Nice staircase... light and delicate in steel. I think that's something you have to model in FEM and use HSS sections due to their closed nature, torsional resistance and strength. One of the issues would be how the members can be bent and twisted without damaging/distorting the rectangular profile. It may be that the shape is too complicated and they have to be fabricated from plate and BAR material. One of the two most difficult projects I've done was a large and fairly concrete 'springing' stair in Regina... 40 years back and still standing, when I was almost a rookie.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

Just write ' HELICAL STEEL STAIR ' and search the web..two of the outcomes ..

This is a specialized plate work ..

https://www.youtube.com/watch?v=exFb5p8KAcM

https://youtu.be/S0qFnz-fSfY


My suggestion would be , search for local manufacturer ..

Tim was so learned that he could name a
horse in nine languages: so ignorant that he bought a cow to ride on.
(BENJAMIN FRANKLIN )

I agree with HTURKAK...find a fabricator who specializes in these. They'll likely have a specialist they use. Never fun to point a client to a different engineer, but for this kind of stuff it can be prudent.

Like a general practitioner sending you to a cardiologist. They know what the heart is, generally what to do to keep it healthy, and they know when something's wrong, but a cardiologist knows how to fix it.

You're the general practitioner who can design a stair when he needs to...the cardiologist is the guy who designs three custom stair cases per day.

That's not to say you can't do it...but there are plenty of issues, particularly with steel stairs. I could see vibration being a bit of a challenge in something like that. Start with the AISC design guide on steel stair design. Other than that, you'll need FEM as dik mentioned and you'll need to dust off some numerical methods to evaluate the shape and check your model.

They're correct... I live for tekkie stuff... My approach would be to design it.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

Like others have typed, you'll probably need an FE model. Definitely check vibration.

ASCE 7 might require a horizontal slip connection for seismic. Be sure to check that out.

AISC has design guides for both stairs and for curved members. YOu would likely need to do a FEM vibration analysis using a FRF and such, which is also covered in AISC vibration guide version 2. Combining them may help give you insight on how to design this appropriately.