Simplified Design for Columns - Simplified Design of Reinforced Concrete Buildings - page 168

5.6 COLUMN SLENDERNESS CONSIDERATIONS

5.6.1 Non-sway versus Sway Frames

The behavior of a column differs depending on whether it is a part of a sway or nonsway frame. Accordingly,
when designing columns, it is important to establish whether or not the building frame is nonsway. A column
may be assumed nonsway if located in a story in which the bracing elements (shear walls, shear trusses, or other
types of lateral bracing) have a such substantial lateral stiffness, to resist lateral movement of the story that the
resulting lateral deflection is not large enough to affect the column strength substantially. There is rarely a com-
pletely nonsway or a completely sway frame. Realistically, a column within a story can be considered nonsway
when horizontal displacements of the story do not significantly affect the moments in the column. ACI 10.10.5
gives criteria that can be used to determine if column located within a story is nonsway or sway. As a simpli-
fied approach, 10.10.1 permits the column to be considered braced against sidesway when the bracing elements
have a total stiffness, resisting the lateral movement of a story, of at least 12 times the gross stiffness of the
columns within the same story.

5.6.2 Minimum Sizing for Design Simplicity

Another important aspect to consider when designing columns is whether slenderness effects must be included
in the design (ACI 10.10). In general, design time can be greatly reduced if 1) the building frame is adequately
braced by shearwalls and 2) the columns are sized so that effects of slenderness may be neglected. The criteria
for the consideration of column slenderness, as prescribed in ACI 10.10, are summarized in Fig. 5-14. M 2b is
the larger factored end moment and M 1b is the smaller end moment; both moments, determined from an elastic
frame analysis, are due to loads that result in no appreciable side sway. The ratio M 1b /M 2b is positive if
the column is bent in single curvature, negative if it is bent in double curvature. For non-sway columns, the
effective length factor k = 1.0 (ACI 10.10.6.3).

In accordance with ACI 10.10.1, effects of slenderness may be neglected when non-sway columns are sized to
satisfy the following:

u

h ≤

12

where ˜ u is the clear height between floor members and h is the column size. The above equation is valid for
columns that are bent in double curvature with approximately equal end moments. It can be used for the first
story columns provided the degree of fixity at the foundation is large enough. * Table 5-4 gives the maximum
clear height ˜ u for a column size that would permit slenderness to be neglected.

For a sway column with a column-to-beam stiffness ratio = 1 at both ends, the effects of slenderness may be

neglected with ˜ u / h is less than 5, assuming k = 1.3 (see the alignment chart, in ACI R 10.10). **

ψ

* For a discussion of fixity of column bases, see PCI Design Handbook-Precast and Prestressed Concrete, 5th Ed.,
Precast/Prestressed Concrete Institute, Chicago, IL, 1999.
** The effective length factor k may be determined for a non-sway or sway frame using ACI R10.10 or using the simplified equations
which are also given in ACI R10.10.