Continuous Reinforced Concrete Structures - Design of Reinforced Concrete - page 446

Figure 14.18 Moment envelope.

In the same fashion, in Figure 14.16, where the beam is loaded to produce maximum
positive moment in span 2, an increase in the negative moments at the supports from 308 ft-
k to 339 ft-k will reduce the maximum positive moment in span 2 from 261 ft-k to 230 ft-k.
Finally, in Figure 14.17, the live-load placement causes a maximum negative mo-
ment at the first interior support of 504 ft-k. If this value is reduced by 10%, the maximum
moment there will be 454 ft-k. In this figure the author has reduced the negative mo-

ment at the other interior support by 10% also. Should it be of advantage, however, it can
be assumed that one negative support moment is decreased and the other one is increased.
It will be noticed that the net result of all of the various increases or decreases in the
negative moments is a net reduction in both the maximum positive and the maximum neg-
ative values. The result of these various redistributions is actually an envelope of the ex-
treme values of the moments at the critical sections. The envelope for the three-span beam
considered in this section is presented in Figure 14.18. You can see at a glance the parts of
the beams that need positive reinforcement, negative reinforcement, or both.
The reductions in bending moments due to moment redistribution as described here do
not mean that the safety factors for continuous members will be less than those for simple
spans. Rather, the excess strength that such members have due to this continuity is reduced
so that the overall factors of safety are nearer but not less than those of simple spans.
Various studies have shown that cracking and deflection of members selected by the
limit design process are no more severe than those for the same members designed with-
out taking advantage of the permissible redistributions. 3,4
(Appendix B of the ACI Code presents quite a few variations which may be used in
design for flexure and axial loads. There are changes in the moment redistribution per-
centages permitted for continuous members, in the reinforcing limits and in the strength
reduction or

factors. These latter changes are dependent on the strain conditions, in-
cluding whether the sections are compression- or tension-controlled.)

14.6 PRELIMINARY DESIGN OF MEMBERS

Before an “exact” analysis of a building frame can be made, it is necessary to estimate the
sizes of the members. Even if a computer design is used, it is often economically advis-

3 Cohn, M. Z., 1964, “Rotational Compatibility in the Limit Design of Reinforced Concrete Continuous Beams,”
Proceedings of the International Symposium on the Flexural Mechanics of Reinforced Concrete , ASCE-ACI
(Miami), pp. 359-382.
4 Mattock, A. H., 1959, “Redistribution of Design Bending Moments in Reinforced Concrete Continuous
Beams,” Proceedings of the Institution of Civil Engineers , 113, pp. 35-46.