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)

Derivation of design formulae 101
0·0035
.....----~~
t
X
t
Fig. 4.6-3
Therefore, for x/d values not exceeding 0.64, tension reinforcement of[y =
460 N/mm 2 (or less) will reach the design strength 0.87/y at the ultimate
limit state.
Example 4.6-2
The design formulae for doubly reinforced beams (eqns 4.6-6 to 4.6-8)
assume that the compression reinforcement reaches the design strength
0.87/y at the ultimate limit state. Determine the limiting value of the d' lx
and d' /d ratios for this to be possible.
SOLUTION
Equations (4.6-6) to (4.6-8) are based on the condition that x/d = 0.5;
that is, the provision of the area A~ of compression steel to the balanced
singly reinforced section is matched by the provision of an additional area
As(actct) of tension reinforcement such that the tensile force 0.87/yAs(actct) is
equal to the compressive force 0.87/yA~, so that x/d remains at 0.5.
Figure 4.6-4 shows that for xld = 0.5, the strain E~ in the compression
reinforcement is
X- d'
E~ = -x-(0.0035)
Fig. 4.6-4