Page 333 - Aircraft Stuctures for Engineering Student

314 Open and closed, thin-walled beams

Fig. 9.34 Twisting of a rectangular section beam.

the shear stress system given by Eq. (9.49). Due to yb the axial displacement of corner 1
in the web is ybb/2 in the positive z direction while in the cover the displacement is
yaa/2 in the negative z direction. Note that the shear strains yb and ya correspond to
the shear stress system produced by a positive anticlockwise torque. Clearly the total
axial displacement of the point 1 in the web and cover must be the same so that
ba0 babe a
-- -+^lYb-=- --^la-
2L 2 2L 2
from which

The shear strains are obtained from Eq. (9.49) and are
T T
^la==' yb =-

Displacement due to rotation
I_
a012
7-

Displacement due to shear strain
(a) Web (b) Cover
Fig. 9.35 Displacements due to twist and shear strain.