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)

so that
Design formulae and procedure-BS 8110 simplified stress block 123
z = d[1 - 0.45(.8b - 0.4)]
Eliminating (.Bb - 0.4) from the expressions for z and K', we have
i.e.
(~Y - (~) + 1.111K' = o
~ = 0.5 + ~(0.25- ~~) forM> Mu of eqn (4.7-4)
where K' is given by eqn (4.7-5).
Note that BS 8110 restricts moment redistribution to not exceeding
30%.
Design procedure for rectangular beams (BS 8110/I.Struct.E. Manual)
The design procedure below is that of the I.Struct.E. Manual [14].
Comments have been added to explain the derivation of the formulae and
the technical background. As explained at the beginning of this section, the
procedure is valid for up to 30% moment redistribution. For flanged
beams, see Section 4.8.
Consider again the beam section in Fig. 4.6-1(a). Suppose the design
bending moment is M. Proceed as follows.
Step I
Calculate Mu for concrete:
Mu = K'fcubd 2 (4.7-8)
where K' is obtained from Table 4.7-1.
Table 4.7-1 K' factors for beams [14]
% moment redistribution 0-10 15 20 25 30
Values K' 0.156 0.144 0.132 0.119 0.104
Comments
Example 4.7-1 explains how the K' factor in Table 4.7-1 can be derived.
See also eqn (4.7-5).
Step2
If the design moment M :5 Mu of Step 1, the tension reinforcement As is
given by
A= M
s (0.87/y)z (4.7-9)
where z is obtained from Table 4.7-2.
Comments
(a) The formula As= M/(0.87/yz) follows from Fig. 4.6-1(b); it is seen