if the carpet is staying then roll the bottom and pad out with an extra bit off underlay if needed its better iff you can avoid cutting the riser at the bottom iff possible to reduce the risk off creaking but should be fine iff everything is tight and well glued
I would (have major misgivings about completely cutting through the bottoms, or tops of the stringers, that is). The weight of stairs and its' load (which could easily be something like two 100kg adults carrying a 50kg bed) is borne by in part by the notched out undersides of the top ends of the stringers (where they sit on the upstairs trimmer). The two flats at the bottoms of the trimmers where the stairs connect with the lower floor is where the majority of the load is transmitted into the building, and is why in multi storey buildings a trimmer or steel is generally sited just below this point. Any side fixings into walls (and bear in mind that with timber or MF stud walls and even many modern masonry built buildings there won't be any) are really only added to stiffen the stair. So if you cut through the stringers and push your laminate under them you are likely to find your laminate carrying the load of the stair as the ends of the stringers settle onto it. That sort of defeats the object of having an expansion joint
So, it's far safer to do a 5 to 10mm undercut (multitool, narrow chisel) because even if you have the side fixings there is no guarantee that they'll carry the load
In fact B-A, you can probably get away with undercutting the bottom tread riser. In many cases it's just something like 12mm plywood and it should be glued and wedged into the housings on the insides of the stringers as well as being glued into a groove on the underside of the first step tread and being fixed with glue blocks at this junction:
It may be an American example, but the same techniques are used to build that as we use for closed riser stairs over here. You should be able to make out the tapered housings, wedges and triangular glue blocks in the example above. When the stairs have been properly fitted there may or may not be brackets or a timber block fixed into the floor behind that first riser to hold the flight in place. Older stairs quite often just have a couple of big nails put in diagonally from behind to spike the stairs to the floor. Either way it's all metal to hit and wreck a blade when undercutting
The big problem comes when you get a bottom step like in this example from Stairplan:
In this instance I'd possibly want to see exactly what was behind the bottom step providing it with rigidity - if it was only an 18mm plywood former laid on the floor, I'd find another way of doing the job than undercutting the lot
I think I can hide the expansion gap with carpet where it meets the riser. I'll very carefully undercut 5 - 10 mm for the expansion gap of the stringer and I'm hoping that will be fine..
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