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Steel Designers' Manual - 6th Edition (2003)
load
Effective lengths 413
Fig. 15.6 Elastic critical load curves for a member subject to flexural–torsional buckling
relative to one another but are able to rotate freely. Compression members in actual
structures are provided with a variety of different support conditions which are
likely to be less restrictive in terms of translational restraint, giving fixity in position,
with or without more restriction in terms of rotational restraint, giving fixity
in direction.
The usual way of treating this topic in design is to use the concept of an effective
column length, which may be defined as ‘the length of an equivalent pin-ended
column having the same load-carrying capacity as the member under consideration
provided with its actual conditions of support’. This engineering definition of effective
length is illustrated in Fig. 15.7, which compares a column strength curve for a
member with some degree of rotational end restraint with the basic curve for the
same member when pin-ended.
In determining the column slenderness ratio the geometrical length, L, is replaced
by the effective length, L E. Values of effective length factors k = L E /L for a series
of standard cases are provided in BS 5950: Part 1, BS 5400: Part 3, etc.; Fig. 15.8 illustrates
typical values. When compared with values given by elastic stability theory, 2
these appear to be high for those cases in which reliance is being placed on externally
provided rotational fixity; this is in recognition of the practical difficulties of
providing sufficient rotational restraint to approach the condition of full fixity. On
the other hand, translational restraints of comparatively modest stiffness are quite
capable of preventing lateral displacements. A certain degree of judgement is
required of the designer in deciding which of these standard cases most nearly
matches his arrangements. In cases of doubt the safe approach is to use a high
approximation, leading to an overestimate of column slenderness and thus an
underestimate of strength. The idea of an effective column length may also be used
as a device to deal with special types of column, such as compound or tapered
members, the idea then being to convert the complex problem into one of an equivalent
simple column for which the basic design approach of the relationship between
compressive strength and slenderness may be employed.