Torsion Capacity of a Single Bolt

[dik]

Does anyone have information on the moment resistance of a single slip critical high strength bolt in torsion?

The direction of the torsion vector is in line with the axis of the bolt.

I have a small moment that must be resisted by the clamping action of a single bolt.

Dik

 

[CoryPad]

VDI 2230 has a calculation example of this type. The basic analysis is:

F = M/(r [·] [μ])


where

F = required fastener preload
M = moment or torque between joint members
r = effective contact radius between joint members
[μ] = friction coefficient between joint members

 

[dik]

Thanks CoryPad...

The problem I have is that I don't know what the effective contact radius is.

The force of friction, I assume, would be nearly uniform underneath the bolt head, extending a short distance from this. Beyond this nearly uniform load, it would vary to zero at some point. The problem is that the further from the centre of the bolt, the greater the resistant moment arm.

Is there a manner of calculating the effective contact radius? that you can une a uniform coefficient of friction?

Dik

 

[BlasMolero]

http://www.tribology-abc.com/calculators/e3_6a.htm

Best regards,
Blas.

 

[rb1957]

dik,

what would happen to your structure if this small torque wasn't reacted by this bolt ? presumably there's another loadpath out of your structure ?? maybe if it's small (<100in.lbs) you can neglect it ??

 

[dik]

BlasModern:
Unless I'm missing something, the calculations appear to give the torsional stress within the bolt, not the torsional resistance of the clamping force.

What I roughly need is a radial distribution of the clamping pressure of a bolt clamping two materials of similar thickness.

rb1957:
The fastener is one of about 30 that are holding together a rack frame without bracing, and the failure of them all could result in collapse of the rack. It's not my design/project or even a firm that I work with, but the other engineer (junior, but good) has been asked to check the design of an existing rack that has been in service for 20 years. Fasteners are 1/2"dia A307 but will be replaced by slip critical A325's. I was carrying this beyond the original question just to see how strong the rack really is (might be). I'm aware of the problems of using a single bolt to determine a moment resistance.

I suggested that several pieces of angle (long and short piece) could be cut and bolted with the short piece secured in a vice and the longer piece be cantilevered. The loads can be applied to the cantilevered long piece to determine the resisting torque of clamping and that this with an appropriate safety factor could be used for checking. I was thinking also that this cannot be a unique type of condition and that there must be a manner of calculating it.

Dik

 

[ishvaaag]

You can get a direct appraisal of the distribution by modeling half your washer and plates. Assume the load of the nut or torque is applied entirely on the upper part of the washer and you can even (for a start) dismiss the ability of slip (it shouldn't, it is a slippage critical connection) of the washer, and then support on vertical fixity out of simmetry the plate. Model 3D in Autocad or Inventor, put the load and restraint, allow xy movement analyze and read the reactions, they will give you the radial distribution you are searching for.

Without that, you can also proceed as in a problem of maximums and minimums: Assume some decaying pressure, say a straight line or quarter of a ellipse from the outer rim of the washer. The total integrated stress must equal the force but the constant stress under the washer is varied in the maxima and minima problem. Taking the lesser torque provided by the minima will be safe IF the law assumed for the pressure models well enough the pressure.

 

[CoryPad]

dik,

You are missing something. The calculation does not provide torsional stress within the bolt because that is given by the torque applied to the fastener, not external moments applied to the parts.

The effective contact radius between the clamped parts (not the bolt/nut contact surfaces) can be simplified to be 1/2[&middot;](r_o+r_i), where r_o is the outer contact radius and r_i is the inner contact radius. For example, if you are joining two frame racks (each 50 mm wide, 1 m long, 11 mm hole for an M10 fastener), then d_o is 25 mm and d_i is 5.5 mm.

 

[rb1957]

i won't model it, i think your test approach is best, but the range of conditions (friction, preload, temp?) is mind boggling ! two pieces well clamped together will be able to resist a reasonable torque.

 

[dik]

Cory:
I'll try to sort through this tonight and see where I get.

rb1957:
I was aware of some of the permutations I can encounter. I was hoping that an analysis would yield a moment requirement of 10% of the bolt torsional capacity... donno yet.

 

[rb1957]

i don't think the bolt is the loadpath. i think the loadpath is friction between the clamped up pieces. i think the loadpath by friction into the bolt head, down the bolt, and out through the nut by friction is 2ndry.

 

[ishvaaag]

http://igor.chudov.com/manuals/Fundamentals-Of-Design/FUNdaMENTALs-Topic-9.PDF

This link recommends (not thinking in your problem) a 60º angle quite keyed on the bolt hence CoryPad quote of a very small clamped area compressed at high stress gets reinforced. It also asserts that by St Venants principle the effect must be dissipated some diameters away, hence you still have some allowance to gain momentum throwing some low clamping stress at such distance. In any case the decay in clamping pressure seems quite strong from the strut cone keyed between head or nut and the shaft.

 

[dik]

rb1957:
The bolt is not really part of the load path but accommodates a little shear. The big contribution is the moment resistance it offers as a result of the torsional resistance provided by the clamping.

The Myz is resisted by the Mzz.

Ishvaaag:
I'll read the material tonight...

Dik