Aluminium Design and Construction John Dwight

Figure 8.6 Asymmetric bending cases.
Examples of this are shown in Figure 8.6:
(a, b) bisymmetric or monosymmetric section with inclined moment;
(c) skew-symmetric section;
(d) asymmetric section.
For (a) and (b), the essential difference from symmetric bending is that
the neutral axis (axis of zero stress) no longer coincides with the axis
mm of the applied moment M. The same applies to (c) and (d), unless
mm happens to coincide with a principal axis of the section. Also, for
any given inclination of mm the plastic and elastic neutral axes will be
orientated differently.
In classifying the section, the parameter � for any element under
strain gradient should be based on the appropriate neutral axis, which
properly relates to the inclination of mm. This should be the plastic
neutral axis for the fully-compact check (Section 10.2.2), or the elastic
one for the semi-compact check (see 2 below).
Having classified the cross-section, a simple procedure is then to use
an interaction formula, such as that given in BS.8118, which for
bisymmetric and monosymmetric sections may be written:
where: M=moment arising under factored loading,
�=inclination of mm (figure 8.6),
M cx , M cy =moment resistance for bending about Gx or Gy,
� m =material factor (see 5.1.3).
(8.6)
This expression may also be used for skew-symmetric and asymmetric
profiles, changing x, y to u, v. It gives sensible results when applied to
semi-compact and slender sections of conventional form (I-section,
channel), but can be pessimistic if the profile is non-standard. In order
to achieve better economy in such cases, the designer may, if desired,
proceed as follows.
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