## Gusset Connection Eccentricity Problem

## Gusset Connection Eccentricity Problem

(OP)

I have a new project to design bracing for an existing building. The force in the bracing is Cf = Tf = 103K... big forces!

The problem is that the gusset will be secured at the centroid of the resisting beams and columns because there is an existing masonry wall located to the centerline of the connection. The EOR want me to design the connection for an HSS 10x4x0.5 (located at the face of the wall), welding the HSS to the face of the gusset, creating an eccentricity of 2" (from the HSS) + half the thickness of the gusset.

I've designed it using elastic combined stresses, based on a Whitmore width for compression. If it weren't for the compressive load, I'd have used the plastic section. I'm looking for some comments how others would design this for the eccentricity. I've suggested going to plate that is roughly 1"x12", in lieu of the HSS, to minimise eccentricity or possibly using the existing masonry wall for lateral forces.

The problem is that the gusset will be secured at the centroid of the resisting beams and columns because there is an existing masonry wall located to the centerline of the connection. The EOR want me to design the connection for an HSS 10x4x0.5 (located at the face of the wall), welding the HSS to the face of the gusset, creating an eccentricity of 2" (from the HSS) + half the thickness of the gusset.

I've designed it using elastic combined stresses, based on a Whitmore width for compression. If it weren't for the compressive load, I'd have used the plastic section. I'm looking for some comments how others would design this for the eccentricity. I've suggested going to plate that is roughly 1"x12", in lieu of the HSS, to minimise eccentricity or possibly using the existing masonry wall for lateral forces.

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

Is this the concept you are describing? If so, probably gonna need a lot of weak-axis stiffening @ the beam and gusset.

For the weld design and interaction of axial, biaxial bending, and shear in the gusset, I would look at "Combined Stresses in Gusset Plates" by W.A. Thornton and "Establishing and Developing the Weak-Axis Strength of Plates Subjected to Applied Loads" by Carter, Muir, & Dowswell. And as a minimum, I'd add stiffeners @ the beam too. Maybe even a "T-shaped" stiffener on the gusset, like this:

## RE: Gusset Connection Eccentricity Problem

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

## RE: Gusset Connection Eccentricity Problem

~~Ask the EOR for his preliminary calculations that prove this arrangement is feasible...~~EDIT: thought Dr.Z's sketch was dik's.

Haven't had to deal with that before. Can you weld stiffeners to the plate to help with bending and resolve the eccentricity there?

## RE: Gusset Connection Eccentricity Problem

pham... that's another part of the problem. The EOR wants me to reduce the plate thickness (from what's calculated) so it is not so stiff and doesn't transfer as much moment into the connection.

It's close... the gusset just moves over to the centreline of the beam and columns.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

## RE: Gusset Connection Eccentricity Problem

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

## RE: Gusset Connection Eccentricity Problem

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

Regarding your second sketch, there is technically zero shear in the direction you're showing since the eccentricity induces pure bending in the brace. However, there will be some incidental moment in the gusset. This is the main reason I propose detailing the gusset to beam/column connections to develop the capacity of the plate. This allows you to take advantage of the lower bound theorem to proportion your forces any way you see fit that satisfies statics.

## RE: Gusset Connection Eccentricity Problem

That is the Whitmore wide for compression?

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

## RE: Gusset Connection Eccentricity Problem

You

candesign the gusset for weak axis moment, but you don'tneedto to satisfy equilibrium. If you choose to design the brace for the entire moment and the gusset for axial force only, you would technically have a moment at the brace-gusset interface equal to P*(tg/2), but that's often neglected in the weld design.Whitmore width is 30 degrees if you need the gusset to behave elastically at design loading, but if you can tolerate some yielding it can be as high as 45 degrees. See this paper: Link.

## RE: Gusset Connection Eccentricity Problem

Maybe I'm misunderstanding something, but I would fundamentally disagree that you don't need to satisfy equilibrium. Looking at a free-body diagram of the gusset, you have axial loads which are offset, therefore, to satisfy equilibrium, there must be some additional forces acting on the gusset which must be taken into account in the design. Looking at dik's last sketch (the one on the right), it might be case where the eccentricity is only 1/2 the gusset thickness and would be very manageable.

