I tried this on the first two steps, it still happened, I could do it the entire length, but I do not think it will work as desired.
I made a drawing of the two ideas I have.
The first will turn the section in a Box with a web.
The second will stiffen the existing flanges and web.
Hello friends, I projected an staircase using a W section beam (W150x13 kg/m), web and flanges about 3/16" thick. It uses a central beam as support with steel steps which will receive a larger wood step later.
It's doesn't move close to the places where it's bolted on.
Some pictures and...