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