Question on moment arm for analysis/design 4

[Lion06]

I hope I don't come across foolish here, but I'm having a hard time understanding something. Let me explain the sketch I've posted before people start tearing it apart. This is not an actual detail, it is merely to help get across the point of my question.
The question is if you have a detail similar to this (whether it is a beam to column, or a column to ftg), would you use d for the moment arm to design the tension in the top anchor or (approximately) d+2g ( I know it would be from the top anchor to the centroid of bearing at the bottom angle, but just for argument's sake say d+2g)?
Does your answer change if you provide stiffeners such that the angles can be considered very stiff?

I'll give my opinion and explanation, then you can tear that apart.
I think you should use d as the moment arm in either case. I am differentiating this from a baseplate because a baseplate is a single (considered rigid) element that has a moment applied to it. This detail (whether stiffeners are present or not) has two individual angles with a tension and compression force applied seperately at a given location. While the baseplate is seeing 0 net force, moment only (assuming moment only and no axial load), these angles are each seeing a tension (or compression) force via the weld (not a moment only with 0 net force like a baseplate). I believe this applied whether the angles can be considered infinitely stiff or not because of the above reasons and the fact that they are so close to the end. If the angles were WT's and extended for some distance into the span of the beam such that the WT's had the opportunity to become fully engaged in helping to resist the moment, I would feel differently, but the angles (as they are currently shown) do not have that ability.

Any opinions?

 

[swearingen]

Absolutely - my fbd shows why this is true, given in your hypothetical that the stiffnesses of the parts can be ignored.



If you "heard" it on the internet, it's guilty until proven innocent. - DCS

 

[JAE]

nutte,

One thing that I sensed in drawing out the second free-body diagram was that the moment in the beam isn't constant.

My first thoughts on this were that there is an "M" in the beam that must be simply resolved through to the end bolts.

However, with the rigid angles welded to the end of the beam, I believe that the "M" that sort of comes in from the left, actually changes across the angle leg widths.

So you can't just say that M/d is the force in the flange because the M varies as you move from the left of the beam towards the end of the beam.

This is tough to visualize because we usually look at beams as single line sticks. This problem, to be correctly analyzed, would need an FEM analysis to really see what is going on since there are moments applied to the end of the beam at the left and at the top and bottom flange ends.

 

[haynewp]

"Cut a section just left of the angles. The flange force in each flange will be M/d. This assumes all the stress is in the flanges, with none in the web."

OK

"Now go right a little, at the angles. At the interface of the flange and angle, the horizontal force, called T1 in JAE's sketch, has to be equal to M/d for the horizontal forces to be in equilibrium"

It's not instantaneously all taken out of the flanges. It is taken out along the length of the angle's horizontal leg. The average shear force in the weld is as shown in JAE's angle FBD.

 

[haynewp]

JAE, you just beat me to it.

 

[miecz]

StructuralEIT-

I would design the anchor for that much smaller force. The weld would have a small shear, but a large moment. The weld would be designed per table 8-4, page 8-66 of the AISC Code, the lower sketch, with a large "a".

 

[swearingen]

JAE and haynewp have it - and again you can see it on the free-body diagram on the bottom of my sketch. The angle redistributes the total moment. My sketch is crude and is discrete, but I did it that way on purpose so it's easier to see.



If you "heard" it on the internet, it's guilty until proven innocent. - DCS

 

[PMR06]

What if you model the free body of angles and beam as another beam? See attached. Just load the beam with a couple equal to M/d and solve the rest using statics.

The the shear and moment diagrams explain what forces the parts are designed for. The extra force not accounted for in a free body of just the angle is the constant shear thru the beam web.

Is this model valid?

 

[Lion06]

If you had a case where the top angle were turned down and the bottom angle turned up, would you then design for a much larger anchor force for a rigid angle (say M/(d-2g)) and design for a smaller force if the angles were not rigid (M/d) as shown in JAE's first sketch?
I suppose so, it's just not so intuitive.

 

[Lion06]

Now that it seems most are in agreement that the weld should be designed for a shear of M/(d+2g) and the additional moment, Can I please get an honest answer as to how many people would have sized the weld for M/d or M/(d+2g) without giving it a second thought prior to this discussion?

 

[msquared48]

I would have used M/d, and it would have been conservative.

Mike McCann
MMC Engineering

 

[PMR06]

M/(d+2g)

 

[PMR06]

Actually M/(d+2g) and if it were 5% overstressed, I would say OK. Haha.

 

[rb1957]

to answer your previous post, i think most would use d-g, assume the compression reaction was applied at the heel of the angle.

 

[nutte]

Hmm, I'm studying it more, free body diagrams of each piece, and I'm ready to concede the point. I sure would have thought the anchor force would be M/d.

As for design, I'm with Mike, I would have used M/d and not thought twice about it.

 

[haynewp]

nutte,

I tried to make what you are suggesting theoretically happen and I can't. If the angles were only attached at the very toe to the beam with welds, and likewise at the very toe with a weld at the wall, then the shear at the angle's toe would be as you say (M/d). But the assumptions don't work with statics. There has to be a different force transfer between the angle and the beam when using the rigid angle assumption or the angle would be unstable.

 

[JAE]

I just think it is amazing that "simple" statics problems like this one can throw us all for a loop.

I'm also impressed by how interested so many of us are in a topic as basic (or essential) as this.

 

[haynewp]

These are my favorite kinds of questions, ones that kind of combine strengths of material and statics. They are not based on one's experience and I think they really test your intuitive engineering ability.

 

[JAE]

Yes, just when you think you have a good talent for visualizing load paths....boom, StructuralEIT lowers the boom on us.

 

[apsix]

I probably would have used M/(d) for the weld and designed the bolt for M/(d+g), assuming there is no prying.

I still believe that M/(d+2g) is potentially unconservative and therefore wouldn't use it.

 

[haynewp]

Well, I would say you are wrong to use M/d for the weld, unless you are using that just to be conservative. I wouldn't use M/(d+2g) either.