Probably need a sketch to get better input on this.

*Post updated per Dik's input in later post.
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:

Something like... The gusset is centered on the centrelines of the beam and column.

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

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?

Doc... the gusset is on the other side of the HSS, adjacent to the wall.

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.

Quote (EDIT: thought Dr.Z's sketch was dik's.)

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

Thanks for the update, dr... I'd thought of adding a stiffener to reduce the thickness of the gusset. The EOR wants to 'reduce' the moment going into the connection, by using a thinner gusset.

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

I don't know where the masonry wall is relative to beam and column centers, and since it's brick it is likely multi-wythe.

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

If he wanted to reduce the weak-axis moment generated by the eccentric axial load, something like a WT brace might be better than an HSS.

I hadn't considered a WT... I suggested a 1x12 or 3/4x16 plate secured to the wall to prevent buckling to minimise the eccentricity.

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

Since the weak-axis stiffness of the brace is orders of magnitude higher than the gusset, does the gusset need to be designed to carry any moment? You could proportion some of the total moment to the gusset, but I think an equally valid approach is to design the brace for the entire moment, design the gusset for in-plane forces only, and detail the gusset-beam/column connections to develop the weak-axis flexural capacity of the plate. This reminds me of this thread where Bill Thornton provided his comments on a similar detail at the end of the thread: thread507-268731: Load Path / Eccentricities.

Decker: Are you suggesting to design the connection of the HSS to the gusset for both the moment and the axial load, but design the gusset for only the axial load?

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

Dik: The HSS for axial + moment, the HSS to gusset connection for shear only, the gusset plate for in-plane forces only, and detail the gusset to beam/column connections to develop the weak-axis capacity of the plate. See the attached comments from Bill Thornton on a similar WT brace connection from the thread I linked above.

• https://files.engineering.com/getfile.aspx?folder=6b74e80b-17e6-4e37-a7a2-6

You are suggesting that this is the model?

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

Yes. If you swap out the WT for an HSS, doesn't this match your condition?

Yes it does...

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

And the added moment caused by the shear to resist the moment?

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

In the OP you mentioned that this connection will take a compression force from the brace and your concern is that this compression will take the plate into a plastic mode.

To clarify... I treated the combined stresses elastically. If the load were tension only, I'd have considered the plastic section.

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

In your first sketch, are you asking about the unbraced length of the gusset? I'd minimize that distance as much as possible for this detail. If for some reason you can't, you can add a stiffener on the gusset to prevent the plate from hinging and folding over...although for a gusset supported on two edges I don't think that's a major concern.

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.

The forces at each end would cancel? What is the stress condition at the junction of the gusset and the HSS? Wouldn't you have to transfer part of the moment load from the centroid of the HSS to the gusset of the or just strictly by shear? Wouldn't the moment be at least the shear x half the thickness of the gusset, then?

Quote (to develop the capacity of the plate.)

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

The model on the right reflects how your brace will be loaded, correct? If so, then yes, there is no shear in the brace, and no out-of-plane shear will be delivered to the gussets at the ends.

You can design the gusset for weak axis moment, but you don't need to 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.

Quote (Deker)

You can design the gusset for weak axis moment, but you don't need to to satisfy equilibrium.

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.

Quote (Deker)

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.

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.

Deker... good link, give me something to read.

Quote (where the eccentricity is only 1/2 the gusset thickness and would be very manageable.)

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.

Quote (moment at the brace-gusset interface equal to P*(tg/2), but that's often neglected in the weld design.)

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...

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

Didn't say that equilibrium doesn't need to be satisfied, but I probably worded that poorly. Should have written "You can design the gusset for weak axis moment, but you don't need to in order to 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.

Thanks Deker... understood and I'm comfortable to proceed based on the reduced eccentricity. As always, you gentlemen (I use the term for male and female, I think it's better than 'you guys') have been a lot of help.

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

Deker (or anybody else), would you mind indulging me in further explaining this.

Quote (Deker)

"You can design the gusset for weak axis moment, but you don't need to in order to satisfy equilibrium." If you design the brace/gusset weld for P*(tg/2), the gusset does not need to resist moment to satisfy equilibrium.

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.

The eccentricity between the line of action at the gusset and line of action at the brace (gusset thickness / 2 + brace width / 2) creates a free moment that has to be resisted somewhere in order to satisfy equilibrium. The elastic force distribution will proportion this moment to each element in the system based on its relative stiffness. If you can allow (i.e. detail) the system go plastic, you can choose any force distribution that satisfies equilibrium based on the lower bound theorem, so you are not bound by the elastic solution.

Deker, thanks for the follow up. I think we're on the same page here. I agree that the brace would likely resolve majority of the eccentricity.

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.

Thanks for the explanation Deker and Canpro. I think I need to ponder this a little further and do a little work myself. It hasn't quite clicked yet but I need to start drawing some load path diagrams and make the connection. I'm sure once I do they it will be a 'of course' silly me moment.

