Aluminium Design and Construction John Dwight

9.6.7 Torsional buckling slenderness
The following is the rigorous procedure for obtaining the slenderness
parameter � needed for entering the selected buckling curve. An alternative
and quicker method, available for certain common shapes, involves the use
of empirical formulae (Section 9.6.10). Under the rigorous procedure we take:
(9.10)
t �=k�
� where t =slenderness parameter based on pure torsional buckling about
the shear centre S, and k=torsion/flexure interaction factor (Section 9.6.8).
The slenderness � parameter t may be determined using the following
general expression, which is valid for aluminium:
(9.11)
where �=St Venant torsion factor, I p =polar inertia about shear centre S,
H=warping factor, and l=effective buckling length.
Here �, Ip and H may be based on the gross section, and can be
found with the aid of Chapter 10. The effective length l is less critical
than with column buckling, and is normally taken equal to the actual
buckling length L. A lower value may be justified if there is significant
warping restraint at the ends, but not if the ends are welded.
The warping factor H for type-R sections is always zero, or virtually
so. It is therefore seen from the previous equation that � t for these is
independent of length and becomes:
(9.12)
The torsional stability of type-R sections can be much improved by
providing liberal bulb and/or fillet material, since this increases �.
Fillet size is less important for non-R shapes, because these have warping
resistance to improve their stability.
9.6.8 Interaction factor
The interaction factor k depends on the symmetry of the section (Figure
9.5) and should be found as follows, using the gross section in every case:
1. Bisymmetric sections. k=1
2. Radial-symmetric sections. k=1
3. Skew-symmetric sections. k=1
4. Mono-symmetric sections, k can be read from Figure 9.10 or else calculated
from the corresponding formula:
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(9.13)