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Determination of the splitting plane when calculating Atr for development length

Determination of the splitting plane when calculating Atr for development length

Determination of the splitting plane when calculating Atr for development length

I have a circular concrete column section with (8) longitudinal bars and circular ties. ACI defines Atr as total area of transverse reinforcement crossing potential plane of splitting through the reinforcement being developed. Do I define the splitting plane as:
1. The shortest length of concrete through one bar (angled through tie, giving largest area)
2. The plane between two adjacent bars (angled through tie, giving less area than #1)
3. Draw circles around two adjacent bars until they touch the column perimeter. The "plane" connects the dots from perimeter intersection to first rebar, to adjacent rebar, to other perimeter intersection (perpendicular through tie, giving smallest area)
4. Something else (probably this one)

Finally, if the splitting plane does cross the tie at an angle, is it even correct to use the area at that angle, or is the code intent to use the circular area as if the plane crosses perpendicular?

I know it won't make that much difference, I would just like to understand it. Most importantly, I would just like to be able to picture the correct splitting path. It seems like if it were to split due to bar tension, the splitting surface would follow the shortest path of #3, but that isn't a plane.

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