Aluminium Design and Construction John Dwight

where � 1 is again found from equation (7.5), or Figure 7.6, but now
putting:
(7.13)
If an element has edge welds, a reduced thickness k z t is taken in each
HAZ region in the same way as for uniform compression (i.e. the areas
X in the figure are removed).
7.3.4 Outstands under strain gradient, general description
Now we turn to outstands, for which there are two possible cases of
strain gradient (Figure 7.12):
Case T peak compression is at the tip;
Case R peak compression is at the root.
In either case, the more heavily compressed edge is called edge 1 as
before. And again we use � (=e 2 /e 1 ) to specify the degree of strain gradient.
The buckling of an outstand is mainly governed by what happens at
the tip. Therefore, case T is only slightly more favourable than uniform
compression, since the effect of � is merely to decrease the stress in the
relatively stable material close to the supported edge. But case R is
clearly more favourable, because � now directly affects the tip stress
which is what matters.
The elastic critical stress � cr (occurring at edge 1) for a simply
supported outstand under strain gradient may be found from the
standard equation (7.2), taking a suitable value for K. Figure 7.13 shows
how K varies with � for the two cases, the curves being plotted from
the following empirical expressions which give a good approximation
to the rigorous values:
Case T K=0.41 for 1 > � > 0.5
=0.50–0.18� for � < 0.5 (7.14a)
Case R K=0.41+1.3(1-�) 4 (7.14b)
Figure 7.12 Outstands under strain-gradient. Cases T and R.
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