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)

BS 8110 design charts-their construction and use 97
section are likewise defined on the basis of the 0.0035 concrete strain and
the 0.87 /y steel stress.
The steel ratio e( = Asfbd) for the balanced section is, from eqn (4.3-6),
(b I d) k.Jcu 0.0035 (4 5 1)
(J a ance = 0.87 /y 0.0035 + Ey • -
where Ey is the design yield strain 0.87/yl £ 5 • Suppose, for example, feu= 40
N/mm2 and/y = 460 N/mm2; from Fig. 4.4-4, kdcu = (0.396)(40) = 15.84
N/mm2; from Fig. 4.5-1, 0.87/y = 400 N/mm2, fy = 0.002. Therefore
()(balanced) = e~~ 4 )(o.003~·0J 3 g_0020) .= 0.0252
For e below the balanced value the beam is under-reinforced, and the
ultimate moment of resistance is given by eqn (4.3-1):
i.e.
[
k2(0.87/y)]
Mu = A5 (0.87/y) 1 - (J k.Jcu d
Mu [ 0.87/yk2 ]
bd2 = 0·87/y(J 1 - kdcu (J (4.5-2)
600
N
E
E
-z
500
400
300
Stress
0·87fy
-
2
Es=200kN/~~"
Strain
High yield steel
. 2 400
fy = 460 N/mm
Ill
Ill
Cll
.!= 200
II)
Mild steel fy = 250 N/mm 2
~-----___::--------1217·5
Cll
Cll
-II) 100
0 0·001 Q-002
Steel Strain
Q-003
Fig. 4.5-l Design stress/strain curves for ultimate limit state-BS SUO