Resisting beam torsion with infill beams 2

[CDLD]

Hello,

I am designing a beam that is carrying welded HSS stubs with a lateral load and moment (causing torsion in the beam).
We intend to brace for the torsion using infill beams with simple shear tab connections.

In the attached PDF, are the stiffeners required to resist moment in Case 2 like they are in Case 1?

And if so, what would the moment on the stiffener be in Case 2?

Thanks,

 

[driftLimiter]

It isn't clear whether you want the beam to carry the torsion out to it's respective ends, or if the torsion is simply transmitted to a 'infill beams' concentrically.

If you want the beam to carry the torsion then you should follow design guide #9.

If you need only to get the moment directly from the post into the infill beam concentrically then you just need to check the shear tab with the moment added to it.

But if those infill beams aren't concentric on the posts you have twisting of the beam that needs to be accounted for and the stiffener plates will do nothing to strength the WF beam for torsion.

And to your question, both Case 1 and Case 2 shear tabs need to take some moment.

Your calc for stiffener plate bending moment capacity is a bit strange in this context, the plate itself isn't really going bend per se but instead it will see the bolt loads that result from the moment. I think that is what your most interested in here.

 

[CDLD]

Thanks driftLimiter.

The posts are concentric with the infill beams.

What would the moment be on the stiffeners?

In case 1, my understanding is that the stiffeners are required to transfer the moment to the infill beam.
If this is not the case, then a standard double angle connection would be more effective.

 

[driftLimiter]

I think the connection has to transfer moment in both case and 1. What I am saying is that the problem is more one of shear and bolt bearing in the stiffener plate than bending. The stiff plate is supported on three sides so it doesn't really displace like it would if it were cantilever or simple support.

 

[BAretired]

I am designing a beam that is carrying welded HSS stubs with a lateral load and moment (causing torsion in the beam).

The stubs are not causing torsion in the beam if torsion is resisted by infill beams. Torsional restraint is not required at beam supports.

Case 1: M_stiffener = 12'k
Case 2: M_stiffener = 24'k

 

[CDLD]

Thanks BAretired.

My question was poorly worded. If it weren't for the infill beams than the stubs would be causing torsion in the beam, you are correct.

Your moment values are what I suspected.
So the 1/2" stiffener with a resistance of 15.3'k would not be adequate for the case 2 moment of 24'k.

 

[CDLD]

BA,

Your response in the following thread seems to contradict with your response on this thread, which one is correct?

"You do not need a stiffener and there is no bending in the web. A slight torsional rotation is not a problem. It is limited by the flexural rotation of the supported beam."

https://www.eng-tips.com/viewthread.cfm?qid=477490

This diagram from design guide 22 shows a moment to be resisted by the stiffeners:

 

[BAretired]

BA,

Your response in the following thread seems to contradict with your response on this thread, which one is correct?

"You do not need a stiffener and there is no bending in the web. A slight torsional rotation is not a problem. It is limited by the flexural rotation of the supported beam."

https://www.eng-tips.com/viewthread.cfm?qid=477490

This diagram from design guide 22 shows a moment to be resisted by the stiffeners:

There is no contradiction. They are both correct.
I do not have design guide 22. Would prefer to review it before commenting on it, but I am not prepared to purchase it.

In your Case 1 and 2, a torsional moment is applied at discrete points along the beam. At each of these points, infill beams are rigidly connected to the beam which counteract the applied moments. There is no need to provide additional torsional resistance at the beam supports.

If torsional resistance is added at each end, the supports will take a small portion of the torque, not because it is needed, but because it is there. It shares the torsional stiffness with all of the infill beams.

 

[KootK]

So the 1/2" stiffener with a resistance of 15.3'k would not be adequate for the case 2 moment of 24'k.

It's conventional to consider the "stiffeners" to be the infill plates between the flanges and web on each side of the beam. Envisioned this way:

1) Your details show stiffener pairs such that there are two stiffeners at each HSS stub.

2) The moment in each stiffener of each pair would be as follows:

Case 1: Mstiffener = 12'k
Case 2: Mstiffener = 24'k 12'k

 

[BAretired]

It seems logical to consider each stiffener pair as a single stiffener 1/2" by 7" because they are welded together through the beam web.

I'm not sure about the calculation in the first sketch (Mr = 15.3'k??). If the applied moments are factored, Mr_stiffener is Z*phi*Fy = (bd²/4)0.9*50 = 275.6"k or 23'k.

 

[KootK]

It seems logical to consider each stiffener pair as a single stiffener 1/2" by 7" because they are welded together through the beam web.

What is important here, I think, is that OP appears to be using design methods that address one stiffener of a stiffener pair considered in isolation. In this, I'm referring to the AISC sketch and not the OP sketches where she is using the full width of the beam as the width of the stiffener for Sx. As such, I feel that she needs to be working with the moment attributable to each isolated stiffener (half stiffener by your logic) lest she accidentally double the demand needlessly.

 

[JoshPlumSE]

Your calc for stiffener plate bending moment capacity is a bit strange in this context, the plate itself isn't really going bend per se but instead it will see the bolt loads that result from the moment. I think that is what your most interested in here.

