Civil Engineering Reference
In-Depth Information
11
Slender Columns
11.1
INTRODUCTION
When a column bends or deflects laterally an amount
, its axial load will cause an in-
creased column moment equal to
P
. This moment will be superimposed onto any mo-
ments already in the column. Should this
P
moment be of such magnitude as to reduce
the axial load capacity of the column significantly, the column will be referred to as a
slender column
.
Section 10.10.1 of the Code states that the design of a compression member should,
desirably, be based on a theoretical analysis of the structure that takes into account the ef-
fects of axial loads, moments, deflections, duration of loads, varying member sizes, end
conditions, and so on. If such a theoretical procedure is not used, the Code (10.10.2) pro-
vides an approximate method for determining slenderness effects. This method, which is
based on the factors just mentioned for an “exact” analysis, results in a moment magnifier
, which is to be multiplied by the larger moment at the end of the column, and that value
is used in design. If bending occurs about both axes,
is to be computed separately for
each direction and the values obtained multiplied by the respective moment values.
11.2
NONSWAY AND SWAY FRAMES
For this discussion it is necessary to distinguish between frames without sidesway and
those with sidesway. In the ACI Code these are referred to respectively as
nonsway
frames
and
sway frames
.
The columns in nonsway frames must be designed according to Section 10.12 of the
Code, while the columns of sway frames must be designed according to Section 10.13. As
a result, it is first necessary to decide whether we have a nonsway frame or a sway frame.
You must realize that you will rarely find a frame that is completely braced against sway-
ing or one that is completely unbraced against swaying. Therefore, you are going to have
to decide which way to handle it.
The question may possibly be resolved by examining the lateral stiffness of the
bracing elements for the story in question. You may observe that a particular column is
located in a story where there is such substantial lateral stiffness provided by bracing
members, shear walls, shear trusses, and so on that any lateral deflections occurring will
be too small to affect the strength of the column appreciably. You should realize while
examining a particular structure that there may be some nonsway stories and some sway
stories.
317
