SPF core stair treads

Wood movement is an important consideration and it's good to know you're thinking about it now and not trying to fix it after the fact.

Wood tends to expand the most across the width of a board and not so much across the thickness. This means that your 11-1/2" (or so) wide tread^† will tend to get wider, pushing the nose of the tread farther out in the "overhang the riser below" position, but won't vary in thickness very much at all. To accommodate this, you'll need to attach your different woods together carefully and design the attachments to the treads carefully, too.

When it comes to attaching the top & bottom hardwood to the construction lumber, you want to have any fasteners in a single row to allow the different woods to expand independently. Your SPF tread core will expand differently than whatever hardwood you choose for the surface. Also, unless you're getting your 3/4" veneer from the same board, your veneers will all expand at slightly different rates, as will the SPF tread cores. Wood is a natural product and no two boards are exactly the same.

Attaching the veneer top to the core at only one point to allow for expansion gives you the possibility that the top will curl and that will be a trip hazard. Quarter or rift-sawn lumber will significantly reduce the likelihood of warping and, for a mission critical portion of the project like a stair tread, is going to be a much less expensive upgrade than the hospital bills or lawsuit from a tumble down the stairs.

A thin veneer of wood (I believe that 1/32" to 1/16" is normal for a commercially purchased veneer, some may be even thinner) shouldn't impact your wood expansion much and it should be attached with normal contact-cement-based veneering methods.

Your update to indicate that you're planning on resawing and laminating the stair core portion will help reduce cupping, but still won't impact expansion. I'm not exactly sure where the "11 pieces of..." lumber will each go, but I'd suggest that 2 or 3 pieces per tread^†† with alternating growth ring patterns should be sufficient to significantly reduce potential for cupping.

To attach the treads to the stringers, I'm envisioning some sort of plate with screw holes welded to the metal stringer section(s). If you have a single row of screw holes, then simple round, countersunk holes will allow the wood to expand on both sides of the screw and should eliminate any splitting issues due to expansion. If you do this, be sure to install the treads away from the stringer's risers to allow the wood to expand and fill the gap. I cannot tell you how much expansion room to leave, but you can find wood expansion tables online and they should serve as a good guide. Remember, each piece of wood is unique and these are guides only, not guarantees.

If you're planning on a square of holes, make sure that the screw holes are elongated into ovals so that when you drive the screws through them, the screws can move in the oval slots as the wood expands and contracts. You want the screws to be tight enough to hold the tread securely, but not so tight that the screw cannot move at all. Overly tight will cause the tread to split where the screw is as the wood tries to expand.

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^†An 11-1/2" deep tread (nominal 2x12 construction lumber) is extremely deep and possibly a violation of building codes. Please make sure that this is acceptable to your local building inspector before investing a lot of money in this lovely sounding custom staircase only to have to scrap the whole thing because it doesn't meet with the inspector's approval.

^††Make sure you use plenty of glue and plenty of clamps and plenty of clamp pressure when gluing these up. Check out Woodworking.SE for loads of Q&A's on doing glue ups to see just how many clamps are necessary to get a good glue up.