Page 496 - Aircraft Stuctures for Engineering Student

11.5 Constraint of open section beams 477

Fig. 11.36 Calculation of axial constraint shear flows.

Finally, the axial constraint shear flow, qr, is obtained from Eq. (11.57), namely

At any section z, qr is proportional to 2&t ds and is computed as follows. Refer-
ring to Fig. 11.36, 2AR = 240 - 2Afi so that in flange 12

Hence

h+d
[2A~tdS=t hd hd -
[ 4 2 (h+Zd)"]
so that
d38 h'd't
qr,l = 0 and qr,2 = -E-
dz3 4(h + 2d)
Similarly
" - 4(h hZd2t 2d) 1
+

whence
d38 h2d2t d38 h'd't
qr:z=-E~ 4(h+2d)' qr~=E~4(,3+2d)
Note that in the above d38/& is negative (Eq. (viii)). Also at the mid-point of
the web where s2 = h/2, qr = 0. The distribution on the lower flange follows from
antisymmetry and the distribution of qr around the section is of the form shown in
Fig. 11.37.
The spanwise variation of qr has the same form as the variation of Tr since
d38
Tr = -ErR -
dz3