Aluminium Design and Construction John Dwight

(7.9a)
(7.9b)
The strain gradient case is always more favourable than that of uniform
compression (�=1), because the peak strain only arises at one point in
the width of the element, namely at edge 1. The strain at this point at
the onset of buckling is higher than it would be for a uniformly compressed
element of the same ß. Also the buckled shape is asymmetric, with the
maximum depth of buckle occurring nearer to edge 1 than edge 2.
The elastic critical stress � cr , which now refers to the stress at edge
1, is a function of �. It may be calculated [25] from the standard expression
(7.2) with K found from the following empirical formulae (plotted in
figure 7.9), which are close enough to the exact theory:
1>�>0 K=4{1+(1-�) 1.5 ) (7.10a)