I want to return to this portion of the conversation.
a) You want to transfer the full 12 ft-kip through the stiffener / shear tab into the infill beam. At which point the in-fill beam must be capable of resisting it and you have an addition shear force in the infill beam connections.

b) You should check the bolts for the infill beam connection for this added shear. But, you also need to check to convert that moment into a series of shear forces on the bolts. My tendency is to think of it as the following:

==> 2*R
=> 1*R
<= 1*R
<== 2*R

M = 12 ft-kip = 2*(2*R*1.5*bolt spacing + 1*R*0.5*bolt spacing)
Solve for R and you get the bolt reactions.
Then sqrt [(2R)^2 + (vert shear)^2] = total shear in bolts.

c) You could also check the shear tab for capacity using the process for and Extended Configuration of a single shear plate connection. See AISC Manual 15th edition page 10-89 and 10-90.

 

[CDLD]

BA,

I agree with your comments.
My calculation was elastic, while yours was plastic strength.

KOOTK,

I get the sense that you are treating the stiffener pair as if they are supported by the top and bottom flange, which means that they are transferring a force to the bottom flange, which is exactly what I am trying to avoid by using infill/roll beams. I am treating the stiffener pair as if it were a cantilever from the top flange.

This is not the same as the design guide 22 case, where there is continuous torque along the beam, being transferred to the stiffeners/roll beams at intermittent points. IN this case, the stiffener would transfer force to both the top and bottom flange.

Additionally, in both case 1 and 2, the weld at the top flange should be sized to transfer the full moment (12 k',24k' respectively. The stiffeners do not have to bear on the bottom flange and could be stopped short without causing any impact to the model.

 

[KootK]

I agree with JP's latest. When one considers the manner in which the moment will be delivered to the stiffeners by the HSS walls -- and resisted by the bolts to the infill beams -- there isn't going to be much here resembling Bernoulli flexure. As dL intimated, in practice, this tends to be mostly about examining the concentrated loads delivered by the HSS walls and the bolts for the failure modes commonly associated with such things:

1) bearing.

2) tear out.

3) crippling.

....

 

[CDLD]

Thanks Josh for the comments.

I have no issue with the bolt calculations and agree with your calculations.

What I am interested in is the moment in the stiffeners.

Let's consider just case 1 for now.
If this were to be a double angle connection as opposed to a shear tab, would the web be OK?

I would think that the bottom flange would kick out due to the inadequacy of the web strength, and would result in some torsion being transferred to the main beam.

What do you think?

 

[KootK]

Additionally, in both case 1 and 2, the weld at the top flange should be sized to transfer the full moment (12 k',24k' respectively).

Certainly. I never meant to suggest otherwise.

I get the sense that you are treating the stiffener pair as if they are supported by the top and bottom flange...

No, not at all. I see the fundamental behavior as you do: as that of a cruciform thing cantilevered down from the HSS. This, however, does not prevent one from examining each half of the stiffener pair in isolation. I anticipated that you would want to do it that way in order to be consistent with the way this stuff is usually presented in the literature. If you don't want to do that, for whatever reason, that is of course fine as well.

 

[KootK]

If this were to be a double angle connection as opposed to a shear tab, would the web be OK?

The web alone, between the top flange and the clip angles, would have to resist the whole 12 kip-ft in out of plane bending. Maybe it works by the numbers and maybe it doesn't. Either way, it's an inferior setup in this regard.

I would think that the bottom flange would kick out due to the inadequacy of the web strength, and would result in some torsion being transferred to the main beam.

The bottom flange would kick out a bit owing to the flexibility of the connection with respect to twist resistance. At the same time, I would not consider this to result in any meaning torsion per se because, so long as the thing held, all of the torsion delivered to the girder by the HSS would still be instantaneously resisted by the infill beams.

Whether or not this condition would produce girder torsion in the real world would depend on how stiff, and how near, any adjacent torsional supports are to the connection being considered.

St. Venant and warping torsion, like Bernoulli flexure, require meaningful distance over which to develop. Where that distance is not available, as is the case here, it really becomes primarily a matter of local connection actions,

 

[CDLD]

KOOTK,

Thanks for the reply.
We are in agreeance.

These are the basic calcs for anyone interested.

I neglected to consider the clipped part of the stiffeners in the bending calc as well as the contribution from the web (cruciform shape).

As Josh pointed out you need to consider the vertical shear as well, although typically small.
EDIT: (in my sketch the vertical shear should be distributed between the three bolts, I showed it incorrectly)

Other checks would be contact bearing of the stiffener on the top flange.
Bearing/tearout checks of the stiffener[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1671674152/tips/calc_sz3ads.pdf[/url]

Thanks all for your input

 

[KootK]

As Josh pointed out you need to consider the vertical shear as well, although typically small.

By the book, you'd have at least four sources of simultaneous bolt shear to vectorially sum in the absence of infill beam axial loads.:

1) That induced by the moment transfer. This is, technically, an instantaneous center of rotation thing but I think that most folks would call it horizontal shear as an approximation.

2) That induced by the beam shears that, themselves, are induced by the moment. Vertical.

3) That induced by the horizontal load that must have created the HSS stub moment. Horizontal.

4) That induced by the ordinary, gravity loads on the infill beams. Vertical.

 

[CDLD]

Thanks KOOTK.

1 and 2 I covered in the calcs.
3. Correct, there is a lateral load that I left out, which would be shared by weak axis bending of the main beam and the beam that the infill beam frames into. The connection will see a portion of this load.

4. Agree, but just self weight of the infill beam in this case.