Page 497 - Aircraft Stuctures for Engineering Student

478 Structural constraint

Fig. 11.37 Distribution of axial constraint shear flows.

giving

qr = -- “r 2ARtds from Eq. (11.57)
rR 0
Hence for a given value of s, ($2A~tds), qr is proportional to Tr (see Fig. 11.33).

11.5.1 Distributed torque loading

We now consider the more general case of a beam carrying a distributed torque load-
ing. In Fig. 11.38 an element of a beam is subjected to a distributed torque of intensity
T,(z), a torque per unit length. At the section z the torque comprises the St. Venant
i.e.
torque Tj plus the torque due to axial constraint Tr. At the section z + Sz the torque
increases to T + ST(= Tj + STj + Tr + STr) so that for equilibrium of the beam
element
Tj + STj + Tr + STr + T~(z)SZ Tj - Tr = 0
-
or
-T~(z)SZ STj + STr = ST
=
. \\

\
T+ 6T
= TJ + 6TJ + T,. +

Fig. 11.38 Beam carrying a distributed torque loading.