Base plate tension distribution to anchor bolts

[Enginerdad]

I have a steel plate which is held down by 8 anchor bolts (labeled A-G, see the attached drawing,). The plate is loaded by an upward (out of plane) force which is eccentric to the center of the plate. Can anyone suggest a reference or method to determine the tension that each bolt will resist? I feel like it should be proportional to the distance of each bolt from the point of load application, but can't figure out how to turn that concept into an actual equation. Thanks for any help you can provide.

 

[cliff234]

This is not the answer you're looking for, but why not make the bolt group symmetrical about centroid of the load?

 

[Once20036]

For the tensile load, it will be evenly distributed between the 8 bolts.
Then, look at the moment created by the eccentricity in one direction. This will create tension in 3 bolts, compression in 3 bolts, and no effect in 2 bolts.
Add these results to the uniform tension calculated in step 1, then, repeat for the eccentricity in the opposite direction.

 

[Shu Jiang PEng SE]

Move the vetical force to the base plate center, and introduce two extra moments due to the force location change. Calculate the bolt force under tension and moments separately, and then add them together.

 

[dozer]

Once20036 has a good approximate solution. Hilti offers a free program called "Hilti PROFIS Anchor" that will solve this problem also. It is also approximate because it assumes the base plate is rigid. When I say these two are approximate, I think they will be pretty dang close. I'm just saying they don't account for things like prying action if the base plate were below a certain thickness or the relative stiffness of concrete vs. the plate.

You can search "Hilti profis" to find the website where it is offered. It requires registration to download it, I believe.

 

[KootK]

In general, you can use the same method that we use for pile groups. See equation 1 here: Link. As with other methods, the plate is still assumed to be rigid. Re-evaluate if any of your bolts wind up in compression. This should produce the same result as Once's for the proposed configuration.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Everynameistaken]

Annex D has the equations to work all this out. There is an "eccentricity" factor that accounts for the fact the tension is not at the centroid.

Also, from above how does a base plate put a bolt into compression?? Unless there is a levelling nut either side this is not the case, the tension goes into the bolts and the compression goes from the base plate to the concrete in bearing, the location of this reaction point is dependant on the stiffness of the base plate.