Page 352 - Aircraft Stuctures for Engineering Student

9.9 Effect of idealization 333

Table 9.1
0 0 0
Boom B [mm2) uz (N/mm2)
1 +660 640 278 x lo6 35.6
2 +600 600 216 x IO6 32.3
3 +420 600 106 x IO6 22.6
4 +228 600 31 x lo6 12.3
5 + 25 620 0.4 x lo6 1.3
6 -204 640 27 x 106 -11.0
7 -396 640 100 x 106 -21.4
8 -502 8 50 214 x IO6 -27.0
9 - 540 640 187 x IO6 -29.0

equation refers to the direct stress carrying thickness iD of the skin (see Section 9.8).
Equation (9.34) may therefore be rewritten

in which tD = t if the skin is fully effective in carrying direct stress or tD = 0 if the skin
is assumed to carry only shear stresses. Again the section properties in Eq. (9.72) refer
to the direct stress carrying area of the section since they are those which feature in
Eqs (9.6) and (9.7).
Equation (9.72) makes no provision for the effects of booms which cause disconti-
nuities in the skin and therefore interrupt the shear flow. Consider the equilibrium of
the rth boom in the elemental length of beam shown in Fig. 9.50(a) which carries
shear loads S, and S,, acting through its shear centre S. These shear loads produce
direct stresses due to bending in the booms and skin and shear stresses in the skin.
Suppose that the shear flows in the skin adjacent to the rth boom of cross-sectional

(a) ( b)
Fig. 9.50 (a) Elemental length of shear loaded open section beam with booms; (b) equilibrium of boom
element.