Page 374 - Aircraft Stuctures for Engineering Student

Problems 355

P.9.21 A uniform, thin-walled, cantilever beam of closed rectangular cross-
section has the dimensions shown in Fig. P.9.21. The shear modulus G of the top
and bottom covers of the beam is 18 000 N/mm2 while that of the vertical webs is
26 000 N/m' .
The beam is subjected to a uniformly distributed torque of 20 Nm/mm along its
length. Calculate the maximum shear stress according to the Bredt-Batho theory
of torsion. Calculate also, and sketch, the distribution of twist along the length of
the cantilever assuming that axial constraint effects are negligible.

Am. T~~ = 83.3N/mm2, 0 = 8.14 x lop9

1.2mm
1
I -- t 2.1 mm
2.1 mm
250 mm
1 1 11.2 mm

Fig. P.9.21

P.9.22 A single cell, thin-walled beam with the double trapezoidal cross-section
shown in Fig. P.9.22, is subjected to a constant torque T = 90 500 N m and is con-
strained to twist about an axis through the point R. Assuming that the shear stresses
are distributed according to the Bredt-Batho theory of torsion, calculate the distribu-
tion of warping around the cross-section.
Illustrate your answer clearly by means of a sketch and insert the principal values of
the warping displacements.
The shear modulus G = 27 500 N/mm2 and is constant throughout.
AFZS. Wi = -Wg = -0.53m, W2 = -W5 = O.O5mm, W3 = -W4 = 0.38m.
Linear distribution.