Civil Engineering Reference
In-Depth Information
Figure 11.2
Columns for
unbraced frames.
for such columns; therefore it seems logical to make preliminary designs with
k
equal to
or larger than that value.
11.4
DETERMINING
K
FACTORS WITH ALIGNMENT CHARTS
The preliminary procedure used for estimating effective lengths involves the use of the
alignment charts shown in Figure 11.3.
1,2
The chart of part (a) of the figure is applicable to
braced frames, whereas the one of part (b) is applicable to unbraced frames.
To use the alignment charts for a particular column,
factors are computed at each
end of the column. The
factor at one end of the column equals the sum of the stiffness
[
)] of the columns meeting at that joint, including the column in question, divided
by the sum of all the stiffnesses of the beams meeting at the joint. Should one end of the
column be pinned,
(
EI
/
is theoretically equal to
, and if fixed,
0. Since a perfectly
fixed end is practically impossible to have,
is usually taken as 1.0 instead of 0 for as-
sumed fixed ends. When column ends are supported by, but not rigidly connected to a
footing,
is theoretically infinity, but usually is taken as about 10 for practical design.
One of the two
B
. After these values are
computed, the effective length factor
k
is obtained by placing a straightedge between
values is called
A
and the other is called
A
and
B
. The point where the straightedge crosses the middle nomograph is
k
.
It can be seen that the
factors used to enter the alignment charts and thus the result-
ing effective length factors are dependent on the relative stiffnesses of the compression
and flexural members. If we have a very light flexible column and large stiff girders, the
rotation and lateral movement of the column ends will be greatly minimized. The column
ends will be close to a fixed condition, and thus the
values and the resulting
k
values
will be small. Obviously if the reverse happens—that is, large stiff columns framing into
1
Structural Stability Research Council,
Guide to Stability Design Criteria for Metal Structures
, 4th ed., T. V.
Galambos, ed. (New York: Wiley, 1988).
2
Julian, O. G., and Lawrence, L. S., 1959, “Notes on J and L Nomograms for Determination of Effective
Lengths,” unpublished. These are also called the Jackson and Moreland Alignment Charts, after the firm with
whom Julian and Lawrence were associated.
