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The ideal total measurement for tread and riser combined is 17", with a minimum of 8" for the tread.
The problem in this basement stairwell is a clearance that is less than 6" high, making it likely that tall individuals will bump their heads as they walk down the stairs.
Check the outside of the stairway to reveal any problem spots. If the beam is supporting the upper section of the stairs the issue is with the landing. It is not feasible to remove the support beam so the span of the basement stairs must be shortened. This will add headroom at the point where an individual would stand beneath the beam.
In this home, the existing stairs have treads that are 11-1/2" deep (Image 1). On a basement stairway like this, a 9-1/2" tread is sufficient.
Shorten each tread by 2", this shortens the overall structure of the stairway and provides greater clearance below the beam.
Use a crowbar to pry up and remove the treads of the existing stairs (Image 2).
Now that the treads are removed, cut out the existing stair-stringers using a reciprocating saw.
With the run and rise of each step known, measure the boards for the new stringers and mark the cuts. Use a framing square as a guide (Image 1).
Construction Tip: When building stairs, the rise and the run of each step should add up to 17". So, for example, if the rise of each step is 7", the run should be 10".
Once marked, cut the notches with a circular saw (Image 2). Finish each notch with a hand saw to avoid cutting too far into the board.
Hang the stair stringers from above using specially designed metal plates (Image 1), which are available at home centers.
Support the lower end of the stringers with metal timber hangers (Image 2).
With the supports attached, the stringers are placed in position and nailed secure at the top (Image 3) and bottom (Image 4).
Before installing the new risers, test the newly heightened headroom by carefully walking down the center stringer (Image 1).
Set the new risers in place and nail them into position (Image 2).
Rip the original threads down to the new dimension of 9-1/2" deep, then reinstall them to complete the stairs.
Patch any damaged areas on the wall where wood was removed. Add any trim detailing desired.