Civil Engineering Reference
In-Depth Information
check the capacities of the sections selected by some other procedure. Exact theoretical
designs of columns subject to biaxial bending are very complicated and, as a result, are
seldom handled with pocket calculators. They are proportioned either by approximate
methods or with computer programs.
During the past few decades, several approximate methods have been introduced for
the design of columns with biaxial moments. For instance, quite a few design charts are
available with which satisfactory designs may be made. The problems are reduced to very
simple calculations in which coefficients are taken from the charts and used to magnify
the moments about a single axis. Designs are then made with the regular uniaxial design
charts.
5-7
Not only are charts used, but some designers also use rules of thumb for making ini-
tial designs. One very simple method (though not too good) involves the following steps:
(1) the selection of the reinforcement required in the
x
direction considering
P
n
and
M
nx
,
(2) the selection of the reinforcement required in the
y
direction considering
P
n
and
M
ny
,
and (3) the determination of the total column steel area required by adding the areas ob-
tained in steps (1) and (2). This method will occasionally result in large design errors on
the unsafe side because the strength of the concrete is counted twice, once for the
x
direc-
tion and once for the
y
direction.
8
Another approximate procedure that works fairly well for design office calculations
is used for Example 10.9. If this simple method is applied to square columns, the values
of both
M
nx
and
M
ny
are assumed to act about both the
x
axis and the
y
axis (i.e.,
M
x
M
y
M
ny
). The steel is selected about one of the axes and is spread around the
column, and the Bresler expression is used to check the ultimate load capacity of the ec-
centrically loaded column.
Should a rectangular section be used where the
y
axis is the weaker direction, it
would seem logical to calculate
M
y
M
nx
M
ny
and to use that moment to select the steel
required about the
y
axis and spread the computed steel area over the whole column cross
section. Although such a procedure will produce safe designs, the resulting columns may
be rather uneconomical because they will often be much too strong about the strong axis.
A fairly satisfactory approximation is to calculate
M
y
M
nx
M
ny
and multiply it by
b
/
h
,
and with that moment design the column about the weaker axis.
9
Example 10.9 illustrates the design of a short square column subject to biaxial bend-
ing. The approximate method described in the last two paragraphs is used, and the Bresler
expression is used for checking the results. If this had been a long column, it would have
been necessary to magnify the design moments for slenderness effects, regardless of the
design method used.
M
nx
5
Parme, A. L., Nieves, J. M., and Gouwens, A., 1966, “Capacity of Reinforced Rectangular Columns Subject to
Biaxial Bending,”
Journal ACI
, 63 (11), pp. 911-923.
6
Weber, D. C., 1966, “Ultimate Strength Design Charts for Columns with Biaxial Bending,”
Journal ACI
,
63 (11), pp. 1205-1230.
7
Row, D. G., and Paulay, T., 1973, “Biaxial Flexure and Axial Load Interaction in Short Reinforced Concrete
Columns,”
Bulletin of New Zealand Society for Earthquake Engineering
, 6 (2), pp. 110-121.
8
Park, R., and Paulay, T., 1975,
Reinforced Concrete Structures
(New York: John Wiley & Sons),
pp. 158-159.
9
Fintel, M., ed., 1985,
Handbook of Concrete Engineering
, 2nd ed. (New York: Van Nostrand), pp. 37-39.
