The question is; Can the stairway hold it’s own weight as well as the working load being put on it.
Osha requirements for a stairway;
From a design standpoint, the specified design loads (e.g., normal live load and moving concentrated load of 1000 lbs.) must be placed where the maximum stress is experienced by the individual structural components of the stair system.
Looking at a framing section of a stairway the sawtooth cut boards are called stair jacks. Looking closer at a jack the deepest cut of the notch for the step into the jack to the bottom side of a jack if your using a 2” x 12” will be 3 1/2” to 4” of uncut material is equal to a 2” x 4” with this understanding we can calculate out what a 2” x 12” stair jack system can carry. With all lumber we do not measure the length of the steps from the top to the bottom but instead from the front edge of the step to the load bearing point that supports the top of the step. A wall height of 8’ and a floor joist of 9 1/2” will make the run of the stairjack 12’5”.
A single 2”x 4” spanning 10’2” can only carry 10 Lbs. per running foot times 3 jacks a total of 300 Lbs. Nailing a 2×4 on the side of the jack doubles the working load to 600 Lbs. But on the problem above we are short 2 1/2 feet. Going to a 2” x 14” stairjack will leave a 2” x 6” amount of material left this will carry a 20 Lbs. 12’9”
With 3 Jacks the total dead and live load for this stairway is now 12.75 x 20 x 3 jacks= 765Lbs. adding 3- 2” x 6” on one side of the Jack doubles the load 1530 Lbs. This is now a legal working stairway for wood steps.
The problem now comes in when the homeowners want stone on the treads and risers. The weight alone is 32 Lbs. per SF or 1153.1 Lbs. for this stairway. And it only leaves 377 Lbs. for live load. Changing and using a LVL or a micro laminated beam works much better. Using a 1 3/4” x 14” LVL beam with a 12’9” span will carry 68 per SF. X 3 Jack you a total working load of 2601 Lbs. this passes with flying colors. This gives you a live load of 1448 Lbs. Or in other words, you can have 6 adults sitting or standing on the stairway for a group photo and it will not wince.