Civil Engineering Reference
In-Depth Information
Figure 17.5(a). Cross sections of the structure are shown through the slab in part (b) of the
figure and through the column in part (c). Then in part (d) the equivalent frame that will
be used for the actual numerical calculations is shown. In this figure,
E
cs
is the modulus of
elasticity of the concrete slab. With section 2-2, a fictitious section is shown that will have
a stiffness approximately equivalent to that of the actual slab and column. An expression
for
I
for the equivalent section is also given. In this expression,
c
2
is the width of the col-
umn in a direction perpendicular to the direction of the span, and
2
is the width of the
slab beam. The gross moment of inertia at the face of the support is calculated and is di-
vided by (1
2
)
2
. This approximates the effect of the large increase in depth provided
by the column for the distance in which the slab and column are in contact.
In Figure 17.6, similar sketches and
I
values are shown for a slab with drop panels.
Figure 13.7.3 of the 1983 ACI Commentary showed such information for slab systems
with beams and for slab systems with column capitals.
With the equivalent slab beam stiffness diagram it is possible, using the conjugate beam
method, column analogy, or some other method, to compute stiffness factors, distribution
factors, carryover factors, and fixed-end moments for use in moment distribution. Tables
A.16 through A.20 of Appendix A of this text provide tabulated values of these properties for
various slab systems. The numerical examples of this chapter make use of this information.
c
2
/
17.4
PROPERTIES OF COLUMNS
The length of a column is assumed to run from the mid-depth of the slab on one floor to
the mid-depth of the slab on the next floor. For stiffness calculations, the moments of iner-
tia of columns are based on their gross dimensions. Thus if capitals are present, the effect
of their dimensions must be used for those parts of the columns. Columns are assumed to
be infinitely stiff for the depth of the slabs.
Figure 17.7 shows a sample column, together with its column stiffness diagram. Sim-
ilar diagrams are shown for other columns (where there are drop panels, capitals, etc.) in
Figure 13.7.4 of the 1983 ACI Commentary.
With a column stiffness diagram, the column flexural stiffness
K
c
can be determined
by the conjugate beam procedure or other methods. Tabulated values of
K
c
are given in
Table A.20 of the Appendix of this text for typical column situations.
Figure 17.7
