Help me find the best way to do an inverted T shape cut in 2.4m oak sleeper

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Those brick panels look fairly tall and are effectively free standing. You have to be sure they do not fall over, I doubt that single skin would be adequate.
 
If this construction goes ahead it could cause some upsets in usual UK windy weather. Each infill panel may experience a total wind loading of between 1500 and 1600 pounds. It may be necessary to have a builders skip on site for a quick clear up.
 
Maybe screw in stainless ties into the oak every few courses would be helpful?
That would certainly transfer some of the loading to light duty posts not intended for this function. The proposed structure is high enough to require planning permission for it to go ahead as proposed.
 
Why not just fabricate it, facing panel, two spacer strips and two wider panels that actually hold it to the post. You could even simplify this by just having a few pieces that you rotate into the post slot to retain.
 
If it is a closed board fence then in windy areas you can have some major issues, even concrete post can snap but if you are building a structure in front that is connected to the fence then you should have no issues but if the structure just stands in front of the fence then it may protect from wind in one direction but it will still be vunerable from the other.
 
Anyone who lived in the path of Storm Arwen knows what wind can do. Woodland behind our house, mostly spruce about 50 years old, is completely flat. And such storms are likely to become more frequent.
 
Those brick panels look fairly tall and are effectively free standing. You have to be sure they do not fall over, I doubt that single skin would be adequate.
I would agree, if single skin with no support and not tied in at the sides, first time anyone leans on the wall it will collapse. You would be much better off to use wood or maybe something like wicker if you want a rustic look.
 
You can reinforce the brick panels by screwing expamet brick reinforcement to the posts at regular heights and bedding it in the mortar.

The panels will come loose and effectively free standing when the oak dries out and could fall out.
 
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I cannot see any dimensions for these panels but assuming they are 1.8m by 1.8m by 0.1 m they will weigh over 600 kg, if they should fall over they could easily cause serious injury or kill someone. As such they should be constructed in accordance with some good design advice or designed by a structural engineer.

Here is some advice from the brick development association. For a 215mm thick brick wall height varies between 1.075m and 1.925m depending on zone and exposure.
https://www.brick.org.uk/admin/resources/s-free-standing-walls.pdf
Here is an old paper on free standing brick walls, some useful advice near the end.
https://www.mbhplc.co.uk/bda/Structure-Free-Standing-Walls.pdf
LABC (building control) advice, anything over 1m, structural engineer.
https://www.labc.co.uk/news/10-dos-and-donts-freestanding-brick-walls
Tying a single skin of brick to a hollowed out piece of wood, fixed somehow to a concrete fence post which has been weakened by cutting the flanges off is not adequate support.

I recently found a structural engineer, Member of the Institution of Structural Engineers, which is just about the top qualification for a structural engineer, very reasonably priced. If you PM me I could send you his details.

Many years ago I designed a bridge over a motorway so I have some experience. I would not do what you are proposing.
 
Give up, as I doubt you’ll be able to do that.

Rip it in half, cut the necessary half channel and glue back together.

Or just cut a groove the width of the T and machine infill strips to neck the groove.

Why do you need to do this?
I agree with your first recommendation, it'll be much simpler and quicker. Nice one.
 
Why not put fence panels between the posts as is usual and then cut up your oak boards into 12mm thick cladding and clad the posts using construction adhesive and some long ss screws into the fence panels?
 
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