This is a tough one. Often in connection design you need to make some assumptions about how/where eccentricity is resolved. If the assumption does not impact the connection design in a significant way I'll often design for the eccentricity being resolved on either side of the connection. In this case, the brace is offset from the centerline of the beam/column - this eccentricity needs to be resolved either in the brace (weak-axis bending), in the beam/column (torsion), or by additional external bracing. Assuming no additional external braces, that eccentricity will be resolved by both the brace and the beam/column and this split will be based on the relative stiffness of the entire system. As noted above, sometimes I'll run two connection checks assuming each side takes 100% and see where that lands me.

In this case, I feel like the EOR is putting dik in a tough spot as a connection designer and I would be sending an RFI asking specifically about how this connection eccentricity is resolved. If the EOR designed this brace properly, they should already be aware of how this connection eccentricity impacts the new and existing members.

## RE: Gusset Connection Eccentricity Problem

That's what I'll use. Because the loads are compression and very high, I'll use the 30deg slope; I'm not keen on plastic compression... if tension, no problem. This has been a real 'eye opener'; I've never designed gussets for such a high eccentricity, and my approach was conservatively flawed.

My SMath program can automatically include for this. I have to revise my program to design from (b

_{HSS}+ t_{g})/2 to t_{g}/2. It's an easy fix... I'll do that tomorrow... I don't design my welds for different directions of load... and include for shear lag...I'll post it when it's updated...

-Dik

## RE: Gusset Connection Eccentricity Problem

in orderto satisfy equilibrium." If you design the brace/gusset weld for P*(tg/2), the gusset does not need to resist moment to satisfy equilibrium.The designer can choose to proportion the total eccentric moment in any way that satisfies equilibrium provided there is sufficient ductility to allow force redistribution. Since the weak-axis stiffness of the brace will be so much larger than that of the gusset, a solution that proportions more of the eccentric moment to the brace is going to better reflect the elastic force distribution. I'm certainly not opposed to designing the gusset to resist an eccentricity of half the plate thickness. Just wanted to remind Dik that it's not strictly necessary provided the moment can be taken by the brace. I do recognize that an elastic force distribution will induce some moment in the gusset, which is why I suggested to detail the gusset to beam/column connections to develop the capacity of the plate. This will allow the plate to shed it's moment back to the brace to satisfy the force distribution assumed in design.

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

It doesn't make sense to me at them moment. But there seems to be a tiny piece of the puzzle regarding the eccentricity that I'm not quite getting. I'll be pondering this myself, because there seems to me an important concept I don't properly grasp here. But anybody who wants to help me along the way would be appreciated.

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

human909, if the brace is able to resist some bending, in terms of both strength and stiffness, then the gusset plate sees direct shear coming from the welds to the HSS...which means the plate only sees an eccentricity of half the plate thickness. If in another case (this is purely hypothetical), the opposite end of the brace could not transmit any shear (roller in two-directions), the end of the brace in question could not carry any bending moment...forcing the beam and column to resist 100% of the eccentricity. This would put significantly more bending in the gusset.

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

I've seen gussets buckle under compressive loadings.He doesn't want to take 'ownership' of the gusset and simply give me a thickness to connect to. That was my original solution when I came up with a conservative thickness. He wants me to design the gusset. He's not happy about me stipulating that the strength of the existing beam-column combination has not been checked. Just cannot seem to 'win' some days.So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Gusset Connection Eccentricity Problem

Something like this could work if you can keep the boltline non eccentric to the beam column, but would be quite an unusual approach to connect things.

## RE: Gusset Connection Eccentricity Problem

his concern is the moment in the other direction:So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

Dekerthose are some sexy FBDs. Thanks for that.## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

https://res.cloudinary.com/engineering-com/image/upload/v1656283107/tips/Gusset_HSS_e_aruaft.pdf

https://res.cloudinary.com/engineering-com/raw/upload/v1656283109/tips/Gusset_HSS_e_vbzry9.sm

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Gusset Connection Eccentricity Problem

Whether or not the HSS10x4x.5 is appropriately sized for the 103k is a separate question. If the brace is long and flexible, the deflection of the member itself will need to converge under P-delta analysis.

