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?

 

[csd72]

I would check the tension in the anchors based on d+2g but the shear in the welds based on d.

Technically one of the lines of anchors will not be taking load and it will be a compressive force on the brick/concrete but I have found it is usually conservative to take loads at the anchors.

 

[Lion06]

I appreciate the response, but can you explain why? I understand the reasoning for a baseplate, but not for the detail shown for the reasons stated.

 

[Teguci]

The tension in the top anchor must be increased to allow for some prying action. To be conservative, use the plastic moment in the steel angle and divide by about 85% of the distance between the anchor and the top of the angle. Add this to the tension given by M/d.

The real answer is somewhere in between. Free body diagram is a vertical beam with a plastic pin at the bottom compression flange and a plastic pin at the tension anchorage with a tension load at the top of the beam.

 

[Lion06]

Teguci-
I agree for a flexible angle, but you can make the angle stiff enough to neglect prying by following the procedures outlined in the steel manual of providing the stiffener. I am more concerned with which moment arm to use.

 

[Teguci]

If the angle is 100% stiff, then tension in the anchorage is T x d/(d+g). aka Moment arm is d+g.

Free body = pin support at the bottom of the compression flange; Tension force at the top of the tension flange; reaction at the wall anchorage

 

[jike]

I would probably use T = M/(d+g).

 

[miecz]

StructuralEIT

As shown, I would base the tension on d+g. The flange with the compressive force will transfer that force to the wall in compression through the angle leg parallel to the flange. I suppose one could adjust for half the thickness of the flange.

I think you wanted to eliminate that bearing action by adding nuts between the angles and the wall. Sort of, like leveling nuts under column base plates without grout. In that case, I would agree with you that the tension/compression forces in the bolts would be based on T/d. The apparent difference in couples is taken by the moments in the welds connecting the angles to the beam. If you draw a free body of each angle, you see that you need a moment in that weld equal to T*[Δ]y.

 

[msquared48]

I agree with Jike as when the moment is applied, one of the bolts will be in tension, and the bottom or top of the beam will be the thrust point for the compression force as the beam is much stiffer than the angle. This leads to M/(d + g) for the force in the wall bolts.

Mike McCann
MMC Engineering

 

[Lion06]

I appreciate the responses, but miecz is the only one who attempted to explain why.

If you believe that the tension in the bolt is less than the shear in the weld where does that force go?
I guess I am picturing a FBD of this angle with a Tension force in the horizontal leg of T1=M/d (pointing to the left), and a horizontal force from the anchor of T2=M/(d+g) (pointing to the right). T1 > T2 and the only other force that can be present is the top of the angle bearing on the wall as it tries to rotate, but this will only add to the forces pointing to the left.
I am failing to see, just by statics, how the force in the anchor can be less than that in the weld (i.e. how T2 applies).

 

[msquared48]

StructuralEIT:

The difference lies in the difference of the moment arms...

It is true that the moment arm for the welds is "D", the distance between the welds and the depth of the beam.

However, assuming that the thickness of the angle is enough to transfer the weld force to the anchor bolt without bending, then the effective moment arm of the connection to the bolts is increased by a distance "g", the gage dimension. If the angle fails, then you have a connection failure. As this is not what we want design for, the angle must be designed to transfer the force without failure.

Mike McCann
MMC Engineering

 

[JAE]

Here's my free body layout.

 

[JAE]

The previous free-body is for a non-stiffened angle. As Teguci mentioned above, there is prying-type action occurring that creates a different force in the bolts when compared to the welds on the flanges.

The attached sketch below is for a stiffened condition. To achieve the "rigid" condition, the welds now must take not only shear but moment along the horizontal leg length. This creates a force at the bolts = M/(d+2g) which is also the shear at the welds. The shear at the welds is no longer M/d since there are new moments at the end of the beam that change the total moment to something less.

 

[apsix]

"I am failing to see, just by statics, how the force in the anchor can be less than that in the weld "

That's because it isn't, shear remains constant, based on the (d+g) moment arm.
(Assuming there is no prying.)

 

[Lion06]

So you reduce the shear in the welds by making the angle rigid (from M/d to M/(d+2g) or M/(d+g) depending on your preference)? I understand that the weld is now also taking moment, but the shear is reduced?
I understand the concept of prying and the additional force it exerts on the bolts. I made a pretty slick spreadsheet using the prying equations for wind moment connections.

 

[apsix]

The shear will never be M/d, the lever arm can't be less than (d+g).
The shear will only be M/(d+2g) if the bottom angle is very stiff, eg. by using stiffeners or the like. I would use (d+g) in my design unless there is a very good reason not to.

 

[Lion06]

apsix-
csd, miecz, msquared, and JAE have all stated that the welds should be based on the "d" dimension. JAE has added the qualification that this would only apply if the angle is not rigid.

 

[miecz]

StructuralEIT-

I believe the force in the tension in the bolt is equal to the shear in the weld but the shear in the weld is less than the force in the flange beyond the weld. Where does that extra force in the flange go? It goes into the web of the beam. It gets there as a couple thru the weld. Looking at JAE's second sketch, you see that moment shown as T'a, where T' is represented as perpendicular to the flanges. Once in the web of the beam, picture the 2 couples in the web with forces parallel to the flanges. Those forces are the difference between the force in the flange and the shear in the weld.

 

[Lion06]

but those are vertical forces. Additionally, if you look at JAE's first sketch (the one assuming the angle is not rigid), he is using the "d" dimension for the shear in the welds.

 

[apsix]

StructuralEIT
Referring to JAE's first sketch; obviously one of us is wrong, at this stage I don't believe that it is me.

I'll try to explain. The lever arm is the distance between the points of compression (C) and tension (T) reactions on the connection.
The location of C depends on the stiffness of the bottom angle; it's either at the bottom flange or near the bottom bolt.
The location of T is always at the top bolt, it makes no difference if the top angle is flexing or not.