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)

Design formulae and procedure-BS 8110 simplified stress block 121
where {Jb :::; 0.9, so that
K' :::; 0.156 (see Comments below)
Comments on eqn (4.7-5)
Equations (4.7-4) and (4.7-5) are based on the condition that xld :::;
({Jb - 0.4), so that xld = 0.5 when {Jb = 0.9. When the simplified stress
block is used, BS 8110 restricts xl d to not exceeding 0.5. This means that in
using eqns (4.7-4) and (4.7-5), {Jb is not to be taken as greater than 0.9
whatever the actual amount of moment redistribution. When {Jb has the
maximum permissible value of 0.9, eqn (4.7-5) gives K' = 0.156 (agreeing
with eqn 4.6-4). Therefore, provided {Jb is taken as not exceeding 0.9, eqn
(4. 7-5) is valid for all% moment redistribution from 0 to 30% (30% being
the maximum permitted by BS 8110).
Example 4. 7-1
Using eqn (4.7-5), calculate the value of K' for the following percentages
of moment redistribution:
(a) 0-10%;
(b) 20%;
(c) 30%.
SOLUTION
For a given percentage of moment redistribution, it is seen from eqn
(4.7-2) that
(a)
(b)
(c)
{J _ 100 - (% of moment redistribution)
b - 100
0-10% moment redistribution. The corresponding {Jb values are
{Jb = 1 for zero moment redistribution
{Jb = 0.9 for 10% moment redistribution
In using eqn (4.7-5), {Jb is not to be taken as exceeding 0.9.
Substituting {Jb = 0.9 into eqn (4.7-5) gives K' = 0.156.
20% moment redistribution. From eqn (4.7-2), {Jb = 0.8. From
eqn (4.7-5), K' = 0.132.
30% moment redistribution. From eqn (4.7-2), {Jb = 0.7. From
eqn (4.7-5), K' = 0.104.
Example 4. 7-2
The bending moment at a beam section is M. Show that, for the whole
range of moment redistribution from 0 to 30%, the lever arm z is given by
the following BS 8110 formulae:*
~ = 0.5 + ~( 0.25 - o~) if M:::; Mu of eqn (4.7-4) (4.7-6)
• The zld factors in Table 24 of the I.Struct.E. Manual [14] are based on these equations,
which are given in BS 8110: Clause 3.4.4.4.