Civil Engineering Reference
In-Depth Information
In applying moment distribution to a particular frame, we need the stiffnesses of the
slab beam, the torsional members, and the equivalent column so that the distribution fac-
tors can be calculated. For this purpose the equivalent column, the equivalent slab beam,
and the torsional members are needed at a particular joint.
For this discussion, reference is made to Figure 17.8, where it is assumed that there is
a column above and below the joint in question. Thus the column stiffness (
K
c
) here is as-
sumed to include the stiffness of the column above (
K
ct
) and the one below (
K
cb
). Thus
K
cb
. In a similar fashion, the total torsional stiffness is assumed to equal that
of the torsional members on both sides of the joint (
K
c
K
ct
K
t
K
t
1
K
t
2
). For an exterior
frame, the torsional member will be located on one side only.
The following approximate expression for the stiffness (
K
t
) of the torsional member was
determined using a three-dimensional analysis for various slab configurations (ACI R13.7.5).
9
E
cs
C
K
t
c
2
2
3
2
1
In this formula
C
is to be determined with the following expression by dividing the
cross section of the torsional member into rectangular parts and summing up the
C
values
for the different parts. This expression is given in ACI Section 13.0.
x
3
y
3
0.63
x
C
1
y
If there is no beam framing into the column in question, a part of the slab equal to the
width of the column or capital shall be used as the effective beam. If a beam frames into
the column, a T beam or L beam will be assumed, with flanges of widths equal to the pro-
jection of the beam above or below the slab but not more than four times the slab thickness.
The flexibility of the equivalent column is equal to the reciprocal of its stiffness, as
follows:
1
1
1
K
ec
K
c
K
t
1
1
1
K
ec
K
cb
K
ct
K
c
K
t
Figure 17.8
