Page 350 - Aircraft Stuctures for Engineering Student

9.9 Effect of idealization 331
-
--. L - , I .-- -__ _.,_ .
-
,
9.9 Efl 'ect of idealization on the analysis of open
an d closed section beams
The addition of direct stress carrying booms to open and closed section beams will
clearly modify the analyses presented in the earlier part of this chapter. Before
considering individual cases we shall discuss the implications of structural idealiza-
tion. Generally, in any idealization, different loading conditions require different
idealizations of the same structure. In Example 9.11, the loading is applied in a
vertical plane. If, however, the loading has been applied in a horizontal plane the
assumed stress distribution in the panels of the section would have been different,
resulting in different values of boom area.
Suppose that an open or closed section beam is subjected to given bending or
shear loads and that the required idealization has been completed. The analysis
of such sections usually involves the determination of the neutral axis position
and the calculation of sectional properties. The position of the neutral axis is
derived from the condition that the resultant load on the beam cross-section is
zero, i.e.

a, dA = 0 (see Section 9.1)

The area A in this expression is clearly the direct stress carrying area. It follows that
the centroid of the cross-section is the centroid of the direct stress carrying area of the
section, depending on the degree and method of idealization. The sectional proper-
ties, Zy,y etc., must also refer to the direct stress carrying area.

9.9.1 Bending of open and closed section beams

The analysis presented in Section 9.1 applies and the direct stress distribution is
given by any of Eqs (9.6), (9.7) or (9.9), depending on the beam section being inves-
tigated. In these equations the coordinates (x,y) of points in the cross-section are
referred to axes having their origin at the centroid of the direct stress carrying area.
Furthermore, the section properties I,,, IFF and Zyy are calculated for the direct
stress carrying area only.
In the case where the beam cross-section has been completely idealized into direct
stress carrying booms and shear stress only carrying panels, the direct stress dis-
tribution consists of a series of direct stresses concentrated at the centroids of the
booms.

Example 9.12
The fuselage section shown in Fig. 9.49 is subjected to a bending moment of 100 kN m
applied in the vertical plane of symmetry. If the section has been completely idealized
into a combination of direct stress carrying booms and shear stress only carrying
panels, determine the direct stress in each boom.