Civil Engineering Reference
In-Depth Information
Figure 10.9
Replacing circular column with equivalent rectangular one.
On some occasions, members subject to axial load and bending have unsymmetrical
arrangements of reinforcing. Should this be the case, you must remember that eccentricity
is correctly measured from the plastic centroid of the section.
In this chapter
P
n
values were obtained only for rectangular tied columns. The
same theory could be used for round columns, but the mathematics would be some-
what complicated because of the circular layout of the bars, and the calculations of dis-
tances would be rather tedious. Several approximate methods have been developed
that greatly simplify the mathematics. Perhaps the best known of these is the one pro-
posed by Charles Whitney, in which equivalent rectangular columns are used to re-
place the circular ones.
2
This method gives results that correspond quite closely with
test results.
In Whitney's method, the area of the equivalent column is made equal to the area of
the actual circular column, and its depth in the direction of bending is 0.80 times the out-
side diameter of the real column. One-half the steel is assumed to be placed on one side of
the equivalent column and one-half on the other. The distance between these two areas of
steel is assumed to equal two-thirds of the diameter (
D
s
) of a circle passing through the
center of the bars in the real column. These values are illustrated in Figure 10.9. Once the
equivalent column is established, the calculations for
P
n
and
M
n
are made as for rectangu-
lar columns.
10.4
USE OF INTERACTION DIAGRAMS
We have seen that by statics the values of
P
n
and
M
n
for a given column with a certain set
of strains can easily be determined. Preparing an interaction curve with a hand calculator
2
Whitney, Charles S., 1942, “Plastic Theory of Reinforced Concrete Design.”
Transactions ASCE
, 107,
pp. 251-326.
