Eccentric load on a wide flange beam. 1

[graybeach]

Hello all,

I have been asked if it would be ok to hang a load of about 1.5 kips per foot (unfactored) along the tip of one of the flanges of a W8x31. The beam is a 16' simple span and only the web and the unloaded flange are supported at the ends. The load is parallel to the web. See attached for a sketch of the configuration.

The beam can handle the strong axis bending (it has cover plates), but I am worried about torsion. Checking the torsion using the AISC guide seems pretty daunting especially since I do not know how to handle the unsupported flange. As a simple check (that seems to show that this is not a good idea) could I just check if the web of the W8 can carry 1.5 kips/ft * 4"?

Doing this I get a moment of 0.5 k.in/in. Dividing by S = .285^2/6 = 0.0135, I get a bending stress of 37 ksi. Not good since our fy is only 33 ksi (it's from the '50s).

Am I oversimplifying here?

Thanks!

 

[BAretired]

You are not oversimplifying. Your theory is just plain wrong.

You say the beam has cover plates. What size are they? Are they continuous from end to end? Your sketch does not show cover plates. Cover plates may have considerable benefit in resisting torsion.

Your sketch indicates the beam is somewhat torsionally restrained. The bottom flange is laterally supported at each end to some extent by the web connection. How well it is supported is not immediately evident, but you could easily improve upon that by adding a bottom extension to the hanging supports. If in doubt, connect the bottom flange to develop torsion.

Checking torsion on a WF is not terribly daunting. I think you should use recognized methods to do it. Don't forget to check the torsional rotation as well as the stresses. And remember that you have the additional complication of considering the unbraced length for flexure combined with torsional effects.

All in all, I would try to avoid the torsion if possible.

BA

 

[InDepth]

You can always at a kicker to take out the torsion.

 

[JoshPlumSE]

The AISC design guide on torsion mentions a simplified hand calculation method. I usually refer to this as an "equivalent Tee" analogy.

Essentially, you take your torque and you resolve it as an equal and opposite shear applied to the centroid of the two flanges.

If you pretend that you can split the wide flange beam in half, then you're left with two tee beams in weak axis bending. Calculate the bending stresses that occur in these fictitious beams and you've got a way to approximate the warping streses that would develop.

It's not a theoretically rigorous method, but it should be conservative.

What I like about this method is it gives a good physical representation of the warping stresses that would occur. It's also much more generalized. In your example, the equivalent tee beam at the top would be considered a fixed-fixed beam, but the tee beam at the bottom would be considered simply supported.

 

[jberg]

Another method I use is a similar procedure from "Steel Structures: Design and Behavior" by Salmon, Johnson, and Malhas. It uses that equivalent flange load like JoshPlum said, but it introduces a warping torsion reduction factor, depending on the beams' warping properties.

Since the current AISC code covers strong-axis bending of plates in detail, I use that part of the spec. for designing for the warping stress. Essentially, I determine the Section Modulus of the flange only (tf*bf^2)/6, and assume the unbraced length is the overall length of the beam. This assumption is valid if the beam is braced against torsion at its ends, as in your example.

Joel Berg

 

[graybeach]

The cover plates are only on the middle third of the span. If the supports can't be modified to provide support to the bottom flange, does the equivalent flange method still apply? That's really my question.

 

[jberg]

As long as you would use a "simple-span" assumption for the bottom flange, I would not see any issue with using the equivalent flange method. I would be curious to see others' comments/thoughts.

If you had a deeper beam that had a "short" connection, I would start to wonder if the web truly is torsionally pinned, but with your W8" using 2 bolts, the web in my opinion is "torsionally" pinned. This type of problem was covered in the Steel Structures textbook, and what facilitates a torsionally pinned connection vs. a torsionally fixed connection.

Joel Berg

 

[graybeach]

Torsionally pinned is something to think about. I also wonder, if there are no intermediate stiffeners along the beam, how does the torsion flow into the whole section? Through the web in bending is the only thing I can think of.

 

[hokie66]

For the torsion to be resisted by the flanges, both flanges have to be connected to resist the resulting horizontal couple.

 

[csd72]

I agree with Hokie, both flanges need to be connected at the ends in order to resist the torsion.

The connection you have shown does not have a positive connection to the bottom flange and needs to be modified to provide this.

The effects of combined torsion and bending on this beam need to be considered including any buckling effects.

 

[civilperson]

Torsion is always greatest at the ends of a span. That is the critical section for analysis.

 

[csd72]

That is the critical section for shear stresses but not for buckling.

axial stresses from the warping are greatest in the middle of the span.

 

[miecz]

I believe DG9 provides for torsional design with unconnected flanges. Figure 3.3(b) of AISC Design Guide 9 shows a torsionally pinned end as a simple bolted connection. Example 5.1 analyzes a beam for torsion with two torsionally pinned ends.

 

[csd72]

What stops the entire beam from rotating?

 

[graybeach]

But say the beam stays as it is, and really gets loaded like this. Do you think the bottom flange would rotate and put the web in bending about the longitudinal axis of the beam? And that there would be distortion at the supports as the T shaped connection tried to resist the torsion reactions?

How bad would it be if it got constructed like this? The load is mostly dead load so distortion would be evident right away. This is a design/build project, and the contractor's engineer is insisting that it's ok. But I am a little worried about construction safety and wondering how big of a fuss I should make.

 

[csd72]

Are you in a position to ask for calculations?

 

[miecz]

What stops the entire beam from rotating?

I've always wondered this myself. I guess the bolted clip angle connection is ignored in the torsion analysis of the beam, but then must be designed to resist the torsional reaction.

 

[graybeach]

I have sealed calculations, but they do not make a convincing case for neglecting torsion. The ball is in the RE's court now. Hopefully he will either see what I'm saying or prove me wrong.

I am going to delve into DG9, but I still wonder how the section gets loaded in torsion if there are no stiffeners welded to the web and flanges.

 

[prex]

Hey guys, no one commented on the calculation initially presented by graybeach!
It is obvious to me (though I didn't check the numbers) that the load cannot be supported by that beam without any stiffeners, the web is yielding in bending under the load over the 4" arm, any other check on torsion or beam bending is useless.
This problem is similar to checking the bottom flange of a beam supporting a hoist: as there are two wheels there, only the flange, not the web, is under bending, but this will often be limiting in the calculation. That's why tapered flanges are normally used for that.

prex

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[BAretired]

Mt = 1.5 * 8 * 4" = 48"k (torsional moment each end)

Rflange = 48/8 = 6k (flange reaction each end)

Web cantilevers about 1" down to bottom flange. Consider 3" length of web effective in bending.

Mweb = 6*1 = 6"k or about 2"k per inch effective width.

S = 0.0135in^3 per inch, so f = 2/0.0135 = 148 ksi (NO GOOD).

In order to develop the bottom flange to take torsion, it would be necessary to extend the web of the hanger down with a clip angle capable of resisting 6k horizontal force.




BA