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)

Moment redistribution-the fundamental concepts 137
over-reinforced
Balanced
M
Vr
Fig. 4.9-4
In current British design practice, the bending moments in the members of
a continuous structure are determined by elastic analysis. BS 8110: Clause
3.2.2 then permits the elastic moments to be redistributed. The aim of such
moment redistribution is to distribute bending moments away from peak
moment regions, such as beam-column joints or supports of continuous
members. This reduces the congestion of reinforcement bars at such
regions and makes the structural members easier to detail and construct.
Of course, certain conditions must be observed. Firstly, equilibrium must
be maintained; this means that where the bending moments are reduced at
some sections they will have to be appropriately increased at others. In
other words, moment redistribution may lead either to an increase or a
decrease in the design bending moment at a given section. For the purpose
of certain design formulae (e.g. eqn 4.9-3 below), BS 8110 formally
defines the moment redistribution ratio {Jb as
= moment at a section after redistribution < 1
{Jb moment at the section before redistribution -
(4.9-2)
Where moment redistribution leads to a reduction in the design ultimate
moment at a cross-section subjected to the largest moment within each
hogging or sagging region, then BS 8110 (Amendment No. 1 of May 1986)
requires that eqn (4.9-3) below should be used to check the x/d ratio of
that section as finally designed:
d :5 ({Jb - 0.4) or 0.6 (4.9-3)
X
whichever is the lesser.
For a singly reinforced beam, x/d increases with the steel ratio e; for a
doubly reinforced beam, it increases with the difference (e - e').
Therefore, in eqn (4.9-3), the {Jb ratio is related indirectly to the ductility
and rotation capacity of the member (see Fig. 4.9-4). To prevent an
excessive demand on the ductility of a structural member, a 15% moment
redistribution is normally to be taken as a reasonable limit [14], though
certainly BS 8110 permits up to 30% moment redistribution. These limits