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Two features
of the section are used to determine the shape factor for bending, the
overall area of the section, A, and the way the material is distributed about
an axis of interest - the geometric moment of inertia (or second moment of
area) I.
In terms of these two quantities: fB
= 4pI/A2, for
the bending response of the shape about an axis normal to the section. For
a circular cross-section of radius, r, A = pr2
, and I
= (pr4/4) so that the shape factor
for bending is fB = 1.
The
twisting (or torsional) response of a section will depend upon a torsional
shape factor, fT = 2pK/A2. Here K is the "torsional moment
of area" about an axis normal to the section. For a cylinder K = pr4/4, and so fT
= 1
for this section.
The shape factors for bending and twisting are shown
for several shapes in the diagram. The superscript, e, is to indicate that
the material's elastic response is of interest. For tubes the values of I
and K are obtained by subtracting the value for the "missing" section
from that for the full section. |
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