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FIGURE 7.25 Effective length factor k: (a) nonsway frames and (b) sway frames. Note: C is the ratio of the summation of column stiffness [^(EI/L)] to beam stiffness at the beam-column joint.

For a building story, a frame is considered to be nonsway if its stability index

V PuD0

Vulc where D0 is the first-order relative deflection between the top and bottom of the story and Pu and Vu are the total vertical load and story shear, respectively.

For sway frames, slenderness may be neglected if the slenderness ratio klu/r < 22. The k factor must be taken as greater than or equal to 1.0 (see Figure 7.25).

For structural design, it is preferable to design reinforced concrete structures as nonsway systems and with stocky columns. Structural systems should be configured with stiff lateral resistant elements such as shear walls to control sway. Column cross-sectional dimensions should be selected with the slenderness criteria in mind.

If slender columns do exist in a design, adopting a computerized second-order analysis should be considered so that the effects of slenderness will be resolved internally by the structural analysis (see Section 7.7). Then, the internal force demands from the computer output can be directly checked against the interaction diagram in like manner as a nonslender column design. Alternatively, the ACI code provides a manual method called the Moment Magnifier Method to adjust the structural analysis results of a first-order analysis.

### 7.14.12 Moment Magnifier Method

The Moment Magnifier Method estimates the column moment Mc in a slender column by magnifying the moment obtained from a first-order analysis M2. For the nonsway case, the factor dns magnifies the column moment:

p2EI

The column stiffness may be estimated as

or a more simplified expression may be used:

In the sway case, the nonsway moments Mns (e.g., gravity loads) are separated from the sway moments Ms (e.g., due to wind, unbalanced live loads). Only the sway moment is magnified:

where Q is the stability index given by Equation 7.47.

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