F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

264 Eccentrically loaded columns and slender columns
(2) /y = 460 Nlmm 2 (BS 44491BS 4461 high yield bars), feu= 40 Nlmm 2 ,
(! = 6.96% so that efyl!cu = 0.80.
(3) /y = 835 Nlmm 2 (BS 4486 high tensile bars), feu = 50 Nlmm 2 , (! =
4. 79% so that e[yl/cu = 0.80.
(4) /y = 1080 Nlmm (BS 4486 high tensile bars)./cu = 40 Nlmm 2 , (! =
2.96% SO that (!/yl/cu = 0.80.
Comparing Fig. 7.1-11 with the column curve for ef/fcu = 0.80 in Fig.
7.3-2, it can be seen that the I.Struct.E. Manual's curve is essentially the
avera~e of the top two curves in Fig. 7.1-11 (i.e. for /y = 250 and 460
Nlmm ). It is thus clear that the I.Struct.E. Manual's column charts are
intended for the normal range of reinforcement bars. Applying the
manual's design charts to very high strength bars (e.g. BS 4486 high tensile
prestressing bars) can lead to structural collapse. Of course, BS 4486's high
tensile bars, for use in prestressed concrete, are designated by their
nominal proof stress and tensile strength. Hence the use of/y for these bars
is not really proper, though it is hoped that Fig. 7.1-11 helps to give a clear
message to the student.
7.2 Effective column height (BS 8110)
The behaviour of a column is much dependent on its effective height [6, 7],
or effective length, le where le is related to the elastic critical buckling load
[6] Ncr by
(7.2-1)
in which EI is the flexural rigidity in the plane of buckling. The ratio lei / 0 of
the effective height to the clear height of the column between end
restraints depends on the end conditions. For a braced column, i.e. a
column whose ends are restrained against lateral displacements (but not
necessarily against rotations), we recall from structural mechanics [6] that,
under ideal conditions, the ratio lell 0 is theoretically equal to 0.5 when the
ends are fully restrained against rotation; when the braced column is
pinned at the ends, lello is theoretically equal to one. However, as
mentioned above, these values of lei 1 0 refer to the ideal rather than the real
end conditions; for example, it is known that the fully encastre effect
hardly exists in practice [6]. In a framed structure, the lello ratio depends
on the stiffness of the column relative to those of the beams framing into it.
In practice, for a braced column with the so-called 'fixed' ends, the lei 10
ratio is often nearer to 0.75 than to 0.5.
For practical design, BS 8110 recommends that the effective height le of
a braced column may be obtained from the equation
(7.2-2)
where 1 0 is the clear height between end restraints, and P is given in Table
7.2-1.