Page 204 - Aircraft Stuctures for Engineering Student

188 Structural instability

From Eqs (6.90)

P ~ ~ = 4.63 ~x io5 N, P~~(~~.~) N, P~~(~) = 1.97 x io5 N
(
)
~
x
io5
8.08
=
Expanding Eq. (6.92)
(P - PCR(.~.~))(P - PCR(8))zO/A - p2xg = 0 (i)
Rearranging Eq. (i)
P2(1 - Axt/zO) - P(pCR(.~.~) + PCR(B)) + PCR(s.~)pCR(8) = (ii)
Substituting the values of the constant terms in Eq. (ii) we obtain

P2 - 29.13 x 105P + 46.14 x 10" = 0 (iii)
The roots of Eq. (iii) give two values of critical load, the lowest of which is

P = 1.68 x 10'N
It can be seen that this value of flexural-torsional buckling load is lower than any of
the uncoupled buckling loads PCR(xx), PCR(yy) or PcR(e). The reduction is due to the
interaction of the bending and torsional buckling modes and illustrates the cautionary
remarks made in the introduction to Section 6.10.

The spans of aircraft wings usually comprise an upper and a lower flange connected
by thin stiffened webs. These webs are often of such a thickness that they buckle under
shear stresses at a fraction of their ultimate load. The form of the buckle is shown in
Fig. 6.24(a), where the web of the beam buckles under the action of internal diagonal
compressive stresses produced by shear, leaving a wrinkled web capable of supporting
diagonal tension only in a direction perpendicular to that of the buckle; the beam is
then said to be a complete tensionJield beam.

W
1 ut Qc ff

A

D ut

(a) (W
Fig. 6.24 Diagonal tension field beam