Plate Thickness in Pure Tension Connection to Uniformly Distribute Load to Fasteners

[ajk1]

I am designing a 24"x24" steel end plate to an HSS 4"x4" section that I am connecting to an existing concrete column.
The HSS is in pure tension.
I require 16 drilled-in epoxy adhesive anchors (3/4" diameter threaded B7 rods, as determined by the PROFIS program), assuming that each rod anchor into the concrete takes the same load.
The anchors are arranged in 4 vertical rows, with 4 anchors per row.
The plate has to be designed to meet 2 critera, namely:
a) the bending strength due to the applied load;
b) that each anchor rod is about equally loaded.

Question: How can I determine the plate thickness to ensure that each of the 16 anchors is about equally loaded?

 

[hokie66]

a) is just a matter of determining the plate bending and sizing the thickness of the plate to suit your allowable stress. I assume you know how to do that.

b) is more difficult. The anchors closest to the tie will be loaded first, then the more remote. As you have a 24" x 24" plate, I assume the anchors are proposed to be on a 7" grid. I would look at using a smaller number of larger anchors, or preferably through bolts.

 

[Ron]

Size the plate such that bending is irrelevant...that's the only way you'll get the same load in each of the fasteners.

 

[JStephen]

I don't know that you can. For that to work, the bolts have to be considerably more flexible than the plate. Otherwise, the relative flexiblity of the plate between inner and outer bolts would be about the same, regardless of plate thickness. Possibly put the bolts in a sleeve, so a longer body acts in tension?

 

[hokie66]

Using plate stiffeners in each direction would help, but would not completely eliminate the inequality of loading.

 

[shobroco]

To load each anchor equally, you either have very difficult and indeterminate figuring of plate bending, anchor strain, etc. or you have a single ring of anchors equidistant from both the HSS and the outer edge of your plate. Or you make a swag & do 2 different sizes/spaces/something for the 2 concentric rings & make sure you have more than enough total capacity.

 

[TLHS]

Deep stiffener plates so that your deflection is low, with each bolt being about equidistant from a stiffener if possible and design the bolts so that the concrete can develop the full yield strength of the bolt, so you have a ductile failure mechanism? You could check the total deflection you could expect through bolt yielding and use that to come up with a differential deflection criteria for the plate/stiffeners. If this is a possible fatigue scenario, you'd want to be careful with this.

Alternately, you could investigate by modelling it in finite element software as a plate with a bunch of rigid pin supports. Then spring them assuming the bolts are yielding. Then throw in some stiffeners and see what happens.

 

[KootK]

It's a long shot but, if the anchors could be made to fail by a ductile failure mode, you could assume redistribution.

 

[ToadJones]

Stiffeners will certainly help.

If you are good with FEA and can model the anchors, concrete, and plate + stiffeners you can get pretty accurate results.

If you have a 4x4 HSS that requires that many 3/4 diameter rods, stiffeners might help you connect the HSS to the plate anyway. Sounds like you have a helluva lot of load to develop there.

 

[ajk1]

Thanks for all the comments. It is significant that there is little to answer the question of how to calculate, except perhaps by FEM. Too bad. the response seemed to be more at how to avoid the problem than how to solve it.
The reason for the large number of anchors is not so much the load as because we only have a limited embedment before the anchors hit the spiral reinforcing in the column, so we had to keep the embedment fairly shallow (at the minmium allowable embedment published in the Hilti catalogue for the anchor). That is also the reason the that larger anchors are not the answer here.
I had considered stiffeners of course, but did not think that solved the problem because the plate still has to bend to get the load back to the stiffener from the bolts closest to the stiffener and the bolts farthest from the stiffener. The stiffener would work if there were say just 2 rows of bolts, but we are bolting to a round coulmn, so this would require extending the plate around much of the column perimeter.
What I did was use a plate about double the thickness required for flexure (2 x 0.75" = 1.5") and this has very little deflection based on calcualtion. The only reason I asked the question was becasue the contractor asked if we could use a thinner plate. Since there is only one of these, I don't think the thicker plate should be a problem, and think I will just stick with that.

 

[slickdeals]

Just a question: Using 16-3/4" anchors in a 24" x 24" plate will require these to be placed at 5.5" to 6" o.c., at which point your interaction effects due to overlapping cones start to control significantly.

What failure more is controlling your anchor design?

