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)

252 Eccentrically loaded columns and slender columns
B
0·10
Fig. 7.1-4 Column interaction diagram (A.2/bh = l%,fcu = 40N/mm 2 ,/y =
460N/mm 2 , d 2/h = 0.15)
opposite direction for higher values of xlh. Irrespective of the value
of xl h, however, the inclination of the vector is constant, being given
by eqn (7.1-11).
(f) When the axial force and bending moment acting on the column
section are such that (a,/3) falls on the point B, the concrete
maximum compressive strain reaches 0.0035 simultaneously as the
reinforcement reaches the tensile design strength; this mode of failure
is referred to as a balanced failure. For (N,M) combinations
represented by points that lie on the curve above B, the reinforcement
does not reach the design strength 0.87fy in tension when the
concrete compression strain reaches 0.0035; similarly, for (N,M)
combinations that lie on AFB, the reinforcement reaches 0.87fy in
tension before the concrete compressive strain reaches 0.0035. It is
thus seen that, for a given column section, whether the balanced
condition is achieved at failure depends on the loading rather than (as it
does in a beam) on the amount of the reinforcement.
Equations (7.1-5) to (7.1-11) refer to an area As 2 of reinforcement
remote from the face at which the concrete compressive strain is a
maximum. If instead we have an area A~ 1 of reinforcement near the
compression face, as in Fig. 7.1-5, the reader should verify that
N(A~t) = A~d~t
M(A~t) = A~d~~(~- d')
Or, in dimensionless form,
a 1
= N(A~t) = (A~t)f~l
5
fcubh bh feu
(7.1-12)
(7.1-13)
(7.1-14)