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Steel Designers' Manual - 6th Edition (2003)
Ê M
Ë M
x
ˆ
¯
z1
z2
y
Ê M ˆ
+ Á ˜
Ë M ¯
rxry � 1
(18.10)
In Equation (18.10) the denominators in the two terms are a measure of the moment
that can be carried in the presence of the axial load F.
For fabricated sections, the principles of plastic theory may be applied first to
locate the plastic neutral axis for a given combination of F, M x and M y and then to
calculate M rx and M ry. This is manageable for uniaxial bending – F and M x or F and
M y – but it is tedious for the full three-dimensional case and some use of approximate
results 1 may well be preferable.
18.6 Cross-section classification under compression and bending
It is assumed in the discussion of the use of the BS 5950: Part 1 procedure that the
designer has conducted the necessary section classification checks so as to ensure
that the appropriate values of M cx, M cy, etc. are used. When the tabulated data of
Reference 1 are being employed, any allowances for non-compactness are included
in the listed values of M cx and M cy, but only if P cx and P cy have been taken from the
strut tables rather than the beam-column tables will these contain any reduction.
The reason is that for pure compression the stress pattern is known, whereas under
combined loading the requirement may be to sustain only a very small axial load;
to reduce P cx and P cy on the basis of uniform compression in each plate element of
the section is much too severe. For simplicity, section classification may initially be
conducted under the most severe conditions of pure axial load; if the result is either
plastic or compact nothing is to be gained by conducting additional calculations with
the actual pattern of stresses. However, if the result is a non-compact section, possibly
when checking the web of a UB, then it is normally advisable for economy of
both design time and actual material use to repeat the classification calculations
more precisely.
18.7 Special design methods for members in portal frames
18.7.1 Design requirements
Special design methods for member in portal frames 525
Both the columns and the rafters in the typical pitched roof portal frame represent
particular examples of members subject to combined bending and compression.
Provided such frames are designed elastically, the methods already described
for assessing local cross-sectional capacity and overall buckling resistance may
be employed. However, these general approaches fail to take account of some
of the special features present in normal portal frame construction, some of
which can, when properly allowed for, be shown to enhance buckling resistance
significantly.
When plastic design is being employed, the requirements for member stability
change somewhat. It is no longer sufficient simply to ensure that members can safely