Civil Engineering Reference
In-Depth Information
necessary to consider both the moments due to the loads that do not cause appreciable
sidesway as well as the loads that do. It will therefore be necessary to compute both
ns
s
values if the column proves to be slender.
The
M
s
values are obviously caused by the lateral load in this case. The reader should
realize, however, that if the gravity loads and/or the frame are unsymmetrical, additional
M
s
or sidesway moments will occur.
If we have an unbraced frame subjected to short-term lateral wind or earthquake
loads, the columns will not have appreciable creep (which would increase lateral deflec-
tions and thus the
P
and
moments). The effect of creep is accounted for in design by reduc-
ing the stiffness
EI
used to calculate
P
c
and thus
d
as specified
in ACI Section 10.11.1. Both the concrete and steel terms in ACI Equation 10-11 are di-
vided by this value.
To illustrate the computation of the magnified moments needed for the design of a
slender column in a sway frame, the author has chosen the simple frame of Figure 11.9.
He hopes thereby that the student will not become lost in a forest of numbers as he or she
might if a large frame were considered.
The beam and columns of the frame have been tentatively sized as shown in the fig-
ure. In Example 11.5 the frame is analyzed for each of the conditions specified in ACI
Section 9.2 using 1.3
W
instead of 1.6
W
.
In the example the magnification factors
s
by dividing
EI
by 1
s
are computed for each of the loading
conditions and used to compute the magnified moments. Notice in the solution that different
k
values are used for determining
ns
and
ns
calculation is determined from
the alignment chart of Figure 11.3(a) for braced frames, whereas the
k
for the
ns
and
s
. The
k
for the
s
calculation
is determined from the alignment chart of Figure 11.3(b) for unbraced frames.
EXAMPLE 11.5
Determine the moments and axial forces that must be used for the design of column CD of the un-
braced frame of Figure 11.9. Consider only bending in the plane of the frame. The assumed member
sizes shown in the figure are used for the analyses given in the problem
f
y
60,000 psi and
4000
psi. For this example, the authors considered the load factor cases of ACI Equations 9-1, 9-4, and 9-6.
For other situations other appropriate ACI load factor equations will have to be considered.
c
f
SOLUTION
1.
Determine the effective length factor for the sway case using 0.35 I
g
for the girder and 0.70
I
g
for the columns.
I
column
(0.70)(
12
)(12)(12)
3
1210 in.
4
I
girder
(0.35)(
12
)(12)(18)
3
2041 in.
4
1210
12
2041
30
B
1.48
A
for pinned ends
(For practical purposes, use 10)
k
1.95 from Figure 11.3(b)
If this k is
2.00, the designer will go back and try a larger column.
