Page 511 - Aircraft Stuctures for Engineering Student

492 Structural constraint

that the torsion-bending constant I? calculated about the shear centre S is I?=
as t sin2 2a. The thickness t is constant throughout.
P.11.12 The thin-walled section shown in Fig. P.11.12 consists of two semi-
circular arcs of constant thickness t. Show that the torsion bending constant about
the shear centre S is

t'

Fig. P.11.12
P.11.13 A thin-walled, I-section beam, of constant wall thickness t, is mounted as
a cantilever with its web horizontal. At the tip, a downward force is applied in the
plane of one of the flanges, as shown in Fig. P. 1 1.13. Assuming the necessary results
of the elementary theory of bending, the St. Venant theory of torsion and the Wagner
torsion-bending theory, determine the distribution of direct stress over the cross-
section at the supported end.
Take
E/G = 2.6, P =200N
h =75mm, d=37.5mm
t =2.5mm, 1 =375mm
2
Ans. -ol =03 = 108.9N/mm2, 06 = -05 = 18.9N/mm ,
CT~ =a4 = ~~224 = 0

tf
Fig. P.ll .I 3