Aluminium Design and Construction John Dwight

estimate for the resistance M c of the section, since element X can just
reach a stress p ° before it buckles. Line 1 in the figure, on which equation
(8.2) is based, approximately represents the stress pattern for this case
when failure is imminent. (We say ‘approximately’ because it ignores
the rounded knee on the stress-strain curve.)
Now consider semi-compact sections generally, again taking the type
of beam in Figure 8.3 as an example. For these, the critical element X
will have a ß-value somewhere between ß f and ß s , and some degree of
plastic straining can therefore take place before failure occurs. This
leads to an elasto-plastic stress pattern at failure such as line 2 in the
figure, corresponding to a bending moment in excess of the value Zp ° .
In the extreme case when element X is almost fully compact (ß only just
greater than ß f ) the stress pattern at failure approaches line 3,
corresponding to an ultimate moment equal to the fully compact value
Sp ° which can be as much as 15% above that based on Z. It is thus seen
that the use of the value Zp ° tends to underestimate M c , increasingly so
as ß for the critical element approaches ß f .
It is therefore suggested that interpolation should be used for semicompact
sections, with M c found as follows:
(8.4)
This expression, in which the ß’s refer to the critical element, will produce
higher values of M c closer to the true behaviour.
8.2.7 Semi-compact section with tongue plates
Figure 8.4 shows a section with tongue plates, in which the d/t of the web
(between tongues) is such as to make it semi-compact when classified in
Figure 8.4 Elastic-plastic method for beam with tongue plates.
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