Aluminium Design and Construction John Dwight

Note that when P is tensile, the first term in equation (9.21) should
be put equal to zero. Also, if the section is of a type not prone to LT
buckling, p b is put equal to M C /S where M c is as in check B.
9.7.5 Alternative treatment (P+uniaxial M)
The checks A and B tend to be oversafe when applied to fully-compact
profiles, and for these a more realistic result can be obtained by using
a direct plastic calculation instead:
(9.22a)
(9.22b)
where p o is the limiting material stress for bending (Section 5.3), and S p
is a suitably reduced value for the plastic modulus that allows for the
presence of P (Section 10.2.3). S p is different for the two checks.
Figure 9.17 compares results thus obtained with those given by the
British Standard rule. It covers check A for a fully-compact box section,
and shows how the reduced moment resistance of the section (in the
presence of axial load) varies with P. It is seen that the British Standard
rule can underestimate by as much as 20%.
9.7.6 Interaction formulae (P+biaxial M)
We now consider the case when the applied moment acts about an axis
mm inclined � at to the major principal axis xx (Figure 9.18). Section
classification follows the same principles as those given in Section 9.7.3,
a single classification being needed which corresponds to the particular
Figure 9.17 Reduced moment resistance of a fully-compact square box cross-section in
the presence of axial load: (1) BS 8118 rule (equation 9.18); (2) Direct plastic calculation
(equation (9.22a)).
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