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)

Chapter 7
Eccentrically loaded columns and
slender columns
Preliminary note: Readers interested only in structural design to BS 8110
may concentrate on the following sections:
(a) Section 7.2: Effective column height (BS 8110).
(b) Section 7.3: Eccentrically loaded short columns (BS 8110).
(c) Section 7.5: Slender columns (BS 8110).
7.1 Principles of column interaction diagrams
The analysis of reinforced concrete members under combined bending and
axial load [1-4] may be based on the same assumptions as those in the
general theory for ultimate flexural strengths in Chapter 4. The member is
considered to be at the ultimate limit state of collapse when the concrete
strain at the more highly compressed face reaches a specified value Eeu,
which is taken as 0.0035 in current British practice.
In the design of eccentrically loaded columns, engineers make extensive
use of design charts called column interaction diagrams. Readers interested
only in the construction of such diagrams may move direct to Example
7 .1-6, omitting the rest of this section.
To obtain an insight into the properties of column interaction diagrams
and the principles governing their construction, we shall first consider a
plain concrete section subjected simultaneously to an axial load N and a
bending moment M. The section (Fig. 7.1-1(a)) is at incipient failure, with
strain and stress distributions as in Figs 7.1-1(b) and (c). The depth de of
the concrete stress block is equal to 0.9x for 0.9x :5 h. (What happens
when 0.9x > h will be explained in Example 7.1-5.) From the equilibrium
condition,
N(concrete) = 0.45feubde = 0.405feubx (7.1-1)
M(concrete) = N[~- ~e] (by taking moments about
the mid-depth of the section)
= 0.225feubde(h - de)
= 0.203feubx(h - 0.9x) (7.1-2)