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9"x9"x0.5" tube embedment in concrete.

9"x9"x0.5" tube embedment in concrete.

9"x9"x0.5" tube embedment in concrete.

(OP)
I designed a column (tube 9"x9"x.5" A500 Grade B Fy 46)for seismic load in cantilever, fixed at the footing and pinned at top, I will embed this column into concrete pile footing 3' Dia x 7' deep. Q How do I should design the embedment of the column into the concrete, not the concrete into the soil.
I used the UBC to calculate the pile footing embedment into the soil. Is any book or article that I can use for design this embedment?

RE: 9"x9"x0.5" tube embedment in concrete.

The fixity of the column into the pile can be considered in several ways.  You'll need to check from a couple of perspectives to get an appropriate answer.

Assuming the column carries some moment at the embedment, compute the crushing force from the moment couple on the tube face against the concrete.  Set the stress level in the concrete to a code-acceptable level with appropriate factoring.

Next check the shear in the concrete caused by the couple.  Again, set to acceptable code level.

Check the pullout bond of the tube against the concrete.  There are several relationships for friction of concrete cast against steel and bond of concrete cast against steel.  You can also add pins in the column to affect better pullout resistance.

Check the pullout shear in the concrete.  Assuming full bond between the concrete and steel, check the shear stress in the concrete (similar to checking for bolt  pullout).

Optimizing each of these should give you a reasonable embedment depth, which will likely be somewhere between 12 and 18 inches.

RE: 9"x9"x0.5" tube embedment in concrete.

  Ron has good points. I would also check the tube crushing with the first check as well as the concrete. I think he meant that.

  I believe that without a net uplift force on the column, pullout strength should still be checked due to the pullout caused by the deflection at the top of the column and rotation of the pile.

 I would consider bearing at the end of the tube and if a bearing plate is req'd for gravity loads. Concrete bond with the steel should help for gravity load also.

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