Plate thickness for headed stud connection 1

[gre2408]

Hi,
I am working on designing a simple tension connection using 4 headed studs (3/4 x 3-1/8, one on each quadrant) welded on 6 x 6 steel plate and have a question regarding the plate thickness. This connection including the plate will be fully embeded in concrete wall and a steel rod (#10 GR.75)coming out from the center of the plate will be loaded to 45 kips in tension.
I looked at my PCI design handbook (3rd edition) as a reference and found that the plate thickness should be at least 2/3 of the stud diameter and there was no more comment on the design. It seems to me that the plate will experience bending moment because of the eccentricity with studs (about 1.5 inch from the edge of the loading to the center of the sutds) and I don't know if it is okay to design the plate with considering the stud diameter only.
Please let me know how you guys think on this.
Thanks for you help.

 

[Lion06]

I believe the 2/3 requirement is for shear, not tension. ACI has a similar requirement. You will have bending in the plate. Can you model the plate as a shell and provide 4 point supports at the anchors to get a moment and design the thickness accordingly?

 

[bigmig]

Your plate will obviously be going into bending. What is the spacing of the HAS's? This will affect how far your plate has to "span" between supports, or in this case, HAS's. I don't think the problem is complex enough to require a finite model plate design, but that is my humble opinion, and is based on the limited info you have provided.

 

[ChipB]

Okay. I'll tell you. But, first, since no one else is calling out the GREAT BIG ELEPHANT in the room:
You've got 45 kips tension.
You've got (4) 3/4" studs embedded 3-1/8" spaced 3" apart.
WHAT!!!! You'd better check your concrete cone failure.

I agree with bigmig, no FEA is required. You've got a true two-way span.

It'd be much easier to explain if I could draw it out on paper and show you. You have 3" between your studs. Each stud is taking 1/4 of your load.
Find the diagonal:
(3^2+3^2)^0.5 = 4.24" (That's "L")
P*= 1/2P = 22.5K
Use fixed-fixed formula: M=P*L/8= 22.5*4.24/8=11.93k-in

S=Bt^2/6
Remember we used fixed-fixed. The concrete triangle under the plate formed by a 45degree angle going through the center of the stud, goes into compression to resist the moment. Yes, you need to check it and make sure it is within allowable. We have to take the section along that 45 degree angle.
So....
B=(1.5^2+1.5^2)^0.5 = 2.12"
M/S<=27ksi
S>=(11.93k-in)/27ksi=0.442in^3
Therefore "t" >= 1.12"
I'd use 1.25" plate.

(Someone check my math b/c I was calcultating as I was writing.)

If the concrete isn't good in compression, and I don't think it will be, use pin-pin across the full section with "L" as 3" & full P & 6" as "B".

Personally, I think you need to re-think your design.

 

[structuresguy]

Well, I just did a quick check using epoxy anchored rods, instead of headed studs (just cause I can do it really quickly without breaking out ACI app. D). Anyway, to get your load in tension, I would need 4 7/8" Gr. B7 rods spaced 8" c/c and embeded at least 8" deep. And even then, it just barely works. I would expect CIP anchors to give similar results.

So definitely you need to check your embed design.

And then based on this setup, with simple bending between the studs, my embed plate would be 12" x 12" x 1" thick.

M=PL/4=22.5*8"/4=45kip-in
Fb=0.75Fy=0.75*36=27ksi
S=M/Fb=45/27=1.67in^3
S=1/6*bt^2
t=sqrt(6*S/b)=sqrt(6*1.67/12)=0.92"
Thus, use t=1.0"

 

[Lion06]

I agree with the above posts about the anchors not working for concrete breakout. I did an App E check (only because I set up a spreadsheet) and for 4-3/4" studs welded to a 6" plate (assuming 3" spacing in both directions) with 8" embed and 4000 psi concrete, no supplemental reinforcement, and cracked concrete.......... I'm coming up with a capacity of 30.4 kips (to compare to a factored load). I don't know if your 45 kips is factored or service, but if it's a service load, then you're in even more trouble. to get up to 45 kips, I used 6" spacing, 5ksi concrete and supplemental reinforcing. This gets it to exactly 45 kips.

 

[ChipB]

structuresguy,
Hilti books are great aren't they?

 

[dik]

They have a fairly decent computer program called Profis which is a little clunky but not too bad. You might look at prying action to have a plate large enough to accommodate the cone... and toss in a couple of 25M dowels to intersect the cone...

Dik

 

[gre2408]

Thanks for all the comments.
Sorry for not describing my problem very cleary. Yesterday I didn't have enough time to describe my problem in detail. The steel plate with 4 headed studs will be fully embedded in 24" thick reinforced concrete wall. the distance from the head of the studs to the back face of the concrete wall (4000 psi concrete) is more than 12". I did check the cone failure and it worked fine. Now my question is more like how to get the design thickness of the steel plate experiencing bending. I am sure that it will be a lot easier to treat it as a simple cantilever beam. However, I was thinking that it could be more economical design if I include lateral resistance from the side of the studs bearing against concrete when the plate is trying to bend. The center to center spacing between studs are 4 inch and I was thinking that the resisting moment coming from the side of the studs might cancel some of the bending moment in the plate if stud welding connection on the plate provides enough capacity for the resisting moment. Do you guys think that I am thinking too much and I should go to design as a simple cantilever beam?
Again, thanks for your opinion.

 

[Lion06]

The load is in the middle of the 4 studs, right? If so, then why treat it as a cantilever? Treat it as pure 2-way bending.

 

[PEinc]

If the plate is the proper size and is encased in the concrete wall, do you really need the studs? Can't the plate be a bearing plate? The studs help; but are they needed?

It sounds like you are designing the anchor-to-facing connection for a tiedback or soil nailed wall. Usually these plates are at least 8" x 8" x 3/4" thick. Also the studs are usually long enough to extend beyond the nearest reinforcing mat.

 

[ChipB]

So....let me get this straight:
The entire plate/studs assembly is embedded in the wall?
If that is the case, in order for your plate to bend, your concrete would have to crack. Given a 24" thick wall, the localized moment of inertia of the wall is significantly greater than that of your steel plate. I think I'd put a set of ties, going from front face horizontal reinforcing to back face horizontal reinforcing, around my embed and let it go for bending.

But...on the other hand, that brings up other items:
Since you are using the concrete cone of your assembly, you have to ignore (or, rather, I would) the partial development of the bar in the wall. As such, the localized shear will likely be the controlling issue on plate thickness. 45k/(2pi*1.25")=5.73k/in use 1/2 min plate.

How do you intend on them welding the bar to the plate? Rebar isn't very weld friendly, and you're using Gr 75.

 

[structuresguy]

structuresguy,
Hilti books are great aren't they?

Yes they are!!!

 

[Tomfh]

PEInc's comment is very sensible. Do you really need the studs?

 

[swearingen]

He did say 45k tension in the OP. Why wouldn't you need studs (or some other tension resisting element)?

And please tell me how (4) 3/4" diameter, 3 1/8" long studs in a 4" square pattern are going to resist 45k tension in 4ksi concrete. The elephant has not left yet - in fact, he's starting to pace around...


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