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Spread Footing - Punching Shear

Spread Footing - Punching Shear

Spread Footing - Punching Shear

(OP)
For a concentric spread footing, when checking punching shear capacity against Vu how should Vu be calculated. I have always done (and seen in examples) as taking the ultimate pressure, qu, multiplied by the footing area minus the area within Bo. I am wondering why I can't take the full projection of 'd' on each side of the column instead of d/2 for the Vu. Is Vu = qu x (F_area - (c+d)^2) or can it be Vu = qu x (F_area - (2c+d)^2)? I realize that the failure plane is taken at the average distance d/2, but that is not the projected area of loading at the base.

RE: Spread Footing - Punching Shear

Not sure equations are quite right, but I get what you're asking.

The punching shear perimeter spreads out from the column at a 45 degree angle. We take the perimeter at d/2 because that's the mid-point and the the best way to calculate capacity.

However, if you project the 45 degree failure down to the soil, it intersects at a distance d from the face of support. right? And, only the load outside this perimeter would contribute to punching. It think that is a theoretically valid assumption. It is somewhat less conservative. So, perhaps that is why the examples don't do it that way. But, it seems valid to me.

RE: Spread Footing - Punching Shear

(OP)
You're right - I wrote those equations quickly and got it wrong, 2nd one you have been c+2d (both times I assumed square column).

It seems logical to me, and if you look at the assumed failure mode the statics should work out to taking a full 'd' on each side. Normally probably doesn't matter too much but if you have a d of 36" then that extra 18" on each side saves a lot of demand. I can't find any examples that do it this way though.. so I guess I'll stick with the more conservative method.

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