Page 210 - Aircraft Stuctures for Engineering Student

194 Structural instability

From Eqs (6.7) the buckling load of a stiffener is then

7? x 70000 x 2000
PCR = 2532 = 22.0 kN
Clearly the stiffener will not buckle.
In Eqs (6.107) and (6.108) it is implicitly assumed that a stiffener is fdy effective in
resisting axial load. This will be the case if the centroid of area of the stiffener lies in
the plane of the beam web. Such a situation arises when the stiffener consists of two
members symmetrically arranged on opposite sides of the web. In the case where the
web is stiffened by a single member attached to one side, the compressive load P is
offset from the stiffener axis thereby producing bending in addition to axial load.
For a stiffener having its centroid a distance e from the centre of the web the combined
bending and axial compressive stress, a,, at a distance e from the stiffener centroid is

P
a, = - +- Pe2
As As?
in which r is the radius of gyration of the stiffener cross-section about its neutral axis
(note: second moment of area I = Ar2). Thus

-
a -'[1+(;)2]
As
or
P
a, = -
Ase
where
(6.109)

and is termed the effective stiffener area.

6.13.2 Incomplete diagonal tension -

In modern aircraft structures, beams having extremely thin webs are rare. They
retain, after buckling, some of their ability to support loads so that even near failure
they are in a state of stress somewhere between that of pure diagonal tension and the
pre-buckling stress. Such a beam is described as an incomplete diagonal tensionfield
beam and may be analysed by semi-empirical theory as follows.
It is assumed that the nominal web shear T(= S/td) may be divided into a 'true
shear' component T~ and a diagonal tension component TDT by writing
TDT = k7, T~ = (1 - k)7 (6.110)

where k, the diagonal tension factor, is a measure of the degree to which the diagonal
tension is developed. A completely unbuckled web has k = 0 whereas k = 1 for a web
in complete diagonal tension. The value of k corresponding to a web having a critical