As mentioned in the previous post, the Reinforced Concrete Design Functions spreadsheet includes a function for ULS analysis of circular sections, using either a rectangular or a parabolic-linear stress block. A new CircuPF function has now been added, for codes that follow a “partial factor” approach to the analysis, as in Eurocode 2. The input for Eurocode 2 specified factors has also been modified, to allow more convenient input for different National Annex factors. The new spreadsheet can be downloaded from:

## RC Design Functions8

The Eurocode parameter input is shown below. At present the only national annexes supported are the Default Eurocode values and the UK:

The output of the CircUPF function has been modified to show only values relevant to the Partial Factor analysis approach:

The graphs below show output comparing results from the spreadsheet, with the parabolic and rectangular stress blocks, with the results from the on-line analysis at EurocodeApplied,

When the rectangular stress block is specified the concrete stress is factored down by 0.9 by default, in accordance with the Eurocode 2 requirements for sections that reduce in width towards the compressive face. For 32 MPa concrete:

- The spreadsheet results with the parabolic stress block and EurocodeApplied results are in near exact agreement, except that the spreadsheet axial load is capped at the value that results in a moment capacity equal to the minimum eccentricity specified in the code.
- With the default 0.9 reduction factor the rectangular stress block is conservative for all axial loads.

Removing the reduction factor the rectangular stress block becomes slightly unconservative at axial loads above the balance load:

For very high strength concrete (of less than 90 MPa strength) the spreadsheet parabolic stress block and EurocodeApplied results remain in excellent agreement. The rectangular stress block results with 0.9m reduction factor are now conservative over the full range, with a reduction in capacity of more than 20% for high axial loads:

Removing the reduction factor the rectangular stress block results become significantly unconservative around the balance load, but remain conservative for high axial loads:

For a concrete strength of 90 MPa (the maximum covered by the current version of Eurocode 2) the spreadsheet gives results consistent with the code, but the EurocodeApplied results terminate at axial loads well below the section capacity (note that compressive axial loads are displayed as negative).

Reducing the concrete strength to 89 MPA generates results over the full range of axial loads: