Cantilevered beam design for stairs landing 2

[DoubleStud]

So the blue area is cantilevered light gauge steel joist. The red is a beam I want to specify that will support the steel stairs. This is a mezzanine inside of a steel building. According to IBC, the live load of the stairs shall be 100 psf. How do you model this red beam? Just put a point load right at the end of the cantilever from one stringer? The load from the other stringer will just go straight to the near column. How much deflection would you allow and how much load shall I put on the back span? I am not sure what people typically do for this situation but the deflection is heavy controlled by the back span loading. But the back span barely has any loading because it runs parallel to the joists.

 

[Greenalleycat]

For a cantilever beam it is convention to check a variety of load patterns
Typically, all spans fully loaded, then both spans individually loaded for the relevant live loads + dead loads
I would always model in the dead loads but I think most codes require you to put a 0.9 factor on the helping backspan
I usually ignore that but will take a more conservative dead load on the cantilever and take a minimal dead load on the backspan which has the same effect anyway

I would just put a uniform load on the cantilever portion and take the full trib width of the stair - it'll work out near enough the same to splitting it into two point loads then ignoring one
There are multiple ways to tackle this problem of course

The deflection criteria is a bit of a tricky one
You'll need to consider multiple cases, as any deflection at the tip of your cantilever beam will be additive in a complex way with the deflection of your stair stringer
I suspect point load vibration will be a governing case

 

[dik]

Make it a little stiffer because loads on stairs include a little 'bounce'.

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

-Dik

 

[Eng16080]

Be sure to account for the uplift at the end of the beam resulting from loading the right span fully and leaving the cantilever unloaded.

In terms of loading the cantilever portion, I would have a single point load at the end as well as another point load just to the left of the support. The point load next to the support will likely have little effect on the beam size, but I like to include it to keep things simple. That way if you were to take the reaction at that support and use it to design a column at that location, there won't be any confusion. Otherwise, you could forget that you didn't include the load from the right stringer.

 

[JAE]

We might model that in RISA and do a dynamic analysis to get the frequency of the beam. Try to keep it higher than 5 Hz.

 

[Eng16080]

JAE, for my own curiosity, where do you get 5 Hz? Is this based on the AISC Design Guide for vibration control (forget which DG number)? Vibration isn't an aspect of the design that I normally check, and I've been meaning to look into this more.

 

[JAE]

Yes - it's a very rough idea of a limit for human comfort I believe. Perhaps based on this from a Thomas Murray article:

Also from Design Guide 11 there's this old chart that is helpful:

 

[JAE]

There's also an old (very old) article on cantilevered beam vibrations from AISC Steel Journal in 1977 by Murray:

 

[Eng16080]

Thanks JAE. Good stuff.