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Steel Designers' Manual - 6th Edition (2003)
528 Members with compression and moments
height. Assuming the presence of a plastic hinge immediately below the haunch,
the design requirement is to ensure stability up to the formation of the collapse
mechanism.
According to clause 5.3.2 of BS 5950: Part 1, torsional restraint must be provided
no more than D/2, where D is the overall column depth, measured along the column
axis, from the underside of the haunch.This may conveniently be achieved by means
of the knee brace arrangement of Fig. 18.14. The simplest means of ensuring
adequate stability for the region adjacent to this braced point is to provide another
torsional restraint within a distance of not more than Lm, where Lm is taken as equal
to Lu obtained from clause 5.3.3 as
L
u
38ry
£
2 2
[ fc/ 130 + ( py/ 275) ( x/
36)
]
1
2
(18.11)
Noting that the mean axial stress in the column fc is normally small, that py is around
275 N/mm 2 for S275 steel and that x has values between about 20 and 45 for UBs,
gives a range of values for Lu/ry of between 30 and 68. Placing a second torsional
restraint at this distance from the first therefore ensures the stability of the upper
part of the column.
Fig. 18.14 Effective torsional restraints
Below this region the distribution of moment in the column normally ensures that
the remainder of the length is elastic. Its stability may therefore be checked using
the procedures of section 18.5. Frequently no additional intermediate restraints are
necessary, the elastic stability condition being much less onerous than the plastic
one.
Equation (18.11) is effectively a fit to the limiting slenderness boundary of the
column design charts 3 that were in regular use until the advent of BS 5950: Part 1,
based on the work of Horne, 4 which recognized that for lengths of members
between torsional restraints subject to moment gradient, longer unbraced lengths
could be permitted than for the basic case of uniform moment. Equation (18.11)
may therefore be modified to recognize this by means of the coefficients proposed
by Brown. 5 Figure 18.15 illustrates the concept and gives the relevant additional formulae.
For a 533 ¥ 210 UB82 of S275 steel for which x = 41.6 and assuming fc =
15 N/mm 2 , the key values become: