Page 203 - Aircraft Stuctures for Engineering Student

6.1 2 Flexural-torsional buckling of thin-walled columns 187

If the column has, say, Cx as an axis of symmetry, then the shear centre lies on this
axis and ys = 0. Equation (6.91) thereby reduces to

(6.92)

The roots of the quadratic equation formed by expanding Eqs (6.92) are the values of
axial load which will produce flexural-torsional buckling about the longitudinal and
x axes. If PCR(,,,,) is less than the smallest of these roots the column will buckle in pure
bending about the y axis.

Example 6.2
A column of length lm has the cross-section shown in Fig. 6.23. If the ends of the
column are pinned and free to warp, calculate its buckling load; E = 70 OOON/mm2,
G = 30 000 N/mm2.

Fig. 6.23 Column section of Example 6.2.

In this case the shear centre S is positioned on the Cx axis so that ys = 0 and
Eq. (6.92) applies. The distance X of the centroid of area C from the web of the section
is found by taking first moments of area about the web. Thus
2( 100 + 100 + 1OO)X = 2 x 2 x 100 x 50
which gives

i 33.3mm
=
The position of the shear centre S is found using the method of Example 9.5; this gives
xs = -76.2mm. The remaining section properties are found by the methods specified
in Example 6.1 and are listed below
A = 600mm2 Zxx = 1.17 x 106mm4 = 0.67 x 106mm4
Zo = 5.32 x 106mm4 J = 800mm4 I? = 2488 x 106mm6