Aluminium Design and Construction John Dwight

where b, t=element width and thickness, and x E , y E =coordinates of the
midpoint E of the element.
C is obtained as follows depending on the element’s orientation:
where X, Y are the projections of the mid-line of the element on either axis.
In applying equations (10.22) and (10.23), the following sign convention
must be used, depending on the sense of the applied moment:
1. X and xE are always taken plus.
2. Axis Gy is directed positive toward the compression side of the
section. (The direction selected for Gx is immaterial.)
3. g is taken positive if S lies on the compression side of G, and negative
if on the tension side.
4. Y is taken positive if on proceeding along the element y increases
with x (as in Figure 10.13(b)), and negative if it decreases.
Note that ßx can be positive or negative, depending on the attitude of the
section and the sense of the moment. For a given section in a given
attitude the sign of ßx reverses if the applied moment changes from sagging
to hogging. Thus for the section in the attitude shown in Figure 10.13(a),
Figure 10.13 Notation used in finding ß x .
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