Aluminium Design and Construction John Dwight

1. Fully compact sections. The limiting value of M is found using expression
(8.1) with the plastic modulus S replaced by a value S m which is a
function of the inclination of mm (angle �). Refer to Section 10.2.2.
2. Semi-compact and slender sections. The applied moment M is resolved
into components M cos � and M sin � about the principal axes, the
effects of which are superposed elastically. A critical point Q is chosen
and the section is adequate if at this position (Figure 8.6(a))
(8.7)
where x, y are the coordinates of Q, the I’s are for the effective
section, and the left-hand side is taken positive. The inclination � of
the neutral axis nn (anti-clockwise from Gx) is given by:
(8.8)
The same expressions are valid for skew-symmetric and asymmetric
shapes, if x, y are changed to u, v. Sometimes the critical point Q is
not obvious, in which case alternative calculations must be made for
possible locations thereof and the worst result taken. It is obviously
important to take account of the signs of the stresses for flexure
about the two axes.
Figure 8.7 gives a comparison between predictions made with the simple
British Standard rule (expression (8.6)) and those obtained using the
more accurate treatments given in 1 and 2 above. The figure relates to a
particular form of extruded shape and shows how the limiting M varies
Figure 8.7 Asymmetric bending example. Comparison between BS 8118 and the more
rigorous treatment of Section 8.2.9, covering the fully-compact case (FC) and the semicompact
case (SC).
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