Aluminium Design and Construction John Dwight

10.5.9 Asymmetric sections
Before starting to find the position of S and the value of H for an
asymmetric section (Figure 10.20), certain preliminary calculations are
needed, namely to locate the centroid G, obtain the orientation of the
principal axes Gu and Gv, and determine I uu and I vv (as covered in
Section 10.3.2). All the elements of the section must be numbered, starting
from O at an outside edge as shown. It does not matter if an element
straddles the uu or vv axis.
In order to locate S we introduce a quantity w g for each element,
analogous to w s , but based on rotation about G. For the rth element, w g
is found as follows (Figure 10.21):
(10.38)
where d g is perpendicular distance from G to the median line of the
element, using an equivalent sign convention to that for d in Section
10.5.3. The coordinates U, V of S (referred to axes Gu, Gv) are found as
follows, the summations being made for all elements:
Figure 10.20 Asymmetric section.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
(10.39a)
(10.39b)