Aluminium Design and Construction John Dwight

10.3.5 Elastic section modulus
The elastic modulus Z, which relates to moment resistance based on an
elastic stress pattern, must always be referred to a principal axis of the
section. It is taken as the lesser of the two values I/y c and I/y t , where I
is the inertia about the axis considered, and y c and y t are the perpendicular
distances from the extreme compressive and tensile fibres of the section
to the same axis. HAZ effects, the presence of holes and local buckling
should be allowed for, when necessary, by basing I and hence Z on the
effective section.
10.3.6 Radius of gyration
This quantity r is required in calculations for overall buckling. It is
simply taken equal to �(I/A) where I is the inertia about the axis considered
and A the section area. It is generally based on the gross section, but
refer to Section 9.5.4 for sections containing very slender outstands.
10.4 TORSIONAL SECTION PROPERTIES
10.4.1 The torque-twist relation
The torsional section properties �, I p , H and � x are sometimes needed
when checking overall member buckling. They should be based on the
gross cross-section.
In order to understand the role of � and H, it is helpful to consider
the simple form of the torque-twist relation for a structural member,
when subjected to an axial torque T:
(10.14)
where �=rotation at any cross-section, �=rate of change of � with respect
to distance along the member (‘rate of twist’), G=shear modulus of the
material, and �=St Venant torsion factor.
This equation would be valid if there were no restraint against warping,
the idealized condition whereby the torque is applied in a way that
leaves the end cross-sections free to distort longitudinally, as illustrated
for a twisted I-section member in Figure 10.7(a).
Figure 10.7 Torsion of an I-beam: (a) ends free to warp; (b) warping prevented.
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