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Steel Designers' Manual - 6th Edition (2003)
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Effective lengths 415
Of fundamental importance when determining suitable effective lengths is the
classification of a column as either a sway case for which translation of one end
relative to the other is possible or a non-sway case for which end translation is prevented.
For the first case, effective lengths will be at least equal to the geometrical
length, tending in theory to infinity for a pin-base column with no restraint at its
top, while for the non-sway case, effective lengths will not exceed the geometrical
length, decreasing as the degree of rotational fixity increases.
For non-standard cases, it is customary to make reference to published results
obtained from elastic stability theory. Provided these relate to cases for which buckling
involves the interaction of a group of members with the less critical restraining
the more critical, as illustrated in Fig. 15.9, such evidence as is available suggests
that the use of effective lengths derived directly from elastic stability theory in conjunction
with a column design curve of the type shown in Fig. 15.3 will lead to good
approximations of the true load-carrying capacity.
For compression members in rigid-jointed frames the effective length may, in both
cases, be directly related to the restraint provided by the surrounding members
by using charts presented in terms of the stiffness of these members provided in
Appendix E of BS 5950: Part 1. Useful guidance on effective column lengths for a
variety of more complex situations is available from several sources. 2–4
When designing compression members in frames configured on the basis of
simple construction, the use of effective column lengths provides a simple means
of recognizing that real connections between members will normally provide some
degree of rotational end restraint, leading to compressive strengths somewhat in
excess of those that would be obtained if columns were treated as pin-ended. If axial
load levels and unsupported lengths change within the length of a member that is
continuous over several segments, such as a building frame column spliced so as to
act as a continuous member but carrying decreasing compression with height or a
compression chord in a truss, then the less heavily loaded segments will effectively
restrain the more critical segments.
Even though the distribution of internal member forces has been made on the
assumption of pin joints, some allowance for rotational end restraint when designing
the compression members is therefore appropriate. Thus the apparent contradiction
of regarding a structure as pin-jointed but using compression member
effective lengths that are less than their actual lengths does have a basis founded
upon an approximate version of reality. Figure 15.10 resents results obtained from
elastic stability theory for columns continuous over a number of storeys which show
Fig. 15.9 Restraint to critical column segment from adjacent segments