Aluminium Design and Construction John Dwight

Figure 10.3 Plastic bending with axial load. NA=neutral axis. Hatched areas carry the
moment.
A similar approach is used for the other symmetrical case, namely
when M acts about an axis perpendicular to ss (Figure 10.3(b)). In defining
region 2, it is merely necessary that, apart from having the right area (to
carry � m P), it should be so located that regions 1 and 3 are of equal area.
Figure 10.3(c) shows an example of unsymmetrical bending, where
the moment M acts about an axis mm inclined at � to the major principal
axis of a bisymmetric section, again in combination with P. In this case,
the modified plastic modulus, which we denote by S pm , is a function of
P and �. Two parameters (w, z) are now needed to define the neutral axis
nn, as shown, and these may be found from the requirements that: (1)
region 2 must have the right area, and (2) the values of S x and S y provided
by regions 1 and 3 (hatched areas) must satisfy equation (10.4). Having
thus located nn, and the extent of the three regions, the required value
of S pm is found by using an expression equivalent to equation (10.5).
An identical approach can be used for a skew-symmetric profile,
where again two parameters are sufficient to define nn. The same principles
apply to other shapes (monosymmetric, asymmetric), but the working
becomes more laborious.
10.2.4 Plastic modulus of the effective section
The plastic modulus should when necessary be based on an effective
section, rather than the gross one, to allow for HAZ softening at welds
and for holes (Section 8.2.4). In considering the HAZ effects, alternative
methods 1 and 2 are available (Section 6.6.1).
In method 1, we take a reduced or effective plate thickness kz2t in
each nominal HAZ region, instead of the actual thickness, and calculate
S accordingly.
Method 2 is convenient for a section just containing longitudinal welds.
For bending about an axis of symmetry, it consists of first obtaining S for
the gross section, and then deducting an amount yAz (1-kz2 ) at each HAZ due
to the ‘lost area’ there, where Az is the nominal softened area and y the
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