I just ran some numbers in RISA. 103k x 2.5" = 21.63'-k. With NO P-delta this causes a

4"(!) deflection in a 25' long 10x4. Yike. If you subdivide the member so that P-little-delta can run then the model doesn't converge. No wonder, the 4" of deflection causes another 43'-k of moment which causes more deflection, and on and on. P-little-delta is often not significant, but this is a prime example of how it works. Just like the toothpick between your fingers.I just don't see how you can make the gusset stiff enough to suck the moment out of the brace and drive it into the connection.

## RE: Gusset Connection Eccentricity Problem

Ya, 285"-K. I didn't run a deflection check on it, but length may only be 15'-20'. My initial gusset thickness was 1-1/2" and the EOR was concerned that I was attracting too much moment into the connection.

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

## RE: Gusset Connection Eccentricity Problem

This question isn't germane to your brace eccentricity question, but how did you get involved in trying to sort this new brace issue out? That is, why are you looking in to this brace, and not the EOR?

## RE: Gusset Connection Eccentricity Problem

I had used Deker's Option 3 and have revised it to Option 1 with the HSS moment to include a moment equal to 1/2 the thickness of the gusset.

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

I ran (4) load cases. The first two load cases have 100% eccentricity resolved within the brace (tension/compression case), the second two load cases have 100% of the eccentricity resolved in the beam/column (tension/compression case). NOTE - I updated the gusset thickness, which changed the eccentricity, but I didn't go through and change the balancing moments...so the results you're seeing are based on loads slightly out of equilibrium (I got lazy, general results still the same).

The overall results are only shown for the worst case. Everything passes but the existing beam connection in the first two cases.

You can see based on the deflected shape that it isn't realistic to assume the beam/column will resist the eccentricity. Far too much movement that will likely be picked up by the brace first.

Goes without saying, but please take this report with a gigantic grain of salt.

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

-Dik

## RE: Gusset Connection Eccentricity Problem

Dik: Seems odd that the EOR reduced the brace size from an HSS8x8 to an HSS10x4 given that the 10x4 not only has to resist the original axial load that the 8x8 was designed for, but an additional weak-axis moment as well. Any indication that the EOR considered the moment in the brace? And how exactly do you coordinate your design with the EOR on something like this? Do you provide a FBD of your gusset to ensure that a consistent set of forces is used in the brace design? Situations like this make me grateful that we design our own connections where I practice. Recently had my first experience doing delegated connection design on a local project designed by an out-of-state EOR...they forced me to use the max UDL reactions even after I went through the trouble of determining the real beam reactions using the load criteria listed on their drawings. What a headache...

rowingengineer: Since you mentioned the article was for roof bracing, any chance it was based on tension-only rod bracing rather than the stockier HSS that dik is dealing with?

## RE: Gusset Connection Eccentricity Problem

The calculations only cover the governing case - i.e. if bolt #7 is governed by load case 5, that is the calculation you'll see. This program does not handle flare bevel welds at all - it is treated as a fillet weld...so for the HSS to gusset weld, you need to take the demand on the fillet weld from the program and evaluated manually.

No trouble at all on my end, its easy to tweak this and re-do the output. Once you get over the learning curve in this program you can model a connection like this in minutes.

EDIT: Deker, I had to circle back and give you start for the FBD's. I wish I could sketch/print that neatly. There was a thread a while back discussing how useful a simple FBD can be, this is the perfect example....you've taken a problem that is not easy for everyone to visualize and made it clear as day with a few simple sketches.

## RE: Gusset Connection Eccentricity Problem

I simply stipulate on the drawings that the EOR is to confirm existing structure is capable of resisting loads and, in this case, the gusset will be 3/4"? thick and connected concentrically at the connection, for the EOR to confirm, the connection is the case.

Regarding the other issue, for UDLs I have an SMath program (also an Excel one) that calculates the max reactions based on UDL and spits out the forces. If there are a lot, I use the Excel one since I cannot get SMath to load from my AISC/CISC database.

As far as redesign, there is some interesting case law (in Canada, anyway) regarding stipulating design loads and using some other criteria, not stipulated, or not clear. Generally with contract law, if there is an ambiguity, then the person that wrote the contract is deemed at fault.

-Dik

## RE: Gusset Connection Eccentricity Problem

## RE: Gusset Connection Eccentricity Problem

-Dik