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)

(c)
e = 200 mm. Therefore
e/h = 200/500 = 0.4
Principles of column interaction diagrams 259
Draw the line elh = 0.4 (Note: e/h =MINh= {3/a) to intersect the
interaction curve K'Q2H' at 0 3. By measurement, a(Q3) = 0.245.
Therefore
N = (0.245)( 40)(150)(500)(10-3) = 735 kN
(d) feu = 30 N/mm2 and fy = 410 N/mm2. Equations (7 .1-7) to (7 .1-11)
show that:
( 1) The direction of the vector a,;2 + Ps2 is independent of feu and fy.
(2) Corresponding to each xlh value, the length of the vector is
proportional to fs2lfeu' i.e. Ests21feu·
(3) The maximum length of that vector (which occurs at fs2 =
0.87fy) is proportional to fylfeu·
(4) The xlh value at whichfs2 reaches 0.87fy depends onfy (see eqn
7.1-9).
Using the above information, the reader should verify that if feu were
30 N/mm2 andfy 410 N/mm2, then the steel stressf.2 would reach the
design stress of 0.87fy ( = 357 N/mm2 in tension) at xlh = 0.563 and at
this value off.2, a.2 = -0.119 and f3s2 = 0.042. Hence show that the
curve C3B', shown as the dotted line in Fig. 7.1-8, is the new
interaction curve.
By measurement, the a value at the intersection of this dotted
curve C 3 B' with the line e/h = 0.3 is 0.24. Therefore
N = 0.24feubh = 0.24(30)(150)(500)(10- 3 ) = 540 kN
Example 7.1-4
In constructing the column interaction diagram in Fig. 7 .1-6, the
stress/strain relation was taken as that of BS 8110, as reproduced here in
Fig. 3.2-1(b), i.e. stresses varied linearly with strains for stresses between
±0.87fr
(a) How will the construction be affected if the steel stress/strain curve
has an arbitrarily specified shape?
(b) If, as stipulated in BS 8110: Clause 3.8.2.4, an eccentricity not less
than emin = 0.05h must be used in design, how would the column
interaction diagram be affected?
SOLUTION
(a) Arbitrarily specified stress/strain curve. For each value assigned to xlh
the steel strain £82 is computed as usual from eqn (7.1-9). The stress
f.2 , instead of being E.e.2 , is now read off the stress/strain curve. The
a.2 and {3.2 values are then computed as usual from eqns (7.1-7) and
(7.1-8), and curve ABCD in Fig. 7.1-6 constructed. Depending on
the shape ofthe given stress/strain curve, there may not be a distinct
point (B) corresponding to the balanced failure. Similar remarks
apply to the construction of curve ALHJK in Fig. 7.1-6.
(b) Effect of emin = 0.05h. The effect of stipulating a minimum