Page 307 - Aircraft Stuctures for Engineering Student

288 Open and closed, thin-walled beams

Fig. 9.10 Second moments of area of an inclined thin section.

The second moment of area of the section about Cy is obtained in a similar
manner.
We see, therefore, that for the purpose of calculating section properties we may
regard the section as being represented by a single line, as shown in Fig. 9.9(b).
Thin-walled sections frequently have inclined or curved walls which complicate the
calculation of section properties. Consider the inclined thin section of Fig. 9.10. Its
second moment of area about a horizontal axis through its centroid is given by
a12
= 2 Jo ty2 ds = 2 S o : t(s sin p)’ ds

from which
a3 t sin’ p
Ixx =
12
Similarly

a3 t cos2 p
IYY = 12

The product second moment of area is
a12
Ixy = 21 txyds

= 2 JY t(s cos p) (s sin p> ds

which gives

We note here that these expressions are approximate in that their derivation neglects
powers of ? and upwards by ignoring the second moments of area of the element 6s
about axes through its own centroid.