The document gives an overview about some of the details related to the O-Calc Pro vertical loading/buckling calculations. O-Calc Pro uses the Euler Buckling equations, with fixed on one end and either free or pinned on the other end. However, the basic load value results are derived from the Finite Element Analysis (FEA) matrix, so it is often difficult to compare the Euler Buckling hand calculations with the FEA results.  

Pole Example Description

In the example below, we are using the “Demo 1 – Tangent” pole from the O-Calc Pro Master Catalog. When adding the pole loading regulations, we used the NESC 2023 (Rule 250B) Grade B Heavy load case. 

The NESC 2023 (Rule 250B) Grade B Heavy load case has the following relevant parameters:

When the O-Calc Pro FEA is performed on this structure with this load case in all 360-degree wind directions, here are the relevant results generated:

These results can be viewed in the Analysis Report in the Pole Buckling table, typically on the last page of the report. Wind angle is shown on page 1 of the Analysis Report.

Buckling Load Factor of Safety (calculation)

By changing the Capacity display to the Numeric option, we can view buckling information as shown below.

The “Buckling %” is the ratio of (Sum_Vertical_Buckling_Load)/(Sum_Vertical_Buckling_Capacity)*100.

The “Buckling Height” is the “Buckling Column Height” displayed in units of feet and inches.  

The “Wind Angle” is 90 degrees. This worst wind angle is based on a 360-degree sweep wind calculation.

Analysis Report Pole Buckling Table Calculations

The O-Calc Pro Analysis Report has a table called ‘Pole Buckling’, find it on the last page of the report.  This section describes how various values within this table are derived from the FEA parameters.

Buckling Load Factor of Safety

The “Buckling Load Factor of Safety” = (Factor of Safety) * (Structure Strength Factor)

The “Factor of Safety” = (1/Vertical Capacity Utilization)/(Structure Strength Factor)

The “Vertical Capacity Utilization” is the “Buckling %” represented as a ratio, not as a percentage

Therefore, for our example we have:

“Vertical Capacity Utilization” = 9.9/100 = 0.099

“Factor of Safety” = (1/0.099)/0.65 = 15.54

“Buckling Load Factor of Safety” = (15.54)*(0.65) = 10.10  

Buckling Load Factor of Safety

“Buckling Load Applied at Height” = (Sum_Vertical_Bucklying_Load)*(Buckling Load Factor of Safety)/100

For this example, we get:
    “Buckling Load Applied at Height” = 2239.989 * 10.10 / 100 = 226.25

Buckling Load Capacity at Height (lbs)

The “Buckling Load Capacity at Height” is the “Sum_Vertical_Buckling_Capacity” expressed as a whole number, or for our example 22,705 lbs.

Buckling Column Height (ft)

The “Buckling Column Height” in the table above is just the BucklingColumnHeight value expressed in feet.  Therefore:

“Buckling Column Height (ft)” = BucklingColumnHeight / 12 = 262.952 / 12 = 21.91 (ft)

Buckling Section Height

The “Buckling Section Height” is the BucklingPercentColumnHeight expressed as a percentage, or

“Buckling Section Height” = BucklingPercentColumnHeight * 100 = 33.49