Design Data

Code

Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19)

References

• Reinforced Concrete Design, 9^th Edition, 2021, Pincheira J. et. al., Oxford University Press, Example 10.20.1

• Notes on ACI 318-11 Building Code Requirements for Structural Concrete, Twelfth Edition, 2013 Portland Cement Association

• spColumn Engineering Software Program Manual v10.00, STRUCTUREPOINT, 2021

• “Biaxial Bending Interaction Diagrams for Square Reinforced Concrete Column Design (ACI 318-19)” Design Example, STRUCTUREPOINT, 2022

• “Biaxial Bending Interaction Diagrams for C-Shaped Concrete Core Wall Design (ACI 318-19)” Design Example, STRUCTUREPOINT, 2022

• “Biaxial Bending Interaction Diagrams for Spiral Reinforced Circular Concrete Column Design (ACI 318-19)” Design Example, STRUCTUREPOINT, 2022

• “Manual Design Procedure for Columns and Walls with Biaxial Bending (ACI 318-11-14-19)” Design Example, STRUCTUREPOINT, 2022

Design Data

f_c’ = 6,000 psi

f_y = 60,000 psi

Cover = 2.5 in.

Column dimensions and reinforcement locations are shown in following figure.

Figure 2 - Reinforced Concrete Column Cross-Section and Reinforcement Locations

Solution

In a reinforced concrete column, the determination of biaxial moment strength for a given axial force involves a trial-and-error process for calculating the neutral axis depth and angle α (Figure 2). The reference shows that using this process for the given column section leads to a value of the neutral axis depth of c = 12.5 in. and an angle of α = 43.9º. In this example the last iteration will be shown for illustration of the procedure as a representative calculation of the complete trial and error procedure.

The steps to calculate biaxial flexural strength of a rectangular reinforced concrete column for a given nominal axial strength and moment ratio of biaxial bending moments are as follows:

1. Assuming a value for the angle of the neutral axis (α) and the neutral axis depth (c) and calculating the strain values in each reinforcement layer

2. Calculating the forces values in the concrete (C_c) and reinforcement layers (F_si)

3. Calculating P_n and M_nx/M_ny using the following equations.

The procedure above should be repeated until the calculated P_n, and M_nx/M_ny are equal to the given P_n, and M_nx/M_ny. The following figure demonstrates the procedure explained above:

Figure 3- Biaxial Flexural Strength Calculation Methods for a Reinforced Concrete Columns