Civil Engineering Reference
In-Depth Information
4.
I
se
moment of inertia of the reinforcing about the centroidal axis of the section.
(This value
the sum of each bar area times the square of its distance from the
centroidal axis.)
5.
The term
d
is defined differently for nonsway and sway frames. For nonsway
frames it is defined as the ratio of the maximum factored sustained axial load di-
vided by the total factored axial load associated with the same load combination.
It is always assumed to have a plus sign.
6.
Next it is necessary to compute
EI
. The two expressions given for
EI
in the Code
were developed so as to account for creep, cracks, and so on. If the column and
bar sizes have already been selected, or estimated,
EI
can be computed with the
following expression, which is particularly satisfactory for columns with high
steel percentages.
(0.2
E
c
I
g
E
s
I
se
)
EI
(ACI Equation 10-11)
1
d
The alternate expression for
EI
that follows is probably the better expression
to use when steel percentages are low. Notice also that this expression will be the
one used if the reinforcing has not been previously selected.
0.4
E
c
I
g
1
EI
(ACI Equation 10-12)
d
7.
The Euler buckling load is computed:
2
EI
P
c
(ACI Equation 10-10)
u
)
2
(
k
8.
For some moment situations in columns, the amplification or moment magnifier
expression provides moments that are too large. One such situation occurs when
the moment at one end of the member is zero. For this situation the lateral deflec-
tion is actually about half of the deflection in effect provided by the amplification
factor. Should we have approximately equal end moments that are causing reverse
curvature bending, the deflection at mid-depth and the moment there are close to
zero. As a result of these and other situations, the Code provides a modification
factor (
C
m
) to be used in the moment expression that will result in more realistic
moment magnification.
For braced frames without transverse loads,
C
m
can vary from 0.4 to 1.0 and is deter-
mined with the expression at the end of this paragraph. For all other cases it is to be taken
as 1.0. (Remember the sign convention:
M
1
is positive for single curvature and is negative
for reverse curvature, and
M
2
is always positive.)
0.4
M
1
C
m
0.6
M
2
0.4
(ACI Equation 10-13)
Should
M
2,min
as computed with ACI Equation 10-14 be larger than
M
2
, the value of
C
m
above shall either be taken as equal to 1.0 or be based on the ratio of the computed end
moments (ACI Section 10.12.3.2).
Example 11.3 illustrates the design of a column in a nonsway frame.
M
1
M
2
