6 ft tall 4×4 PT post out of plumb by 1-3/8". Excellent condition. Years old. Set in cement. Rock solid in part because tree roots have encased the cement. Tree too valuable to risk damaging roots by removing old post and cement, or placing new post nearby.
I plan to replumb the post by crosscutting about 2/3 the way through the post at 12" above the top of the cement. This will weaken it enough to bend at the kerf. Once replumbed (past plumbed, actually, to balance out forces), scab on 30" length of 2×4 PT, fitted to the bend, on the side with the kerf.
Question is on which side of the post should the kerf be placed? on the "overhanging" side so that the kerf opens when bent plumb? or on the sloped side so that the kerf closes when plumbed? Aesthetically doesn't matter.
EDIT: or maybe snap a plumb line from top to bottom, then saw off the "overhanging" 6 ft wedge, then scab it on to the sloping side.
Best Answer
Stronger if the kerf pinches, the reason being ...
Consider a post that is simply crosscut as mentioned (not reinforced with the 2x4 scab). This weak point will fail much more easily when the post takes a load (bent) in the direction that opens the kerf, as opposed to the opposite direction. This is because the post, when loaded in that direction, is vulnerable to splitting-out at the kerf. When loaded in the opposite direction (that closes the kerf), the post is not vulnerable to splitting out, but would break due to tension failure. Intuitively, it would take much less load to split out than to fracture under tension. If you don't trust my intuition, try this on a 2x4 to see which direction it more easily breaks.
Now consider a post that is crosscut and then reinforced with 2x4 scab as mentioned. If the kerf was placed so that replumbing opened the kerf, then the post would be under a permanent partial load to split out. If the kerf was placed so that replumbing closed the kerf, then the the post would be under a permanent partial negative load to split out, and under a permanent partial load for tension failure. Intuitively, the later makes for a much stronger repair.
The theoretical kerf width required for the closed-kerf scenario is 4 * 1.375 / 60 = 0.092, or about 3/32".
Attach the 2x4 scab with numerous smaller fasteners (not in the same grain line) rather than a couple large fasteners.
As for option two, snapping a plumb line, the easier thing to do is cut a short piece of 2x4 that is 1-3/8" long, then use it to space off one end of straight 6' 2x4 when screwing (or clamping) the 6 footer temporarily to the the post on the opposite side of the cut, then use an adjustable ripping T-guide (that came with the circular saw) to carry out a uniform width rip. Make the rip top to bottom on one side, then bottom to top on the other, keeping the wide part of saw shoe on the post. If the post is too thick for the rips to meet (6x6) complete the rip with a third pass using a sawzall.
In the end, I used the closed kerf method, and attached the trimmed-to-fit 2x4 scab with 12 torx head 3" screws and full caulk. When hit with a fist, it vibrates just as the intact post did, like a tuning fork, though rigidity and strength are not the same. If I had to do it over again, I'd use the same approach.