Aluminium Design and Construction John Dwight

of ss, but from a start-point O now located at an outer edge of the
section, as shown, and with the trial axis B taken at the upstream end
of the web. A quantity w mb is introduced, analogous to w m , but based
on rotation about B and defined as follows for the element r:
(10.33)
in which d b is defined as for the type 1 monosymmetric case (Section
10.5.7). The constant term w ob is found from the requirement that the
value of w mb for the web must be zero, since this element does not
warp, giving:
(10.34)
The summation is for the elements on the direct route from O as far as
the web (which is element s), excluding any side-branches.
The distance e of the shear-centre S from the trial position B is then
given by the following expression:
(10.35)
in which a, c and I ss are defined in the same way as for type 1, with the
summation made for the elements to the right of ss only. A positive
value obtained for e indicates that S lies above B, and a negative one
below.
Having located S, the warping factor H can be calculated from the
standard expression (10.29), in which the summation can be conveniently
made for the elements on one side of ss and then doubled. The quantities
d and w m , which relate to rotation about the true axis S, should be
found as in Section 10.5.3. In applying equation (10.26) to obtain w m , we
can take w o as follows:
(10.36)
The summation covers the same elements as for expression (10.34).
This correctly brings the warping in the web to zero. Note that, for
sections of this type, w o is more conveniently found thus, rather than
using equation (10.28).
Alternatively H may be obtained from the following formula, which
is equivalent to (10.29) and sometimes more convenient:
The summation is for the elements on one side of ss only.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
(10.37)