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)

Principles of column interaction diagrams 261
1.983, (a, {3) falls on the a axis and remains there for all larger values
of x/h. Note that the points (a,{3) for xlh > 1.111 in fact fall within
the region excluded by the BS 8110 line eminlh = 0.05, referred to in
Example 7.1-4(b). Therefore, cases where xlh > 1.111 are of little
practical interest.
Example 7.1-6
In this section, our emphasis has been on the fundamental principles, the
aim being to obtain an insight into the properties of column interaction
diagrams. The worked examples have been designed with the above aim in
mind. (Indeed, Example 7.1-3 has been adapted from a past examination
paper of Cambridge University.) However, if our aim is merely the
straightforward construction of column interaction diagrams for use as
routine design charts, then we can use a very simple procedure, such as
that explained below.
SOLUTION
For the typical section in Fig. 7.1-10, it is immediately seen that the direct
compression is
N = 0.45fcubdc + ~~~A~l - fs2As2 (7.1-20)
Taking moments about the mid-depth of the section,
M = 0.45fcubdc(~- ~c) +~~~A~~(~- d')
+ fs2As2(~- d2) (7.1-21)
where de= 0.9x and compressive stresses in the reinforcement are taken as
positive.
Next proceed as follows.
Step I
Assume a value for xlh.
Column section
(a)
Forces
(b)
Fig. 7.1-10