Instead of drilling 16 holes into the column, hitting rebar and creating Swiss cheese, you could probably drill 4 through-holes in the column and put a plate on the back to transfer the loads.

 

[hokie66]

A scheme where the anchors are limited in depth to the extent where they stop "before the anchors hit the spiral reinforcing in the column" would not be an acceptable solution to me.

 

[ajk1]

to Slickdeals:
The anchors were designed using the Hilti PROFIS software, so yes the reduction due to interaction definitely has been accounted for where applicable, but due to the shallow embedment it was not hard to space the anchors so that there is no reduction due to this effect;
It is not possible to drill thru the circular column because we will hit the column verticals which are #18 bars at mimimum spacing.

to Hokie66: you usually have well thought out comments but I am puzzled this time as to why this would not be acceptable to you without giving a reason. You seem to be saying that you do not trust the Hilti data for capacity at minimum embedment. Or do you have some other reason? I can think of no reason why this is not accptable, except if the rebar should corrode and spall off the cover concrete, but there is no leakage and no corrosion of the column rebar and there is a waterproofing membrane on all floors. Perhaps in a seismic event the covercrete could spall off but I think this is the least of our worries as the steel we are installing is supplementary to the post-tensioned beam and has the capcaity to support most of the load if more tendons should break (a not liklely event since we are drying and greae injecting all the tendons).

 

[rb1957]

it looks to me as though you've got a single row of fasteners, 5 per edge, about 4" pitch as noted above.

the load is being introduced by a 4x4 column, presumably welded to the plate, 16" of weld in tension = 16 3/4" bolts in tension ?

load distribution would not be equal; the corner fasteners would be less loaded, quite likely the corner ones would be loaded in compression (review Roark for square plates).

you'll get closer to a uniform distribution if you have a circular fastener pattern and plate.

 

[KootK]

I second hokie's concern regarding the embeddment depth. Fancy maths and software output aside, delivering a large tensile load to only the cover concrete of a column feels "icky".

In a similar situation in the past, I've used two semicircular bands of steel plate wrapping the entire column. Where the bands abutted one another, they were detailed to connect through bolted flange plates. I included a few shallow anchors as well just to hold the thing in place. If access and fire proofing concerns would permit such a solution, it might be worthy of consideration in your case.

 

[ToadJones]

Column reinforcing seems fishy in terms of being capable of handling such a large tensile load (assuming it causes a large bending moment on the column).
Has the column been checked for this load?

 

[ajk1]

To Kootk and Hokie: I should have been clearer - the embedment depth is 86 mm. Where we have chipped out the concrete to expose the spirals and measure the cover on other columns indicate that in most locations in columns in this structure, that embedment depth is possible. We have already installed dozens of rods at this depth in other columns in the structure, but it is possible that in this particular column we will not be so lucky, in which case we will probably have to use a collar that goes around to the far sdie of the column and bears there.

to Toadjines: The load is applied as a horizontal load within about a foot of the concrete beam soffit at the top of the 36" diameter heavily reinforced columns which were designed origonally in 1975 to accommodate a future hotel; since then another floor of parking has been added but the hotel plans have been abandoned. The column has oodles of excess capacity. In any event, I would expect that a load applied so close to the column top (the column has a large dead load on it from the 4 floors of parking above) will produce relatively very small moments and e/t ratios. We have already checked the column for far greater horizontal force and the effect is very tiny.

Reminder - My original question was how to determine the plate thckness to districute the load equally. I think there amy be some information in the Hilti Manual on this. I will check. I will aslo checck with my academic contacts and see what they say.

 

[KootK]

I think that the reason that folks are dodging your question about plate thickness is that it's going to be impossible / impractical to guarantee a uniform anchor force distribution. A very thick plate or the use of stiffeners will improve your situation but not ameliorate it altogether. I looked at this for a base plate condition using FEM software once. The conclusion was that the plate would need to be ridiculously thick (>5") in order to truly approximate a uniform stress distribution. If you really need all of the anchors to be uniformly loaded, wrap the plate around to the sides of the columns so that your anchors will be loaded in shear instead of direct tension.

 

[rb1957]

review Timoshenko "Theory of Plates and Shells" for the difference between round and square/rectangular plates

 

[hokie66]

ajk1,
KootK said it for me...I wouldn't trust anchors just in the cover for this sort of application...don't know if Hilti would recommend that or not, but 86mm is not enough for me. If these anchors were cast in, would that be enough? Of course not. So why accept less embedment for glued in anchors?