Biaxial Bending Interaction Diagrams for C-Shaped Concrete Core Wall Design (ACI 318-19)
Biaxial bending of columns and walls occurs when the loading causes bending simultaneously about both principal axes. Columns and walls exposed to known moments about each axis simultaneously should be designed for biaxial bending and axial load.
A uniaxial interaction diagram defines the load-moment strength along a single plane of a section under an axial load P and a uniaxial moment M. The biaxial bending resistance of an axially loaded column or wall can be represented schematically as a surface formed by a series of uniaxial interaction curves drawn radially from the P axis. Data for these intermediate curves are obtained by varying the angle of the neutral axis (for assumed strain configurations) with respect to the major axes.
The difficulty associated with the determination of the strength of reinforced columns or walls subjected to combined axial load and biaxial bending is primarily an arithmetic one. The bending resistance of an axially loaded column or wall about a particular skewed axis is determined through iterations involving simple but lengthy calculations. These extensive calculations are compounded when optimization of the reinforcement or cross-section is sought.
This example demonstrates the determination of the design axial load capacity, φPn, and the design φMnx and φMny moments corresponding to the following case: The neutral axis depth of 36.12 in., at an angle of 120ยบ counterclockwise from the x-axis of the cross section. The figure below shows the reinforced concrete C-shaped core wall cross section in consideration. The calculated values of the wall axial strength and biaxial bending strength are compared with the exact values from spColumn engineering software program from StructurePoint.
The steps to develop the three-dimensional failure surface (interaction diagram) using spColumn will be shown in details as well.
This core has been extracted from the complete design example presented in Chapter 6 of “Simplified Design of Reinforced Concrete Buildings” book to provide lateral support of a multi-story building. Additional background information about the building geometry and loads can be found in the reference.
Figure 1 - Reinforced Concrete C-Shaped Core Wall Cross-Section