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)

r
r-b--j_l
d'
• A~ •• T
Principles of column interaction diagrams 253
h
Cross
section
(a)
Fig. 7.1-5
Strain
distribution
(b)
Concrete stress
distribution
(c)
(7.1-15)
where the compressive stress f~ 1 in the reinforcement corresponds to the
strain e~ 1 in Fig. 7.1-5(b):
f~t x-d' xlh-d'/h
0.0035 = -x- = xl h (7.1-16)
For any assigned value of xlh, therefore, a.1 and f3st can be computed,
since for a given column section the quantities A~ 1 /bh, d' lh, feu and the
steel properties are known. As shown in Fig. 7 .1-6, the effect of A~ 1 is
represented by the vector a 51 + Pst, which is inclined at a constant angle to
the a-axis:
. 1. . f -t[Pst (eqn 7.1-15)]
me mat10n o vector = tan
asl (eqn 7.1-14)
= tan -t [ ~ - ~· J (7.1-17)
In Fig. 7 .1-6, therefore, ALHJK is the interaction curve for the column
section with reinforcement at both faces. As before, E. has been taken as
200 kN/mm2 and the reinforcement stress/strain curve assumed linear
between /~ 1 = ±0.87/y where /y is 460 N/mm2. (See Example 7.1-4 for
other stress/strain relations.) For any point on this curve, a and {3 are,
respectively aconc + as2 + asl and Pconc + Psz + f3st· In fact, adding eqns
(7.1-1)(7.1-5) and (7.1-12), we have
N = 0.405/cubx + ~~~A~1 + fszAsz (7.1-18)
Similarly, adding eqns (7.1-2), (7.1-6) and (7.1-13), we have
M = 0.203fcubx(h- 0.9x) + f~tA~t[g-
d'] - fszAsz[g- dz]
(7.1-19)