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 263
that a 52 and f3sz ( a 51 and f3s 1) do not depend on the individual
values of(! and feu but only on the ratio elfcu·
(b) No, it is theoretically incorrect to use only the two variables (efculfy;
and dlh). The reason is as follows. It is true that as long as the
quantity Q/ylfcu is kept constant, then neither the magnitude nor the
direction of the vector a 52 + Psz can be affected by the value of /y
itself-see eqns (7.1-7) and (7.1-8). However, a close examination
of eqn (7 .1-9) shows that the xl h value at which the vector a 52 + Psz
reaches its maximum length does depend on the value of /y.
Therefore, in Fig. 7.1-7, the position of the point C2 will vary with /y
(even though the quantity ef/fcu is kept constant). Hence curve II,
and for the same reason curve III, will both vary with /y itself.
Comments on Part (b)
We have seen that it is theoretically impossible to use the two variables
(Q/ylfcu; d/h) to define a column interaction curve. However, provided we
restrict the /y values to those of the common grades of reinforcing steel,
then the column curves do become practically independent of/y as Q/ylfcu is
kept constant. Indeed, for a given value of Q/ylfcu' the curves for /y = 250
N/mm 2 and/y = 460 N/mm 2 are quite close to each other (see Fig. 7.1-11).
Of course it is important that the student should know the basic
principles (see Section 7.1), so that he understands the limitations of the
column curves in the I.Struct.E. Manual [5]. For example, Fig. 7.1-11
shows the interaction curves for a rectangular column section for which d/ h
= 0.85 and ef/fcu = 0.80. Specifically, the details for the curves in Fig.
7.1-11 are:
(1) /y = 250 N/mm 2 (BS 4449 mild steel bars)Jcu = 25 N/mm 2 , (! = 8.0%
so that ef/fcu = 0.80.
1.0
'
ci/h=0·85
0.4
0.2
Fig. 7.1-11