Page 308 - Aircraft Stuctures for Engineering Student

9.1 Bending of open and closed section beams 289

-
X--. X

Fig. 9.1 1 Second moment of area of a semicircular section.
Properties of thin-walled curved sections are found in a similar manner. Thus, JYx
for the semicircular section of Fig. 9.11 is

Expressing y and s in terms of a single variable 8 simplifies the integration, hence

Ixx = ~~t(rcos8)*rdB

from which
rr3 t
I =- 2
xx
Example 9.3
Determine the direct stress distribution in the thin-walled Z-section shown in Fig.
9.12, produced by a positive bending moment M,.

The section is antisymmetrical with its centroid at the mid-point of the vertical web.
Therefore, the direct stress distribution is given by either of Eqs (9.6) or (9.7) in which
My = 0. From Eq. (9.7)

Fig. 9.12 Z-section beam of Example 9.3.