Civil Engineering Reference
In-Depth Information
moments for buildings of normal proportions. The values calculated in this manner will
usually be somewhat larger than those that would be obtained with an “exact” analysis. As
a result, appreciable economy can normally be obtained by taking the time or effort to
make such an analysis. In this regard, it should be realized that these coefficients are con-
sidered best applied to continuous frames having more than three or four continuous spans.
In developing the coefficients, the negative-moment values were reduced to take into
account the usual support widths and also some moment redistribution, as described in
Section 14.5 of this chapter. In addition, the positive-moment values have been increased
somewhat to account for the moment redistribution. It will also be noted that the coeffi-
cients account for the fact that in monolithic construction the supports are not simple and
moments are present at end supports, such as where those supports are beams or columns.
In applying the coefficients,
w
u
is the design load while
n
is the clear span for calculat-
ing positive moments and the average of the adjacent clear spans for calculating negative
moments
. These values were developed for members with approximately equal spans (the
larger of two adjacent spans not exceeding the smaller by more than 20%) and for cases
where the ratio of the uniform service live load to the uniform service dead load is not
greater than three. In addition, the values are not applicable to prestressed concrete mem-
bers. Should these limitations not be met, a more precise method of analysis must be used.
For the design of a continuous beam or slab, the moment coefficients provide in ef-
fect two sets of moment diagrams for each span of the structure. One diagram is the result
of placing the live loads so that they will cause maximum positive moment out in the
span, while the other is the result of placing the live loads so as to cause maximum nega-
tive moments at the supports. To be truthful, however, it is not possible to produce maxi-
mum negative moments at both ends of a span simultaneously. It takes one placement of
the live loads to produce maximum negative moment at one end of the span and another
placement to produce maximum negative moment at the other end. The assumption of
both maximums occurring at the same time is on the safe side, however, because the re-
sulting diagram will have greater critical values than are produced by either one of the
two separate loading conditions.
The ACI coefficients give maximum points for a moment envelope for each span of a
continuous frame. Typical envelopes are shown in Figure 14.19 for a continuous slab,
Figure 14.19
Moment envelopes for continuous slab constructed integrally with beams.
