Page 504 - Aircraft Stuctures for Engineering Student

References 485

The direct stress distribution is therefore linear around the base of the column (see
Fig. 11.42) with
a,, = a,, = 20.0N/mm2

a,, = or, = -68.0N/mm2

11.5.4 Shear flow due to Mr

The self-equilibrating shear flow distribution, qr, produced by axial constraint is
given by

(see derivation of Eq. (I 1.27))

From the last term on the right-hand side of Eqs (1 1.76)
dUr - dkfr ~AR
- --
-
dz dz rR
From Eq. (1 1.74)

d28
Mr = -ErR-
dz2
so that

(see Eq. (11.58))

Hence

and

(as before)

7.-
rences
1 Argyris, J. H. and Dunne, P. C., The general theory of cylindrical and conical tubes under
torsion and bending loads, J. Roy. Aero. SOC., Parts I-IV, Feb. 1947, Part V, Sept. and Nov.
1947, Part VI, May and June 1949.
2 Megson, T. H. G., Extension of the Wagner torsion bending theory to allow for general
systems of loading, The Aeronautical Quarterly, Vol. XXVI, Aug. 1975.
3 Vlasov, V. Z., Thin-walled elastic beams, Israel Program for Scientific Translations,
Jerusalem, 196 1.