need to reinforce stair stringers?

I just put in three stair stringers - about 16 inches apart for a 38 inch wide set of stairs - 5 steps in total.

I used 2x12 and cut the risers and runs out. Riser=7 and run=10.

I know this is the wayto do it (right?) But I just want to check and make sure thatthe 2x12 will still be strong eno0ugh. There is approx. 5 inches of wood atthe lowest point of each rise/run point. This wouldnt break, would it? I didnt overcut, sostrength wasnt compromised there.

Im just wondering if I should glue/screw a 2x4 along the side of the stringer, belwo the cuts and on the inside where it would not be seen, as reinforcement.

Is this just overkill?

 

You don't need to reinforce it with only 5 steps. If you had more than about 7 steps, you would simply add a post at mid-span under each of the outside stringers and a beam across to support the center stringers.

 

Cut-out stingers sometimes can have one more drawback than simply weakening the stringer. I have seen the triangles fall off, due to straight line grain connecting the two ends of the cut.