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]]>They use a very large number of segments, so the error introduced by that approximation is very small, and much less than the difference between the parabolic and rectangular stress block. In the ULS design functions spreadsheet I use trapezoidal elements with a rectangular stress block, but I will shortly be posting an update to my RC Design Functions which has a CircU function which has an option to use the parabolic-linear stress block with circular section properties, rather than dividing into multiple layers. That gives very close agreement with the on-line calculator.

The rectangular stress block isn’t too bad with circular sections with low strength concrete, but with higher strength concrete, as the Eurocode curve becomes more triangular with a very small (or zero) rectangular part, the difference becomes more significant.

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]]>DonB’s reply is pretty much what I was going to say. Since analyses are normally done with columns treated as lines positioned on the concrete centroid, it seems to me that it makes sense to use that point as the reference for bending moments due to axial loads. A column with very high axial loads would normally have symmetrical reinforcement anyway, but if it doesn’t it seems to me that the analysis should allow for that.

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]]>Hi Eduardo – I don’t get that. Could you send a copy of your spreadsheet to my gmail account (dougaj4) and let me know your Excel version.

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]]>Overall I would guess if using the parabolic stress block the error is likely in the same range the rectangular stress block so probably limited impact on design strength by maybe some impact if you need to get into curvature checks.

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]]>you can evaluate moments at any point in the cross section as long as you transform your analysis results to that point/axis orientation.

The geometric centroid is convenient because most modeling programs have you modeling bar elements using the elements centroidal axis, so the analysis results are reported about the cross section centroid.

The use of the plastic center is convenient for the compression side of the interaction diagram because summing moments about that point yields 0 moment at maximum compression, the same isn’t always true for the tension side of the interaction curve depending on how the plastic center was computed.

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]]>Hi Doug,

Sorry, maybe I didn’t explain the question very well.

Yes, I’m talking about non-symmetric sections under significant compression or tension loads, which as you note would have an associated bending moment relative to the uncracked concrete centroid.

My question was about the comparison of design actions (e.g. out of an analysis package, or hand calculations) against the interaction diagram. Is it always appropriate to take that uncracked concrete centroid as the basis point for generating the interaction diagram, or would the plastic centroid (for significant compression loads) be a more appropriate point, at least in some cases?

For interest, I checked what RAPT does for a column interaction diagram and it seems to evaluate moments relative to the plastic centroid (so at crush load there is no moment).

Cheers

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]]>Hi James,

There’s actually always asymmetry in the cross-section in a cracked section unless the section is all in tension or all in compression, but the effect of that is included in the moment calculation.

For a circular section (assuming uniform reinforcement) the all tension and uniform compression cases will always have zero moment, but for a rectangular section with non-symmetrical reinforcement, or a non-symmetrical section the extreme load conditions will have an associated bending moment, since the moment is calculated with respect to the uncracked concrete centroid, ignoring reinforcement.

Does that answer your question?

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]]>I was just wondering your conceptual thoughts on cross-section asymmetries. Particularly, where cross-section asymmetry (either due to concrete shape, reinforcement quantity etc.) leads to a ‘skew’ in the interaction diagram, with apparent moments associated either Crush or Max Tension capacities.

I am thinking that (depending on the structure configuration) this skew may actually manifest or may not – e.g. depending on whether the section is loaded by an action with a determinate eccentricity (like a single bridge pier loaded from beams above), or whether it forms part of an indeterminate frame (like a pile group, where any minor eccentricity would be distributed).

Is this something you have looked at before? I am yet to see this treated well in any textbooks.

Cheers

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