Aluminium Design and Construction John Dwight

Usually the conditions are such as to provide some degree of restraint
against warping, leading to an increase in the torque needed to produce
the same total twist. Figure 10.7(b) shows an extreme case in which the
warping at the ends is completely prevented. In any case where warping
is restrained, referred to as ‘non-uniform torsion’, the torque-twist relation
becomes:
(10.15)
where = third derivative of �, E=elastic modulus of the material, and
H=warping factor.
The quantity is always of opposite sign to , so that the EH-term
in fact represents an increase in T as it should. The section property �
roughly varies with thickness cubed, whereas H is proportional to
thickness. The contribution of the EH-term therefore becomes increasingly
important for thin sections.
Equation (10.15) also applies when the torque varies along the length,
which is what happens in a beam or strut that is in the process of
buckling by torsion. However, ‘type-R’ sections composed of radiating
outstands (Figure 9.7) are unable to warp. For these, H is therefore zero
and equation (10.14) is always valid.
10.4.2 Torsion constant, basic calculation
The torsion � constant for a typical non-hollow section composed of
flat plate elements (Figure 10.8(a)) can be estimated by making the
following summation for all of these:
(10.16)
where b and t are the width and thickness of an element . For a curved
element, it is merely necessary to measure b around the curve. If the
Figure 10.8 Sub-division of the section for finding �.
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