Aluminium Design and Construction John Dwight

post (Section 8.6.4) or by some other means. Not so doing will reduce the
resistance of an end bay to LT buckling, since some lateral movement of
the compression flange over the point of support will then become possible
(accompanied by distortion of the web). For a beam that is free to buckle
over its whole length, the absence of end-posts can be allowed for by
increasing l by an amount 2D above the value that would otherwise apply.
(c) Cantilevers
The LT buckling of cantilever beams is a complicated subject, and beyond
the scope of this book. The designer is referred to BS.8118, where it will
be seen that the effective length for such a member can be anywhere
between 0.5L and 7.5L, or he/she may refer to Trahair’s book [27].
8.7.8 Beams of varying cross-section
The above treatment of LT buckling has assumed the member to be of
uniform section over the length of the bay considered. We now consider
the case where the section is non-uniform, either with a tapering depth
or else with a varying flange area. A simple procedure for such beams
is to employ the same basic equation (8.30), but with the relevant quantities
evaluated as follows:
1. S is based on the cross-section at X, the point in the bay where the
maximum moment acts.
2. In selecting the appropriate buckling curve, p 1 in equation (8.31) is
based on the section at X.
3. In entering the buckling curve to obtain p b , the slenderness � is obtained
according to Section 8.7.5 using the section properties at X, but with
the effective length l found as in (4) below.
4. l is taken as the value found in Section 8.7.7 for a beam of uniform
section multiplied by a factor K:
(a) When the variation in section simply consists of a variation in
depth, along the length of the beam, the flange areas remaining
constant, it is accurate enough to take K=1.
(b) If, however, the flange areas vary along the length, K (� 1) should
be found thus:
K=1.5–0.5R f
(8.38)
where R f is the ratio of minimum to maximum flange area along the
length, based on the average for the two flanges when these differ.
5. M – in equation (8.30) is taken as the maximum moment arising in the
bay (under factored loading).
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