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)

254 Eccentrically loaded columns and slender columns
H
0 0·10 012 0·14
Fig. 7.1-6 Column interaction diagram (A~ 1 /bh = 1%, Adbh = 1 %.feu=
40 N/mm 2 ,fy = 460 N/mm 2 , d 2/h = 0.15, d' /h = 0.15)
where the column reinforcement stresses /~ 1 and fs2 are conventionally
taken as positive if they are compressive. These two equations represent
the equilibrium conditions for a column section reinforced at both faces.
Example 7.1-l
The details of a column section are: b = 300 mm, h = 400 mm, A~ 1 /bh =
1%, As21bh = 1%, d'lh = d2/h = 0.15, feu= 40 N/mm 2 and /y = 460
N/mm 2 (notation as in Figs 7.1-5 and 7.1-6).
(a) Determine the direct load N and its eccentricity e for which a
balanced failure occurs.
(b) Determine N and e for which the steel A~ 1 reaches 0.87/y in
compression simultaneously as the concrete compressive strain
reaches 0.0035.
(c) If the column is subjected to an eccentric load whose magnitude is
gradually increasing, determine the range of eccentricities for which
both the reinforcements A~ 1 and A 82 would have reached 0.87/y when
the concrete compressive strain reaches 0.0035.
SOLUTION
(a)
From statement (d) following eqn (7.1-11), the balanced condition
occurs if xlh = 0.541. The (N,M) combination should therefore
correspond to the point H in Fig. 7 .1-6.
By measurement,
a(H) = 0.219; /J(H) = 0.126