Page 320 - Aircraft Stuctures for Engineering Student

9.4 Shear of closed section beams 301

Fig. 9.23 Shear of closed section beams.
Let us suppose that we choose an origin for s where the shear flow has the unknown
value qs,o. Integration of Eq. (9.33) then gives

or

We observe by comparison of Eqs (9.35) and (9.34) that the first two terms on the
right-hand side of Eq. (9.35) represent the shear flow distribution in an open section
beam loaded through its shear centre. This fact indicates a method of solution for a
shear loaded closed section beam. Representing this 'open' section or 'basic' shear
Aow by qb, we may write Eq. (9.35) in the form

4.7 = qb + qs,O (9.36)
We obtain qb by supposing that the closed beam section is 'cut' at some convenient
point thereby producing an 'open' section (see Fig. 9.24(b)). The shear flow

Fig. 9.24 (a) Determination of q,,o; (b) equivalent loading on 'open'section beam.