Page 393 - Aircraft Stuctures for Engineering Student

374 Stress analysis of aircraft components

Example 10.2 that for moments about the centre of symmetry

Therefore, taking moments about the centre of symmetry

100 x lo3 x 600 = 2qI2 x 600 x 300 + 2(qI2 - 43.8)600 x 300
+ (912 - 76.65)600 x 600 + (q12 + 32.85)600 x 600

from which
qI2 = 62.5N/mm
whence

q23 = 19.7N/mm, q34 = -13.2N/mm, q45 = 19.7N/mm
q56 = 63.5 N/mm, q61 = 96.4 N/mm

so that the solution is almost identical to the longer exact solution of Example 10.2.
The shear flows q12, q23 etc. induce complementary shear flows qI2, q23 etc. in the
panels in the longitudinal direction of the beam; these are, in fact, the average
shear flows between the two sections considered. For a complete beam analysis
the above procedure is applied to a series of sections along the span. The distance
between adjacent sections may be taken to be any convenient value; for actual
wings distances of the order of 350mm to 700mm are usually chosen. However,
for very small values small percentage errors in P,,l and P2,2 result in large percentage
errors in AP. On the other hand, if the distance is too large the average shear flow
between two adjacent sections may not be quite equal to the shear flow midway
between the sections.

Aircraft fuselages consist, as we saw in Chapter 7, of thin sheets of material stiffened
by large numbers of longitudinal stringers together with transverse frames. Generally
they carry bending moments, shear forces and torsional loads which induce axial
stresses in the stringers and skin together with shear stresses in the skin; the resistance
of the stringers to shear forces is generally ignored. Also, the distance between
adjacent stringers is usually small so that the variation in shear flow in the connecting
panel will besmall. It is therefore reasonable to assume that the shear flow is constant
between adjacent stringers so that the analysis simplifies to the analysis of an idealized
section in which the stringers/booms carry all the direct stresses while the skin is
effective only in shear. The direct stress carrying capacity of the skin may be allowed
for by increasing the stringer/boom areas as described in Section 9.9. The analysis of
fuselages therefore involves the calculation of direct stresses in the stringers and the
shear stress distributions in the skin; the latter are also required in the analysis of
transverse frames. as we shall see in Section 10.4.