Bolt Group Max Tension due to Moment 1

[krismac]

Hi,

Hopefully simple but I can't find anything on the internet and have no text-books to hand right now.

I need to use a formula to calculate the maximum tension in a bolt group (4 bolts - 2 x 2) due to a moment. The bolts are in a base plate which has a beam protruding from it, and the force is applied laterally to the beam at the top (cantilever beam with end load).

I believe the formula for max tension includes (2A^2 + 2B^2)/B ; where A and B are distances from the edge of the base plate to the first and sedond bolts rows respectively.

Please can someone help me with the correct formula, and also a reference would be great if possible.

Thanks,
Kris

 

[Ron]

Resolve the moment into a force couple, with the line of action being through the bolt axes. Two of the bolts will have no load on them and two of the bolts will be in tension. Divide the tension load by two. This approach is conservative.

You can get more complicated in the analysis by considering bending across the base plate and the point of rotation being at one edge of the base plate. This puts all of the bolts in tension, with different distribution of the load between the two bolt pairs. Now the force couple shifts more toward the bolt group centerline and you can analyze as a two-span beam.

The more accurate way, obviously, is to analyze the plate with FEA, getting vertical reactions for the bolts from the moment applied to the plate.

 

[desertfox]

Try this site:-

http://www.roymech.co.uk/Useful_Tables/Screws/Bolted_Joint.html

Scroll down till you see this heading:-

Strength of bolt joints withstanding bending forces


desertfox

 

[krismac]

Thanks both, the conservative force couple approach gives 56kN and the correct representation of the bolt group gives 48kN. I looked on RoyMech initially for that calc but must have missed it!

Another thing, do I add or subtract this tensile force to the bolt pre-tension to get the total force on the bolt?

I'm a bit rusty with these calcs at the moment.

Thanks
Kris

 

[Ron]

Anchor bolts are generally not pre-tensioned. Snug tight condition only.

 

[CoryPad]

If the bolt is pretensioned, then a fraction of the external force is added to the pretension. The fraction is based on the stiffness of the bolt and of the clamped joint. You can learn more about bolted joints from Guide to Design Criteria for Bolted and Riveted Joints, available for free download here:

http://www.boltcouncil.org/files/2ndEditionGuide.pdf