Page 399 - Aircraft Stuctures for Engineering Student

380 Stress analysis of aircraft components

constant between adjacent booms. Suppose that the shear flow in the panel 21 is qZl.
Then from symmetry and using the results of Table 10.3

49 8 = 49 IO = ql6 1 = q2 1
q32 = qS7 ‘?loll = q1516 = 30.3 + q21

q43 = q76 = 411 12 = q1415 = 53.5 + 921
q54 = 965 = 912 13 = q13 14 = 66.0 + q21
The resultant of these shear flows is statically equivalent to the applied shear load so
that

4(29.oq21 + 82.5932 + 123.7q43 + 145.8q54) = 100 x lo3
Substituting for 932, q43 and q54 from the above we obtain
4(381q21 + 18740.5) = 100 x lo3
whence
q21 = 16.4N/mm
and
932 = 46.7 N/mm, q43 = 69.9 N/mm, q54 = 83.4N/mm etc.
The shear flow distribution due to the applied torque is, from Eq. (10.18)

15 x lo6
= 2 x 4.56 x 105 = 16.4N/mm
acting in an anticlockwise sense completely around the section. This value of shear
flow is now superimposed on the shear flows produced by the shear load; this gives
the solution shown in Fig. 10.13, i.e.

q21 = 16.4 + 16.4 = 32.8 N/mm
q161 = 16.4 - 16.4 = 0 etc.

We have seen in Chapters 7 and 9 that wing sections consist of thin skins stiffened by
combinations of stringers, spar webs and caps and ribs. The resulting structure
frequently comprises one, two or more cells and is highly redundant. However, as
in the case of fuselage sections, the large number of closely spaced stringers allows
the assumption of a constant shear flow in the skin between adjacent stringers so
that a wing section may be analysed as though it were completely idealized as long
as the direct stress carrying capacity of the skin is allowed for by additions to the
existing stringer/boom areas. We shall investigate the analysis of multicellular wing
sections subjected to bending, torsional and shear loads, although, initially, it will
be instructive to examine the special case of an idealized three-boom shell.
The wing section shown in Fig. 10.15 has been idealized into an arrangement of
direct-stress carrying booms and shear-stress-only carrying skin panels. The part of