Aluminium Design and Construction John Dwight

The summation in the first term is made for the elements up to, but
not including the one considered (element r). In a bifurcating section,
it is made for the (r–1) elements on the direct route from O, ignoring
side-branches. The first term is zero for the first element.
The value of w o defines the datum plane, from which z is measured.
It can be determined from the requirement that the weighted average
of w m for the whole section should be zero (�btw m =0). The value of w °
is therefore given by:
(10.28)
in which the summation is for all the elements in the section, and A is
the section area. For bisymmetric, radial-symmetric and type 1
monosymmetric sections, the start-point O, which is taken at the point
of symmetry, is also a point of zero warping, giving w ° =0. In all other
cases, w ° is non-zero and must be calculated.
Figure 10.16 compares the warping of an I-section (bisymmetric) and
a zed (skew-symmetric). With the zed it is seen that the web, including
the point of symmetry O, warps by a uniform non-zero amount.
10.5.4 Formula for the warping factor
The warping factor H can be calculated from the following standard
expression, valid for any of the section types covered below:
(10.29)
in which the summation is for all the plate-elements comprising the
section. For any element b, t and d are as defined in Figure 10.15, and
w m is found as in Section 10.5.3.
Figure 10.16 Variation of the unit warping w in typical bisymmetric and skew-symmetric
sections.
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