Page 387 - Aircraft Stuctures for Engineering Student

368 Stress analysis of aircraft components

Fig. 10.5 Modification of moment equation in shear of closed section beams due to boom load.
The shear flow distribution in an open section beam is now obtained using Eq. (9.75)
in which S, is replaced by Sx,w and Sy by Sy,w from Eqs (10.15). Similarly for a closed
section beam, S, and Sy in Eq. (9.80) are replaced by Sx,w and Sy,w. In the latter case
the moment equation (Eq. (9.37)) requires modification due to the presence of the
boom load components P,,, and PY,,. Thus from Fig. 10.5 we see that Eq. (9.37)
becomes
ds m m
SxVO - SyCO = f qbp 7 -t 2Aqs,0 - px,r'% + Py& ( 10.16)
r=l r=l
Equation (10.16) is directly applicable to a tapered beam subjected to forces posi-
tioned in relation to the moment centre as shown. Care must be taken in a particular
problem to ensure that the moments of the forces are given the correct sign.

Example 10.2
The cantilever beam shown in Fig. 10.6 is uniformly tapered along its length in both x
and y directions and carries a load of 100 kN at its free end. Calculate the forces in the

Y

(a)
Fig. 10.6 (a) Beam of Example 10.2; (b) section 2 m from built-in end.