Structural Analysis II Section I.7
**
SECTION
I.7 Torsion -
Shear
Flow
Relations in
Multiple-Cell
Thin-
Wall
Closed
Sections
**

The torsional moment in terms of the internal shear flow is
simply

** Derivation **
For equilibrium to be maintained at a exterior-interior wall (or web)
junction point
(point m in the figure) the shear flows entering should be equal to those
leaving the junction.

Summing the moments about an arbitrary point O, and assuming clockwise direction
to be positive, we obtain

NOTE: It is important to realize that point "O" can be anywhere in space,
interior or
exterior of the cross-section. As long as we can determine the area
enclosed by the **ends** of each web and point **O**, we can relate the
torque to the
shear flow in the web and the enclosed area.

The moment equation above can be simplified to

Notice that in this equation the shear flow of the interior wall is not explicitly shown because it is a function of the shear flows in the exterior walls. Also
notice that the terms in the right hand side of the equation are independent of
moment point "O". This is a very important fact, and should be kept in mind
when
solving single- or multi-cell, closed, thin-walled sections under pure torsion.

To Index Page of
Pure Torsion
To Section I.6
To Section
I.8