Page 315 - Aircraft Stuctures for Engineering Student

296 Open and closed, thin-walled beams

Using the relationships of Eqs (9.11) and (9.12), i.e. aMy/az = S, etc., this expression
becomes

(SXZXX - SyZxy)
-- - + (SyZyy - SxZxy) Y
az zx,zyy - z:y zxxzyy - Ey
Substituting for &Jaz in Eq. (9.22) gives

(9.32)

Integrating Eq. (9.32) with respect to s from some origin for s to any point around the
cross-section, we obtain

(9.33)

If the origin for s is taken at the open edge of the cross-section, then q = 0 when s = 0
and Eq. (9.33) becomes

For a section having either Cx or Cy as an axis of symmetry Zxy = 0 and Eq. (9.34)
reduces to

Example 9.4
Determine the shear flow distribution in the thin-walled 2-section shown in Fig. 9.19
due to a shear load Sy applied through the shear centre of the section.

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2
Fig. 9.19 Shear-loaded Z-section of Example 9.4: