How to build up height of concrete wall to use as beam support for deck

Question

I have two concrete walls on either side of a proposed deck area. In the middle of the span I have some concrete columns that will support a beam for a deck. My proposed deck design has 2x12s sitting on the concrete walls and attached with 2x12 joists to the center beam that rests on the columns. The height of the walls is ~6" lower than the columns.

How should I build up the concrete wall to support the 2x12s at the same height as the center columns?

If it was 1.5" lower than the columns then I would put down a sill gasket, epoxy in some anchor bolts and put a plate down and have 2x12s sit on it. With it 6" lower I have to build up 5.5 inches.

Ideas?

Maybe I put down a plate, anchor bolt it, add two 2x members cut to 4" high, top it with another plate to make a box for the 2x12s to sit on and have the anchor bolt high enough that I bolt the top of the box to the concrete.

Concrete walls are level and flat. I'll plan for a 2% slope from the top of the plan view to the bottom - away from the house. This deck is self supported and does not tie into the house.

Attached a sketch of the plan view of the structure. Ignore the first level deck

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                               |  |  |
      6" gap                   |  |  |
      ______                   |  |  |                       ______
     |      | <-- concrete     |  |  |<-- 2x12 beam         |      |
     |      |     wall         |  |  |                      |      |
     |      |                  |__|__|                      |      |

Answer 1

Your final suggestion is probably the simplest, but you don't need to run anchor bolts all the way from the top of the sleeper beam. You also don't need a top plate. Just bold down the plate, then fasten the other two beam components to it.

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If you'd rater keep the space over the beam open for airflow or light or whatever, you can probably find an elevated post/beam support that will reach that far and not break the bank. Then you could put in a flush beam, like the one at the center of your current plan.

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You'd need to install supports at intervals that suit the beam size and load.