10. Conclusions & Observations

The analysis of the reinforced concrete section performed by spColumn conforms to the provisions of the Strength Design Method and Unified Provisions with all conditions of strength satisfying the applicable conditions of equilibrium and strain compatibility.

In the calculation shown above a P-M interaction diagram was generated with moments about the X-Axis (Uniaxial bending). Since the reinforcement in the section is not symmetrical, a different P-M interaction diagram is needed for the other orthogonal direction about the Y-Axis (See the following Figure for the case where f_s = f_y).

Figure 12 - Strains, Forces, and Moment arms (f_s = f_y Moments About x- and y-axis)

When running about the Y-Axis, we have 2 bars in 4 layers instead of 4 bars in just 2 layers (about X-Axis) resulting in a completely different interaction diagram as shown in the following Figure. Further differences in the interaction diagram in both directions can result if the column cross section geometry is irregular.

Figure 13 - Comparison of Column Interaction Diagrams about X-Axis and Y-Axis (spColumn)

In most building design calculations, such as the examples shown for flat plate or flat slab concrete floor systems, all building columns are subjected to M_x and M_y due to lateral forces and unbalanced moments from both directions of analysis. This requires an evaluation of the column P-M interaction diagram in two directions simultaneously (biaxial bending).

StucturePoint’s spColumn program can also investigate column and wall sections in biaxial mode to produce the results shown in the following Figure for the column section in this example. In biaxial run mode, M_x and M_y diagrams at each axial force level can be viewed in 2D and 3D views.

Figure 14 - Nominal & Design 3D Failure Surfaces (Biaxial) (spColumn)

Figure 15 - Tied Column Interaction Diagram and 3D failure Surface Viewer (spColumn)

Figure 16 - Tied Column 3D Failure Surface with a Horizontal Plane Cut a P = 350 kip (spColumn)

Figure 17 - Tied Column 3D Failure Surface with a Vertical Plane Cut a 45º (spColumn)