I would check that neither the brace nor the gusset is too flexible. Treating the gusset as a pin means it follows the slope at the end of the brace caused by the uniform moment --> additional eccentricity. Then, if the gusset is long as Dik suggested, you may get a p-delta increase there as well if too flexible.

P-delta... another thing to add to SMath program... I thought it was way too stiff... maybe not.

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

-Dik

May be worrying about nothing, but not sure exactly what 'several inches' means, or how much thinner the EOR wants the plate. If it's only just working with linear calcs, it may not with non-linear.

The EOR wants it thin so the gusset doesn't transfer moment to the connection. The thicker the gusset, the greater moment is transferred to the connection. 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

Sounds like the EOR wants you to design a perfect hinge at a point that in not eccentric to the beam/column. That is a tall ask.

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.

Something like... 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

human909: Check out the FBDs below and see if it clicks. If there's sufficient ductility in the system to allow force redistribution, any of these options are valid. The elastic solution would likely fall between options 1 and 2, so either of these options could produce an efficient design. Given the proportions discussed in this thread, option 3 would be irrational (though still valid) and would result in a very inefficient design.

Deker those are some sexy FBDs. Thanks for that.

Thanks Deker for those drawings, above an beyond in your assistance. It has now 'clicked' for me.

First Kick at the cat...

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

I see it as the simple axial force in the gusset. Sort of like when you squeeze a toothpick between your fingers and make it bend out of plane. The connection at the fingers is pinned, for sure.

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.

Thanks, that was one of my first concerns about the use of this eccentric bracing (making it more flexible in the plane of bending). The heavy loaded bay, the one with the 103K is not cross braced. The lighter loaded one is... with the cross-bracing it is somewhat restaind, and I suspect only a small part of the load will go into it. The loading is +/- 103K. I've already noted noted my concerns.

Quote (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.)

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

In addition to the challenges of dealing with design of the brace for the eccentric loading, you’ll also need to look at the secondary stresses and torsion induced on the beam and column due to the brace eccentricity.

The EOR does, not my circus, not my monkey...

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

-Dik

dik,

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?

My current employment is designing connections for steel fabricators. the original connection had a concentric HSS 8x8 with a factored design load of 103K. Because of an existing brick wall, the new bracing was changed to HSS 10x4, offset, to clear the wall. I designed the gusset plates and the original offset gusset was 1-1/2" thick due to the eccentricity caused by 1/2*(tg+bHSS). As a result of the discussion here, I feel comfortable using a 3/4" thick gusset. The EOR was concerned that the thicker gusset would transfer too much moment to the existing connection. As it stands the EOR will be responsible for the existing connection plus any p-delta effects.

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.

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

-Dik

It's unfortunate the EOR didn't design the frame as a tension-only system... Maybe a little extra steel tonnage but saves a lot of heartbreak as far as connection design is concerned, particularly given the inevitable eccentricity.

That was one of the first questions I asked... normally if tension and compression are used at the same time, the compression is about 40% of the tension value. The one with the highest load is chevron braced which may be more problematic.

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

-Dik

We had an article in our local steel mag about the effect in she roof bracing and option 3 is most likely. an ideastatica is a great program for this, it is how I do my more difficult connections.

Do you have any reference to this? rowing...

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

-Dik

dik, I scaled one of your previous sketches to get rough beam and column size, made some assumptions on the existing loads/connections and ran the connection through Idea Statica - report is attached. I used the 3/4" gusset you noted above.

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.

• https://files.engineering.com/getfile.aspx?folder=471d5816-6eb8-4770-8320-a

Thanks so much... it appears to be a really neat program. I will revisit the calculations and the approach... never with a grain of salt...

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

-Dik

canpro... can I trouble you to run this again using only load case 2, which is the one I'm using. I cannot distinguish in the attached output, the results for the individual load cases. Does it output the calcs at the end; I'd like to be able to compare my calcs with a 'real output'. or is this a compendium of all load cases? Also if you can use 300MPa for the gusset strength... sorry to be such a pain, and thanks if you can.

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

-Dik

Enable, human909: No problem, glad the sketch was helpful.

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?

hey dik, updated report is attached. Load case 2 only - brace in compression, eccentricity resolved in the brace. I adjusted the bending moment in the HSS to get equilibrium.

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.

• https://files.engineering.com/getfile.aspx?folder=9ee08d55-9fd2-4911-933b-4

Deker... my error, the original was HSS 6x6x0.5 and the loading was concentric. I checked the HSS 10x4x0.5 and it's OK for P/A and M/S; I didn't check the original HSS 6d6. The HSS 10x4 is loaded eccentrically. The weak axis moment is actually fairly high. Checking for member strength is outside... If I see something that is wildly out of whack, I note it. My SMath program checks for elastic strength (not buckling, though). Even with the HSS 10x4, I note that any bracing required to the existing wall for buckling or any P-delta moments is by the EOR.

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.

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

-Dik

Thanks for the compliment, CANPRO. Glad it was helpful. And thanks for modeling the connection and confirming our intuition. If only my brain didn't turn to mush once I start reading the metric units.

Yes gentlemen (Dik's binary term for political correctness ), it's been a neat learning experience.

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

-Dik