Civil Engineering Reference
In-Depth Information
Figure 16.9
negative moments may vary appreciably, and the use of a more detailed method of analy-
sis is desirable. The equivalent frame method (Chapter 17) will provide rather good ap-
proximations for such situations.
The relative stiffnesses of the columns and slabs of exterior panels are of far greater
significance in their effect on the moments than is the case for interior panels. The magni-
tudes of the moments are very sensitive to the amount of torsional restraint supplied at the
discontinuous edges. This restraint is provided both by the flexural stiffness of the slab
and by the flexural stiffness of the exterior column.
Should the stiffness of an exterior column be quite small, the end negative moment
will be very close to zero. If the stiffness of the exterior column is very large, the positive
and negative moments will still not be the same as those in an interior panel unless an
edge beam with a very large torsional stiffness is provided that will substantially prevent
rotation of the discontinuous edge of the slab.
If a 2-ft-wide beam were to be framed into a 2-ft-wide column of infinite flexural
stiffness in the plane of the beam, the joint would behave as would a perfectly fixed end,
and the negative beam moment would equal the fixed-end moment.
If a two-way slab 24 ft wide were to be framed into this same 2-ft-wide column of in-
finite stiffness, the situation of no rotation would occur along the part of the slab at the
column. For the remaining 11-ft widths of slab on each side of the column, there would be
rotation varying from zero at the side face of the column to maximums 11 ft on each side
of the column. As a result of this rotation, the negative moment at the face of the column
would be less than the fixed-end moment. Thus the stiffness of the exterior column is re-
duced by the rotation of the attached transverse slab.
To take into account the fact that the rotation of the edge of the slab is different at dif-
ferent distances from the column, the exterior columns and slab edge beam are replaced
with an equivalent column that has the same estimated flexibility as the column plus the
edge beam. It can be seen that this is quite an involved process; therefore, instead of re-
quiring a complicated analysis, the Code (13.6.3.3) provides a set of percentages for di-
viding the total factored static moment into its positive and negative parts in an end span.
