Page 355 - Aircraft Stuctures for Engineering Student

336 Open and closed, thin-walled beams

It can be seen from Eq. (i) in Example 9.13 that the analysis of a beam section which
has been idealized into a combination of direct stress carrying booms and shear stress
only carrying skin gives constant values of the shear flow in the skin between the
booms; the actual distribution of shear flows is therefore lost. What remains is in
fact the average of the shear flow, as can be seen by referring to Example 9.13.
Analysis of the unidealized channel section would result in a parabolic distribution
of shear flow in the web 23 whose resultant is statically equivalent to the externally
applied shear load of 4.8 kN. In Fig. 9.52 the resultant of the constant shear flow
in the web 23 is 12 x 400 = 4800N = 4.8 kN. It follows that this constant value of
shear flow is the average of the parabolically distributed shear flows in the unidealized
section.
The result, from the idealization of a beam section, of a constant shear flow
between booms may be used to advantage in parts of the analysis. Suppose that
the curved web 12 in Fig. 9.53 has booms at its extremities and that the shear flow
q12 in the web is constant. The shear force on an element Ss of the web is q&,
whose components horizontally and vertically are qlzSscos 4 and qIzSs sin 4. The
resultant, parallel to the x axis, S,, of q12 is therefore given by

or

S, = q12[cosQds

which, from Fig. 9.53, may be written

(9.76)

Fig. 9.53 Curved web with constant shear flow.