Civil Engineering Reference
In-Depth Information
An assumed location is selected for the neutral axis, and the appropriate strain trian-
gles are drawn as shown in the figure. The usual equations are written with
C
c
times the shaded area
A
c
and with each bar having a force equal to its cross-sectional area
times its stress. The solution of the equation yields the load that would establish that neu-
tral axis—but the designer usually starts with certain loads and eccentricities and does not
know the neutral axis location
. Furthermo
re, the neutral axis is probably not even perpen-
dicular to the resultant
e
c
0.85
f
(
e
x
)
2
(
e
y
)
2
.
For column shapes other than circular ones, it is desirable to consider three-dimensional
interaction curves such as the one shown in Figure 10.22. In this figure the curve labeled
M
nxo
represents the interaction curve if bending occurs about the
x
axis only, while the one
labeled
M
nyo
is the one if bending occurs about the
y
axis only.
In this figure, for a constant
P
n
, the hatched plane shown represents the contour of
M
n
for bending about any axis.
Today, the analysis of columns subject to biaxial bending is primarily done with
computers. One of the approximate methods that is useful in analysis and that can be han-
dled with pocket calculators includes the use of the so-called reciprocal interaction equa-
tion, which was developed by Professor Boris Bresler of the University of California at
Figure 10.22
