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)

274 Eccentrically loaded columns and slender columns
T
I
l
(a)
Triangular
curvature
distribution
(b)
Rectangular
curvature
distribufion
(c)
Fig. 7.4-1
Mt = Mi + Neadd (7.4-1)
where Neadd is the additional moment due to the slender column effect, and
the deflection eadd is often referred to as the additional eccentricity-to
distinguish it from the initial eccentricity e = M/ N. Suppose the applied
load N is progressively increased until failure occurs; it is instructive to
superimpose the N - Mt curve on the column interaction curve, as shown
in Fig. 7.4-2.
There are three cases to consider:
(a)
If the column is short, the deflection eadd is small and hence the
additional moment Neadd is negligible compared with the initial
moment Mi. As the load N is increased, the total moment Mt remains
sensibly constant at the initial value Mr-see line AB in Fig. 7.4-2.
Failure occurs when the (N,Mt) combination, as represented by the
point B, falls on the column interaction curve. This type of failure is
called a material failure; at every stage of the loading from A until B,
the column is stable.
(b) If the column is slender, the deflection eadd is no longer small and the
additional moment Neadd (eqn 7.4-1) becomes significant compared
with Mi; according to current design thinking, the additional moment
should be considered in design if the effective height/depth ratio is
not less than 15. For a slender column, Mt = Mi + Neada-See line
AC in Fig. 7.4-2. Failure occurs when the (N,Mt) combination as
represented by the point C falls on the column interaction curve. At
every stage of the loading from A until C, the column is stable; the