Civil Engineering Reference
In-Depth Information
Round columns. (Digital Vision.)
Effective Length Factors
To calculate the slenderness ratio of a particular column, it is necessary to estimate its ef-
fective length. This is the distance between points of zero moment in the column. For this
initial discussion it is assumed that no sidesway or joint translation is possible. Sidesway
or joint translation means that one or both ends of a column can move laterally with re-
spect to each other.
If there were such a thing as a perfectly pinned end column, its effective length would
be its supported length, as shown in Figure 11.1(a). The
effective length factor k
is the
number that must be multiplied by the column's unsupported length to obtain its effective
length. For a perfectly pinned end column,
k
1.0.
Columns with different end conditions have entirely different effective lengths.
For instance, if there were such a thing as a perfectly fixed end column, its points of
inflection (or points of zero moment) would occur at its one-fourth points, and its ef-
fective length would be
u
/2, as shown in Figure 11.1(b). As a result, its
k
value would
equal 0.5.
