Page 196 - Aircraft Stuctures for Engineering Student

180 Structural instability
,ri-
1 i1
Stiffener cuts = 1
Stiffener flanges = 4
Skin cuts = 1
Skin flanges = -
2
9 =a
/ I
I
j-t I frt J-L Stiffener flanges = 8
Cut not included
Stiffener cuts = 3
Skin cuts = 2
~
Skin flanges = 4
-
g 'E
I / I
Cut not included
Fig. 6.20 Determination of g for two types of stiffenerkkin combination

combination of both. At the moment there is no theory that predicts satisfactorily
failure in this range and we rely on test data and empirical methods. The NACA
(now NASA) have produced direct reading charts for the failure of 'top hat', Z-
and Y-section stiffened panels; a bibliography of the results is given by Gerard' '.
It must be remembered that research into methods of predicting the instability and
post-buckling strength of the thin-walled types of structure associated with aircraft
construction is a continuous process. Modern developments include the use of the
computer-based finite element technique (see Chapter 12) and the study of the
sensitivity of thin-walled structures to imperfections produced during fabrication;
much useful information and an extensive bibliography is contained in Murray3.

It is recommended that the reading of this section be delayed until after Section 1 1.5
has been studied.
In some instances thin-walled columns of open cross-section do not buckle in bend-
ing as predicted by the Euler theory but twist without bending, or bend and twist simul-
taneously, producing flexural-torsional buckling. The solution of ths type of problem
relies on the theory presented in Section 11.5 for the torsion of open section beams
subjected to warping (axial) restraint. Initially, however, we shall establish a useful
analogy between the bending of a beam and the behaviour of a pin-ended column.
The bending equation for a simply supported beam carrying a uniformly distribu-
ted load of intensity wy and having Cx and Cy as principal centroidal axes is
d4v
EI.y.x - w (see Section 9.1) (6.65)
=
dz4
Also, the equation for the buckling of a pin-ended column about the Cx axis is (see
Eq. (6.1))

(6.66)