Program Notes for the FDOT Biaxial Column Program

# How to use

To run the program, go to the start menu, select the FDOT Programs group and then the Biaxial Column Program. One selected, a dialog box will appear where you can enter the column specifics. Most of entries are self-explanatory. The only one that may not be is the General -> Number of Divisions. This value is the number of interaction diagrams that will be calculated for the 3D representation. For example if a value of 4 is entered interaction diagrams will be calculated for the neutral axis oriented at 0, 90, 180 and 270 degrees to the section. For most sections this will not be sufficient and a minimum of 8 divisions is recommended thereby calculating interaction diagrams at 45-degree increments. After the section of interest is created it should be saved (file ->save) with a unique name before pressing the Calculate File 1 button. In the Mathcad file, make sure you enter Math -> Calculate Worksheet so that all the critical data will be saved allowing you to use the Calculate File 2 button for another section. Once the Calculate File 1 Mathcad file has been run, use of the Calculate File 2 button to open a second identical Mathcad file, allowing you to avoid recalculating the interaction diagrams for the saved shape and reinforcing layout in File 1. Note that new loads may be added without running the Calculate mode again.

# Entering Custom Shapes and Voids and Bar Layouts

Custom shapes and voids must be entered in a clockwise direction using Concrete Column -> Shape -> Custom. In addition, the last coordinate entered must match the first coordinate for a shape or a void. For all custom shapes, voids and bar layouts the coordinates entered must all lie within the positive quadrant.

# Modeling Curved Shapes

Curved shapes must be modeled with polygons (Concrete Column -> Shape -> Regular Polygon) that have enough points to closely approximate the area of the shape. For example, a circle can be modeled with a regular polygon of 24 sides and be within 1.5% of the area of a true circle; 32 sides would deviate by less than 1% of the area of a circle. The program allows a regular polygon with up to 94 sides to be created.

# Application of Phi Factors

The program can apply phi factors using two different algorithms, General -> phi for Flexure, Axial. The default method is shown in the current AASHTO LRFD 5.5.4.2, which uses a defined phi factor for compression controlled, tension controlled, or an interpolation between the two based on strain in the reinforcing. The alternative is the LRFD method prior to 2005, where the phi factor is based upon loading type (axial, flexure, or both).

# What it does

The program generates a scatter plot of the 3D interaction diagram (Pn, Mn) and the 3D interaction diagram multiplied by the appropriate phi factor (Pr, Mr). The interaction diagrams have a flat top that reflects the maximum allowed axial capacity based on the AASHTO LRFD formula for tied columns. Columns with spiral reinforcing would have a slightly higher maximum axial capacity and at present this is not included. The engine for this portion of the program is Mathcad 15 Professional. In addition to the 3D interaction diagrams the programs also draws a slice through the combined interaction diagrams (Mnx,Mny) at the value of the axial load of the selected point of interest. These slice graphs can be used to check the capacity of the section to carry the required loads. Secondary effects are not included directly and the moments of the loads of interest should reflect any required magnification. After pressing the Calculate File 1 or the Calculate File 2 button, the Mathcad file should normally be closed without saving since it acts only as an engine and this will prevent inadvertent changes.

# What can go wrong

There are typically two possible problems. The first is that Mathcad may have some problems caused by memory management problems or other internal errors, to resolve this, try running the file again (after closing the Mathcad file) with a different Number of Divisions (usually a smaller value). This will normally fix the problem with a little persistence. The second problem occurs if the program cannot resolve the shape into the correct trapezoids such that the combined area of these trapezoids does not equal the gross area of the shape. When this happens, the program for this location of the neutral axis does not return any values and continues on to the next angle of interest. If a void is entered counterclockwise instead of clockwise this will happen for all divisions.

# Areas of Concern for Eccentrically Prestressed Sections

Because there is not a constant location for the plastic centroid for eccentrically prestressed sections, the moment capacity is calculated about the centroid of the gross concrete section. As a result of this centroid location, application of the phi factor may result in an erroneous factored interaction diagram. This is due to the fact that the phi factor in the program is used to compute a new point by reducing the length of the vector extending from the origin to the point on the full interaction diagram. If the 3D interaction diagram is not centered about the origin, the reduction of the vector length will not necessarily shift the factored capacity value to a more conservative position that would correctly reflect the intent of the code.