Aluminium Design and Construction John Dwight

10.5.6 Skew-symmetric sections
Figure 10.17(c) shows a skew-symmetric profile. For such a section, S
again lies at the point of symmetry, and we take the start-point O for
numbering the elements at the same position. But this is not now a
point of zero warping and w o must be evaluated using equation (10.28),
enabling w m to be found for each element. H is then calculated using
equation (10.29). The summations in equations (10.28) and (10.29) may
conveniently be made for the elements in one half of the section (as
shown numbered), and then doubled.
Skew-radial-symmetric sections are treated similarly (Figure 10.17(d)),
the summations being made for the elements in one arm, and then
multiplied by n (the number of arms).
10.5.7 Monosymmetric sections, type 1
The shear centre S always lies on the axis of symmetry ss for a
monosymmetric section, but not generally at the same position as the
centroid G. Before H can be calculated it is necessary to locate S, which
involves taking a trial centre-of-twist B at a suitable point on ss.
Firstly, we consider monosymmetric sections in which ss cuts across
the section at its midpoint (Figure 10.18), referred to as type 1. For
these, we take B at the point of intersection with ss, as shown, which
coincides with the start-point O for the numbering of the elements. A
quantity w b is introduced, analogous to w s , but based on rotation about
the trial axis B instead of the true axis S (which has yet to be located).
For element r we thus have:
(10.30)
where d b is the perpendicular distance from B to the median line of an
element, using an equivalent sign convention to that employed for d
(Section 10.5.3). The summation in the first term is for elements lying
above ss, up to but not including the one considered. The location of S is
then given by:
Figure 10.18 Monosymmetric section, type 1.
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