Page 187 - Aircraft Stuctures for Engineering Student

6.6 Buckling of thin plates 17 1

I I I I
I I I
I I I I
I
I
2 , I I I I I I I I

or
kgD
Nx.CR - (6.55)
b2
where the plate buckling coeficient k is given by the minimum value of
k= -+- (6.56)
(:b Zb)’
for a given value of a/b. To determine the minimum value of k for a given value of a/b
we plot k as a function of a/b for different values of m as shown by the dotted curves
in Fig. 6.15. The minimum value of k is obtained from the lower envelope of the
curves shown solid in the figure.
It can be seen that m varies with the ratio a/b and that k and the buckling load are a
minimum when k = 4 at values of a/b = 1,2,3,. . . . As a/b becomes large k
approaches 4 so that long narrow plates tend to buckle into a series of squares.
The transition from one buckling mode to the next may be found by equating
values of k for the m and m + 1 curves. Hence
mb a (m+l)b+ U
-+-=
a mb a (m + l)b
giving
’= &qzq
b