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# the formula for the beams to take lateral moment

## the formula for the beams to take lateral moment

(OP)
Hi just want to know a formula/table for the beams to take lateral moment.
The beam will take moments at strong axis, and also will take lateral moment, which comes from offset load from the beam.

Thanks

### RE: the formula for the beams to take lateral moment

That sounds like strong axis bending plus torsion to me. No direct weak axis moment.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: the formula for the beams to take lateral moment

Agreed. If that is actually the case, I recommend first making sure the offset load isn't avoidable, and then AISC Design Guide 9.

### RE: the formula for the beams to take lateral moment

What kind of beam? What is the material and shape?

### RE: the formula for the beams to take lateral moment

(OP)
A regular w21x50 composite floor beam. Customer wants to open slab and cantilever a 20'long stair onto the beams.

### RE: the formula for the beams to take lateral moment

If you do in fact have weak axis bending to contend with, the procedure is generally to consider strong and weak axis uniaxial bending independently and then combine the two using a code specified interaction equation. If you're in the US, you'll find that in the AISC steel construction manual.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: the formula for the beams to take lateral moment

(OP)
no there is no weak axis beaning. it's strong axis bending and torsion, I just cant find the formula.
Also will composite beam help for torsion?

### RE: the formula for the beams to take lateral moment

#### Quote (jdengos)

no there is no weak axis beaning. it's strong axis bending and torsion, I just cant find the formula.

The information that you seek is in that AISC design guide that Lomarandil mentioned. In particular, I'd recommend the bi-moment method.

#### Quote (jdengos)

Also will composite beam help for torsion?

Probably not in any way that you'll be able to quantify using established design procedures. That said, your best bet here may well be to brace your beam to the floor deck and detail things such that the W21x50 doesn't actually need to deal with the torsion. This is generally the best strategy for dealing with torsion in wide flange steel beams as they suck at resisting torsion, particularly with regard to stiffness. If you post framing plan / stair section sketches, we can help you with that aspect of things.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: the formula for the beams to take lateral moment

(OP)
The w21x50 would be able to take much torsion, even composite deck wont help on torsion as I think.
If I add several beams on the other side of the W21x50 with moment connections, will they be able to balance the torsion, if so, how?

### RE: the formula for the beams to take lateral moment

#### Quote (jdengos)

If I add several beams on the other side of the W21x50 with moment connections, will they be able to balance the torsion, if so, how?

I believe so. We call those roll beams in my neck of the woods. As the W21 would tend to twist, the roll beams would tend to flex in strong axis bending. Since the strong axis bending mechanism is the stiffer by far, you would effectively shield the W21 from attracting significant torsion.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: the formula for the beams to take lateral moment

If this is a situation with a floating stair mid-landing, I'm not sure that you'll have torsion on the w21. Your original description of lateral bending may be more accurate. And the concrete deck may be your best friend here as that will be a great place to dump horizontal loads. Do you have any stringer-beam connection details developed?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: the formula for the beams to take lateral moment

(OP)
The slab will help only the top flange, not the bottom flange. Plus the lateral moment is huge (144 k*feet on one stringer, total 288 k*feet).
I am thinking opening up the other side of slab, and install moment connections cross the W21x50, then pour back the composite slab.

### RE: the formula for the beams to take lateral moment

Having dealt with issues related to floating monumental stairs before, I thought I'd look into your question as well as overall scope of this stair.

First, are you are framing it like this?

As for torsion / weak bending, the existing W21 shouldn't get either if you run the stringer backspans through it. Given how close your new header is to the existing W21, I'd consider having them shore the W21, cut it at the new stringer backspans, and then re-connect it to the stringer backspans. Sounds counter-intuitive, but it permits a better stringer backspan and avoids six moment/torsion connections through the web. Also addresses your OP question by eliminating the question or torsion altogether.

You can learn a lot about monumental stairs via modeling in Elements and toggling the support fixities. Doesn't replace learning it yourself, but sure helps speed up the process. Your concrete slab should be able to take any lateral thrust, but this is where toggling can help you verify that.

Overall, deflection of your landing is the biggest concern.
You'll want to consider construction sequence, cambering, tread material, etc. My suggested framing plan forces contractor to erect the lower flight last, which can also help your deflection challenges.

Last point---never hurts to add up the steel tonnage/\$ savings if you were to add a single round post at the center of the landing. Back-pocket negotiation.

### RE: the formula for the beams to take lateral moment

(OP)
Thanks for the great input.
It's very smart to use a new beam to attach the stair, rather then using the existing W21. But we still need to demo the slab in order to install the moment connections, right? This way the two new beams on the other side of the W21 is a problem.
Before I am only thinking attach the stair to existing W21.

### RE: the formula for the beams to take lateral moment

Can you confirm that this is indeed a floating stair jdengos? It makes a big difference to the advice that we're giving you.

#### Quote (jdengos)

The slab will help only the top flange, not the bottom flange.

Not necessarily. With the addition of some angle braces up to the slab/beam intersections behind the stringer connection, the slab can be made to effectively restrain the bottom flange as well.

#### Quote (jdengos)

Plus the lateral moment is huge (144 k*feet on one stringer, total 288 k*feet).

Regardless of what detailing you go with, I'd recommend modelling the connection at the bottom of the stringers (point A in my sketch) as a flexural hinge. Three reasons for this:

1) As you're finding out, dealing with all that torsion (lateral moments) is tough and;

2) Even if you successfully deal with the torsion, the supporting beam will be very flexible with regard to twist and, therefore, likely not behave as you've modeled it.

3) The dominant behavior for these kinds of stairs tends to be axial load in the stringers being resisted by the axially stiff floor slabs. Modelling and designing your system to suit this mechanism will likely be the path of least resistance and best performance.

Without knowing anything about your particular string/slab detailing, I've sketched a possible detail that I think would work well here. There would be no appreciable torsion in the W21x50. All of the reactions would really be springs of sorts of course as there is flexibility in all things, particularly the beams.

Often times, demolishing some of the slab is the only way to keep the transition detail clean.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

### RE: the formula for the beams to take lateral moment

Also, in my experience, it is vibration that is the most critical issue for floating stairs. In particular, the tendency for the floating landing to vibrate laterally. Another great reason to stick to a very stiff load path.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

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