Page 371 - Aircraft Stuctures for Engineering Student

352 Open and closed, thin-walled beams

Calculate and sketch the distribution of shear flow due to a vertical shear force S,
acting through the shear centre S and note the principal values. Show also that the
distance & of the shear centre from the nose of the section is tS = 1/2( 1 + a/b).
Am. q2 = q4 = 3bSY/2h(b + a), q3 = 3SY/2h. Parabolic distributions.

P.9.15 Show that the position of the shear centre S with respect to the intersection
of the web and lower flange of the thin-walled section shown in Fig. P.9.15, is given
by
5's = -45a/97, 7s = 46a/97

Fig. P.9.15

P.9.16 Figure P.9.16 shows the regular hexagonal cross-section of a thin-walled
beam of sides a and constant wall thickness t. The beam is subjected to a transverse
shear force S, its line of action being along a side of the hexagon, as shown.
Find the rate of twist of the beam in terms oft, a, S and the shear modulus G. Plot
the shear flow distribution around the section, with values in terms of S and a.

Fig. P.9.16