Civil Engineering Reference
In-Depth Information
(b)
Total moment including secondary moment:
2
EI
(
k
u
)
2
P
c
Euler buckling load
(ACI Equation 10-10)
1
12
12
12
3
2
)(3160)
(
1663.4 k
(1.0)(12
15)
2
1
1
P
P
c
Magnified moment
75
1
75
82.4 ft- k
150
1663.4
1
As we have seen, it is possible to calculate approximately the increased moment due
to lateral deflection by using the (1
P
/
P
c
) expression. In ACI Code 10.12.3 the factored
design moment for slender columns with no sway is increased by using the following ex-
pression, in which
M
c
is the magnified or increased moment and
M
2
is the larger factored
end moment on a compression member:
M
c
ns
M
2
(ACI Equation 10-8)
Should our calculations provide very small moments at both column ends, the Code
provides an absolutely minimum value of
M
2
to be used in design. In effect, it requires the
computation of a moment based on a minimum eccentricity of 0.6
0.03
h
, where
h
is the
overall thickness of the member perpendicular to the axis of bending.
M
2,min
P
u
(0.6
0.03
h
)
(ACI Equation 10-14)
Or in SI units
M
2,min
P
u
(15
0.03
h
), where
h
is in mm, as is the number 15.
ns
is used to estimate the effect of member curvature or lateral
deflection in a column in a nonsway frame. It involves a term
C
m
, which is defined later in
this section.
A moment magnifier
C
m
ns
1.0
(ACI Equation 10-9)
P
u
0.75
P
c
1
The determination of the moment magnifier
ns
involves the following calculations:
c
.
1.
E
c
2.
I
g
57,000
f
gross inertia of the column cross section about the centroidal axis being
considered.
3.
E
s
10
6
psi.
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