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)

250 Eccentrically loaded columns and slender columns
0·5
0·1
0·02 D-04 0·06
f3 [= fc~bh 2]
Fig. 7.1-2 Column interaction diagram-plain concrete section
to the strain E 52 in Fig. 7.1-3(b). (Note: According to current convention,
reinforcement stresses in columns are designated positive when compressive.)
The contribution to the bending moment about the mid-depth of the
section is
M(Asz) = -Aszfsz(~- dz) (7.1-6)
where the negative sign is used because the compressive steel force Asz!sz
produces a moment acting in an opposite sense to that produced by the
concrete stress block. In dimensionless form, these equations are
_ N(AsZ) _ (Asz)fsz (7.1-7)
asz - f. bh - bh f.
cu cu
(7.1-8)
For a given column section, the quantities A 52/bh, d 2/h and feu are
known. Therefore a 52 and f3s 2 are completely defined by the steel stress fsz,
which for a given steel depends only on the strain E52 • From Fig. 7.1-3(b),
Esz d2 - (h - x) xlh - (1 - dzlh) ( 7 . 1 _ 9 )
0.0035 = x = xlh
That is, e 52 and hence a 52 and f3s 2 are completely defined by the xlh ratio.
For a given column section, therefore, the a 52 and f3s2 ratios can be
computed for a range of values assigned to xlh. When these ratios are
superimposed on aconc and f3conc• we obtain Fig. 7 .1-4. The figure shows
that, for any specified value of xlh, the effect of the reinforcement is
represented by the vector a 52 + f3s2 where