Page 436 - Aircraft Stuctures for Engineering Student

10.5 Cut-outs in wings and fuselages 417

200 mm
I Station
3000 Is

1500 rnm
R
e
_I Fm;t F I 10 kN m a war r
w

(a) ( b)
Fig. 10.54 Differential bending of front spar.

and the flanges would be unloaded. However, the removal of the lower skin panel in
bay @ results in a torsionally weak channel section for the length of bay @ which
must in any case still transmit the applied torque to bay (iJ and subsequently to
the wing support points. Although open section beams are inherently weak in torsion
(see Section 9.6), the channel section in this case is attached at its inboard and
outboard ends to torsionally stiff closed boxes so that, in effect, it is built-in at
both ends. We shall examine the effect of axial constraint on open section beams
subjected to torsion in Chapter 11. An alternative approach is to assume that the
torque is transmitted across bay @ by the differential bending of the front and
rear spars. The bending moment in each spar is resisted by the flange loads P as
shown, for the front spar, in Fig. 10.54(a). The shear loads in the front and rear
spars form a couple at any station in bay @ which is equivalent to the applied
torque. Thus, from Fig. 10.54(b)
800s = 10 x 106Nmm

i.e.
S = 12500N

The shear flow q1 in Fig. 10.54(a) is given by
12 500
41 = - 62.5 N/mm
=
200
Midway between stations 1500 and 3000 a point of contraflexure occurs in the front
and rear spars so that at this point the bending moment is zero. Hence
200P = 12 500 x 750 N lzl~ll

so that
P = 46 875N