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)

Additional moment due to slender column effect 275
N
«add
0 A
~
Total moment Mt
Fig. 7.4-2 Slenderness effect on column capacity-axial-load and end moments
(c)
final collapse at point Cis again due to material failure. Note that as a
result of the slenderness effect,
N(point C) < N(point B)
i.e. the slenderness effect reduces the load-carrying capacity.
If the column is very slender, the peak load may be reached before a
material failure occurs-see line AD in Fig. 7.4-2. In this case, if the
applied load N is not reduced at point D, the column will quickly
collapse; such a failure is called instability failure.
Figure 7.4-2 refers to a column under an axial load N and constant end
moments Mi. For a column under an eccentric load N, the respective N-
Mt relations up to collapse are as shown in Fig. 7.4-3.
OB: material failure of short column
OC: material failure of slender column
OD: instability failure of (very) slender column
Reinforced concrete columns in practical structures are rarely slender
enough for instability failure to occur; therefore what the designer needs is
a method which is sufficiently accurate for material failures and conservative
(though not necessarily accurate) for instability failures [16].
For a column subjected to combined axial load and bending, it was
pointed out earlier that the additional eccentricity eadd can be calculated
easily (see Problems 7.6 and 7.7) provided the column is elastic and
homogeneous. Near the ultimate condition, a reinforced concrete column
is not elastic, is subject to creep and to cracking if tension occurs on the
convex side of the column. Thus a conventional elastic analysis is not
directly applicable (nor is a conventional plastic analysis). It turns out that,
for design purpose, it is better to work from curvatures. Returning to Fig.