Civil Engineering Reference
In-Depth Information
Avoiding Slender Columns
The design of slender columns is appreciably more complicated than the design of short
columns. As a result, it may be wise to give some consideration to the use of certain mini-
mum dimensions so that none of the columns will be slender. In this way they can be al-
most completely avoided in the average-size building.
If
k
is assumed equal to 1.0, slenderness can usually be neglected in braced frame
columns if
u
/
h
is kept to 10 or less on the first floor and 14 or less for the floors above the
first one. To determine these values it was assumed that little moment resistance was pro-
vided at the footing-column connection and the first-floor columns were assumed to be
bent in single curvature. Should the footing-column connection be designed to have ap-
preciable moment resistance, the maximum
u
/
h
value given above as 10 should be raised
to about 14 or equal to the value used for the upper floors.
4
Should we have an unbraced frame and assume
k
1.2, it is probably necessary to
u
/
h
to 6 or less. So for a 10-ft clear floor height it is necessary to use a minimum
h
of about 10 ft/6
keep
1.67 ft
20 in. in the direction of bending to avoid slender
columns.
Example 11.1 illustrates the selection of the
k
factor and the determination of the
slenderness ratio for a column in an unbraced frame. For calculating
I
/
L
values the au-
thor used 0.70 times the gross moments of inertia for the columns, 0.35 times the gross
moments of inertia for the girders, and the full lengths of members center to center of
supports.
EXAMPLE 11.1
(a)
Using the alignment charts of Figure 11.3, calculate the effective length factor for col-
umn AB of the unbraced frame of Figure 11.4. Consider only bending in the plane of
the frame.
(b)
Compute the slenderness ratio of column AB. Is it a short or a slender column?
The maxi-
mum permissible slenderness ratio for a short unbraced column is 22, as will be described
in Section 11.9 of this chapter.
Assume single curvature with
M
1
M
2
75 ft-k.
SOLUTION
(a) Effective Length Factor for Column AB
0.7
8000
12
10
A
2.99
0.35
5832
12
20
0.35
5832
12
24
0.7
8000
12
10
0.7
8000
12
12
B
2.31
0.35
13,824
12
20
0.35
13,824
12
24
4
Neville, G. B., ed., 1984,
Simplified Design Reinforced Concrete Buildings of Moderate Size and Height
(Skokie, IL: Portland Cement Association), pp. 5-10-5-12.
