Civil Engineering Reference
In-Depth Information
monolithically as part of frames in both directions or where columns are supporting heavy
spandrel beams. Bridge piers are almost always subject to biaxial bending.
Circular columns have polar symmetry and thus the same ultimate capacity in all di-
rections. The design process is the same, therefore, regardless of the directions of the mo-
ments. If there is bending about both the
x
and
y
axes, the biaxial moment can be
computed by combining the two moments or their eccentricities as follows:
(
M
ux
)
2
(
M
uy
)
2
M
u
or
(
e
x
)
2
(
e
y
)
2
e
For shapes other than circular ones, it is necessary to consider the three-dimensional
interaction effects. Whenever possible, it is desirable to make columns subject to biaxial
bending circular in shape. Should it be necessary to use square or rectangular columns for
such cases, the reinforcing should be placed uniformly around the perimeters.
You might quite logically think that you could determine
P
n
for a biaxially loaded
column by using static equations, as was done in Example 10.2. Such a procedure will
lead to the correct answer, but the mathematics involved is so complicated due to the
shape of the compression side of the column that the method is not a practical one. Never-
theless, a few comments are made about this type of solution, and reference is made to
Figure 10.21.
Figure 10.21
