Page 471 - Aircraft Stuctures for Engineering Student

452 Structural constraint

Fig. 11.7 Equilibrium of boom element.

obtain expressions for the warping displacement and the distributions of boom stress
and load. Thus, for the equilibrium of an element of the top right-hand boom shown
in Fig. 11.7

(a,+~&')B- aZB+qa&-qb&=O

i.e.

(11.13)

Now
aw
az = E - (see Chapter 1)
a2
Substituting for a, in Eq. (1 1.13) we obtain

a2W
BE-+q,-qb=o (1 1.14)
aZ2
Replacing 4, and qb from Eqs (1 1.12) gives

d2W 8Gtbt, T (bt, - atb)
BE-- w = --
89 bt, + atb ab (bta + atb)
or
a2w 2 T (bt, - atb)
-- pw=-- (11.15)
a9 abBE (bt, + atb)