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)

96 Reinforced concrete beams-the ultimate limit state
0·4Sfcu
I ~ \"f-u•.. u;n I
r
IEcui
~O·OOJS
(k2= 0·451
T --:tx
o.g x *
i
·-:----·-·-·- J
X
Stress block
(a)
Strain distribution
(b)
Fig. 4.4-5 Simplified design stress block for ultimate limit state-BS 8110
i.e.
Clearly
ktfcubx = (0.45fcu)(b)(0.9x)
= 0.405fcubx
k, = 0.405
4.5 BS 8110 design charts--their construction and
use
The general theory in Section 4.2 and the equations in Section 4.3 become
directly applicable to British design practice if the ultimate concrete strain
Ecu is taken as 0.0035 and the characteristic ratios k 1 and k 2 are taken as
those associated with the stress block in Fig. 4.4-3 or Fig. 4.4-5. Of
course, the design stress/strain curves for the reinforcement are to be
derived from Fig. 3.2-l(b), which is equally applicable to mild steel
(characteristic strength /y = 250 N/mm 2 ), and high yield steel (/y = 460
N/mm 2 ). With the partial safety factor Ym taken as 1.15 (see Table 1.5-2),
the design stress/strain curves are then as shown in Fig. 4.5-1.
In Section 4.3, the balanced steel ratio was defined on the basis of the
yielding of the steel (eqn 4.3-6). In design, the definition is based not on
the actual yield stress of the reinforcement but on the attainment of the
design strength 0.87 /y, as shown in the inset diagram in Fig. 4.5-1, where
/y is the characteristic strength of the reinforcement. Therefore, a balanced
section is defined for design purposes as one in which the steel stress
reaches the design strength 0.87/y simultaneously as the concrete reaches
the strain 0.0035. The under-reinforced section and the over-reinforced