I-beam mono stringer stair torsional stiffness problem

Hello guys,
 
I recently mounted a single stringer i-beam stair. And it's unstable along it's axis. There's strong torsional movement as you step. So now I'm looking for a solution of this problem, so that after all the stringer will still look like an i-beam. I-beam was chosen because of design preferences, it's obvious that closed shape like rectangular pipe is much better against torsional forces. Here's a video of a problem https://youtu.be/N8_HAGHyPIY Stair is 4.2 meters long. I beam height is 16cm, 8cm is width. Also there will be glass mounted to the steps on the left side, with approx. load 20-25 kg/meter.
 
At the moment I see several solutions:
 
1)Weld a big plates to flanges all along the length on both sides. But not to the ends of flanges, like usual reinforcement. Instead weld it closer to web, leaving just 0.5 - 1 cm there. In the end it still gonna look like an I-beam, but with very wide web. Like here: https://res.cloudinary.com/engineering-com/image/upload/v1546982155/tips/Web_Idea_gj0nbk.jpg
What width of a plates should be? Is 0.5 cm enough? And how much space between plate and web is just enough?
 
2)Weld several perpendicular plates to flanges, like here:
https://qph.fs.quoracdn.net/main-qimg-e8dda2df0fabfd393dfc8131f5c36a9a
Have no idea how effective this is going to be for torsional stiffness.
 
Thanks in advance!

Hi,

Interesting problem. Yeah, an I-beam isn't the "best" section to resist torsion. I'm not sure what your background is, but did you (or another engineer) do any calculations? Calculating the torsional deflection isn't a hard problem, but retrofitting to eliminate it, is more involved. I think your option 1 would help a little. I'm not sure option 2 would help much.

You said it has to be an I-beam for design preferences. Could it be a larger I-beam? That would probably be the better solution.

Here's an online calculator which could help you determine the deflection. https://www.engineersedge.com/calculators/i_beam_section_torque_14325.htm
If you want more therotical references, here's a couple: 
https://engineeringlibrary.org/reference/beam-torsion-air-force-stress-manual
https://www.steelconstruction.info/images/6/6f/Sci_p385.pdf

But, in my opinion you should definitely have a qualified engineer to run some calculations.