Civil Engineering Reference
In-Depth Information
677 k,
which is satisfactory. Should the reader go through the Bresler equation here, he or she
must remember to calculate the correct
e
x
and
e
y
values for use with the interaction dia-
grams. For instance,
A review of the column with the Bresler expression gives a
P
ni
804 k
(12)(363)
677
e
x
6.43 in.
When a beam is subjected to biaxial bending, the following approximate interaction
equation may be used for design purposes:
M
y
M
x
M
ux
M
uy
1.0
In this expression
M
x
and
M
y
are the design moments,
M
ux
is the design moment ca-
pacity of the section if bending occurs about the
x
axis only, and
M
uy
is the design moment
capacity if bending occurs about the
y
axis only. This same expression may be satisfacto-
rily used for axially loaded members if the design axial load is about 15% or less of the
axial load capacity of the section. For a detailed discussion of this subject, the reader is re-
ferred to the
Handbook of Concrete Engineering
.
10
Numerous other methods are available for the design of biaxially loaded columns.
One method that is particularly useful to the design profession is the PCA Load Contour
Method, which is recommended in the ACI
Design Handbook
.
11
10.9
CONTINUED DISCUSSION OF CAPACITY
REDUCTION FACTOR,
As previously described, the value of
can be larger than 0.65 for tied columns, or 0.70 for
spiral columns, if
values are applicable to compression-
controlled sections because of their smaller ductilities. Such sections are more sensitive to
varying concrete strengths than are tensilely controlled sections. The Code (9.3.2.2) states
that
t
is larger than 0.002. The lower
for a particular column may be increased linearly from 0.65 or 0.70 to 0.90 as the net
tensile strain
t
increases from the compression-controlled strain 0.002 to the tensilely con-
trolled one of 0.005.
For this discussion, Figure R9.3.2 of the Code (previously shown as Figure 3.5 in this
text) is repeated as Figure 10.25. From this figure you can see the range of
t
values for
which
may be increased.
The hand calculation of
t
for a particular column is a long and tedious trial-and-error
problem, and space is not taken here to present a numerical example. However, a descrip-
tion of the procedure is presented in the next few paragraphs. The average designer will
not want to spend the time necessary to make these calculations and will either just use
the smaller
values or make use of a computer program such as SABLE32. This program
provides a routine for computing
t
and
for columns.
10
Fintel, M.,
Handbook of Concrete Engineering
, p. 38.
11
American Concrete Institute, 1997,
Design Handbook in Accordance with the Strength Design Method
, Vol. 2,
Columns
, Publication SP-17(97), ACI, Farmington Hills, MI.
