Simplified Design for Columns - Simplified Design of Reinforced Concrete Buildings - page 153

5.5 SIMPLIFIED DESIGN FOR COLUMNS

5.5.1 Simplified Design Charts—Combined Axial Load and Bending Moment

Numerous design aids and computer programs are available for determining the size and reinforcement of columns
subjected to axial forces and/or moments. Tables, charts, and graphs provide design data for a wide variety of
column sizes and shapes, reinforcement layouts, load eccentricities and other variables. These design aids
eliminate the necessity for making complex and repetitious calculations to determine the strengths of columns, as
preliminarily sized. The design aids presented in References 5.1 and 5.2 are widely used. In addition, extensive
column load tables are available in the CRSI Handbook. Each publication presents the design data in a somewhat
different format; however, the accompanying text in each reference readily explains the method of use. Computer
programs may also be used to design or investigate rectangular or circular column sections with any
reinforcement layout or pattern.

In general, columns must be designed for the combined effects of axial load and bending moment. As noted
earlier, appreciable bending moments can occur in columns because of unbalanced gravity loads and/or lateral
forces. Simplified interaction diagram, such as the one depicted in Figure 5-4, can be created. For simplicity
the diagram is plotted by connecting straight lines between points corresponding to certain transition stages.
The transition stages are as follows (see Fig. 5-4):

Stage 1: Pure compression (no bending moment)

Stage 2: Stress in reinforcement closest to tension face = 0 (f s = 0)

Stage 3: Stress in reinforcement closest to tension face = 0.5 f y (f s = 0.5 f y )

Stage 4: Balanced point; stress in reinforcement closest to tension face = f y (f s = f y )

Stage 5: Pure bending (no axial load)

Note that Stages 2 and 3 are used to determine which type of lap splice is required for a given load combina-
tion (ACI 12.17). In particular, for load combinations falling within Zone 1, compression lap splices are
allowed, since all of the bars are in compression. In Zone 2, either Class A (half or fewer of the bars spliced at
one location) or Class B (more than one-half of the bars spliced at one location) tension lap splices must be
used. Class B tension lap splices are required for load combinations falling within Zone 3.

For the general case of a rectangular column section (Fig. 5-4):

1. Point 1

φ f c ʹ f c ʹ P n(max) = 0.80A g [0.85 + ρ g (f y − 0.85 )] (kips)

Where A g = gross area of column, in 2
A st = total area of longitudinal reinforcement, in 2
ρ g = A st /A g
φ = strength reduction factor = 0.65