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 141
need be drawn, because elsewhere eqn (4.9-4) is not critical (that is,
elsewhere Mu exceeds 70%Me)·
Step6
For Case 2, the reader should verify that the elastic moment diagram is
shown by the chain-dotted line. (Hint: Use hint in Step 3.) Adjust M 8
and Me to -768 kNm for uniformity with Case 1. The maximum redistributed
moment in span BC becomes 762 kNm. That this moment
should be 762 kNm in both Case 1 and Case 2 is not accidental, but
follows from the laws of equilibrium; in both Case 1 and Case 2 the span
BC supports the load 1.4Gk + 1.6Qk and is acted on by moments of
-768 kNm at the ends.
Step7
For Case 3, the elastic moments at B and C are again adjusted to
-768 kNm for uniformity with Case 1. The maximum redistributed
moments at AB and BC become 632 kNm as in Case 1.
Step8
On the basis of the above-drawn moment diagram, the design moment
envelope for the ultimate limit state is as shown in Fig. 4.9-7(a). Note
that over the length ab the condition Mu <1: 0.7Me governs the design.
Step9
For comparison, the elastic moment envelope is shown in Fig. 4.9-7(b),
which is constructed from the chain-dotted curves in Fig. 4.9-6. Of
course, this elastic moment envelope may legitimately be used to
proportion the beam sections for the ultimate limit state; however, the
-768
762
( aJ Redistributed-moment
envelope
\ I
\ .
\.730 /
·:.;:::/
(b) Elastic-moment
envelope
Fig. 4.9-7