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)

276 Eccentrically loaded columns and slender columns
N
Total moment Mt
Fig. 7.4-3 Slenderness effect on column capacity-eccentric load
7.4-1(a), the additional eccentricity eadd depends on the curvature llr of
the column and on the distribution of this curvature-see curvature-area
theorem in Section 5.5. Cranston [16] of the Cement and Concrete Association
has shown that, for a reinforced concrete column at the ultimate
limit state, the curvature at the critical section could be assumed to depend
only on the depth of the column section and the effective height/depth
ratio:
(7.4-2)
where le is the effective height of the column and h is its depth in the
appropriate plane of bending. The curvature distribution is not known, but
may reasonably be assumed to lie somewhere between the triangular
distribution which implies only one critical section (Fig. 7 .4-1(b )), and the
rectangular distribution which implies an infinite number of critical
sections (Fig. 7.4-1(c)). Fortunately, the transverse deflection is insensitive
to the curvature distribution; in fact Example 5.5-1 shows specifically
that
eadd (triangular distribution) = ~; (,~)
eadd (rectangular distribution) = [: (,~)
eadd (parabolic distribution) = ~. 2 6 (,~)
eadd (sinusoidal distribution) = 1 ~(1._)
7l rm
It is therefore reasonable to assume, as Cranston has suggested [16], that