Some carpenters attach a top riser to the two stair stringers, then lift them both up and attach the top stair riser to the floor joist. The riser in this case would be 3/4" plywood screwed securely into the upright part of the stair stringers and into the floor joists. Allow for this thickness when cutting the end of the stair stringer.
What I prefer to do is attach the stair stringer to the floor joist with toe nails (from the side of the stringer into the floor joist). Then place posts under the stair stringer, every 4-5 feet. This also eliminates any spring in the stair stringers. Don't rely on nails alone holding the stair stringer. If posts under the stringer would look unsightly, say on an outside stair from a deck, I try to use 4x4 posts for the handrail to support the stair stringer (from a pad on the ground up to under the rail) a couple of carriage bolts at each intersection would do the trick there. (For more info see Stair Rises and Runs.)
Dave(Ask Dave) (About Dave)
Hi, I'm Dave Osborne. With over 50 years experience as a journeyman carpenter, foreman and contractor in heavy construction I enjoyed working with apprentices and sharing the tricks of the trade that others shared with me. Now I get emails from Members all over the world and we include many of my answers in our Free Monthly Newsletters. Some of my answers include drawings and instructions specific to a project, but may also answer your questions. I use correct construction terminology, so you can confidently inform your building supply dealers or contractors exactly what you need.
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