (c) extruded Z; (d) formed 'top hat'.

two distinct categories: flanges which have a free unloaded edge and webs which are
supported by the adjacent plate elements on both unloaded edges.
In local instability the flanges and webs buckle like plates with a resulting change in
the cross-section of the column. The wavelength of the buckle is of the order of the
widths of the plate elements and the corresponding critical stress is generally indepen-
dent of the length of the column when the length is equal to or greater than three
times the width of the largest plate element in the column cross-section.
Buckling occurs when the weakest plate element, usually a flange, reaches its
critical stress, although in some cases all the elements reach their critical stresses
simultaneously. When this occurs the rotational restraint provided by adjacent
elements to each other disappears and the elements behave as though they are
simply supported along their common edges. These cases are the simplest to analyse
and are found where the cross-section of the column is an equal-legged angle, T-,
cruciform or a square tube of constant thickness. Values of local critical stress for
columns possessing these types of section may be found using Eq. (6.58) and an
appropriate value of k. For example, k for a cruciform section column is obtained
from Fig. 6.16(a) for a plate which is simply supported on three sides with one
edge free and has a/b > 3. Hence k = 0.43 and if the section buckles elastically
then 7 = 1 and

cCR = 0.388E (i)2 (v=0.3)
-
It must be appreciated that the calculation of local buckling stresses is generally
complicated with no particular method gaining universal acceptance, much of the
information available being experimental. A detailed investigation of the topic is
therefore beyond the scope of this book. Further information may be obtained
from all the references listed at the end of this chapter.

It is clear from Eq. (6.58) that plates having large values of b/t buckle at low values of
critical stress. An effective method of reducing this parameter is to introduce stiffeners
along the length of the plate thereby dividing a wide sheet into a number of smaller
and more stable plates. Alternatively, the sheet may be divided into a series of wide
short columns by stiffeners attached across its width. In the former type of structure
the longitudinal stiffeners carry part of the compressive load, while in the latter all the