Aluminium Design and Construction John Dwight

8.2.2 Section classification
The discussion in Section 8.2.1 relates to beams that are thick enough
for local buckling not to be a factor. We refer to these as fully compact.
For thinner beams (semi-compact or slender) premature failure occurs
due to local buckling of plate elements within the section, causing a
decrease in M c below the ideal value Sp ° .
The first step in determining M c is to classify the section in terms of
its susceptibility to local buckling (see Chapter 7). To do this the
slenderness ß (=b/t or d c /t) must be calculated for any individual plate
element of the section that is wholly or partly in compression, i.e. for
elements forming the compression flange and the web. Each such element
is then classified as fully compact, semi-compact or slender by comparing
its ß with the limiting values ß f and ß s as explained in Section 7.1.4.
The least favourable element classification then dictates the classification
of the section as a whole. Thus, in order for the section to be classed as
fully compact, all the compressed or partly compressed elements within
it must themselves be fully compact. If a section contains just one slender
element, then the overall section must be treated as slender. The
classification is unaffected by the presence of any HAZ material.
In classifying an element under strain gradient, the parameter ? (Section
7.3) should relate to the neutral axis position for the gross section. In
checking whether the section is fully compact, this should be the plastic
(equal area) neutral axis, while for a semi-compact check it should be
the elastic neutral axis (through the centroid).
8.2.3 Uniaxial moment, basic formulae
First we consider cases when the moment is applied either about an
axis of symmetry, or in the plane of such an axis, known as symmetric
bending (Figure 8.2). For these the calculated moment resistance Mc of
the section is normally taken as follows:
Fully compact section M c =Sp ° (8.1)
Semi-compact or slender section M c =Zp ° (8.2)
where p ° =limiting stress for the material (Section 5.2), S=plastic section
modulus, and Z=elastic section modulus. By using these formulae we
Figure 8.2 Symmetric bending.
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