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G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

thread404-262508: Obtaining Old Reference - Torque Capacity Hex Features
thread404-200026: Hex torque strength


Both of the above threads reference G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" (1926), specifically with regard to the following formula, for calculating rounding of a hex feature:

TH = CH · WAF2 · WR.H · UTS · NC


TH is the hex torque capacity
CH is a constant (=0.103)
WAF is the width across flats
WR.H is the wrenching height
UTS is the ultimate tensile strength
NC is the number of pairs of driving contacts (NC = 3 for a hexagon

(Credit to CoryPad on the original thread).

I've been trying to get hold of that reference. I've checked Google Scholar, my University's online library, the Institution of Mechanical Engineers online library, and even Amazon (long shot). I can't find it - other than 3 citations found on Google Scholar.

Does anyone know where I can get hold of a copy of this?
In the same vein; this is an old reference (1926) - has anyone seen any more up to date literature for calculating at what torque an internal hex drive will fail?

Thanks in advance.

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

You will also want to take into account the modulus of elasticity and the head profile in that study. Titanium bone screws are notorious for allowing the drive tools to 'pop' through the flats because of the low modulus. The effective wrenching height is also a function of the head design irrespective of the recess penetration depth- a flat head design is going to have a better defined recess with less fall away than a pan head design that is run in a free flow punch. This formula appears to be for an external hex and the mechanism for an internal hex reaming failure will be different than for the corner rounding that occurs on an external hex. You could probably adjust the constant from some empirical testing to get your results to correlate.

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

Thanks - I wasn't sure if the above equation related to an internal or external hex. That's partly why I'm looking for the original work.
That's an interesting note about allowing drive tools to 'pop' through the flats; no doubt Titanium combined with a pan head design would make this even more likely.

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

Are you interested in that old reference for intellectual curiosity/entertainment/satisfaction ?
Or, are you really designing or evaluating a fastener ?

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

I am designing a fastener.

I work for a company in orthopaedic medical devices. For clarity, I also study part time for my degree. This is for work though.

I have hand calculations for every other aspect of the screw (and associated assembly). I haven't been able to track down any calculations for rounding out a hex so far, I'm hoping that this reference has some answers or at least a direction to follow.

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

I would think that failure of a driven male hex is highly dependent on some variable factors that are not included in that formula, unless there's some average effects baked into that constant. The effect of a poorly fitting wrench is dramatic, as any mechanic can tell you. Even the surface finish of the wrench has a noticeable effect; polished chrome wrenches are smooth and a little more eager to smear the corners off of something.

I had an open end wrench that measured a little larger than all my other wrenches, so I ran some improvised tests with a good dial torque meter. (Yes, I am insane.) There was no mistaking it, the few thousandths of an inch of extra room made a big difference.

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

Is the fastener designed with a non-standard ( small) hex compared to a conventional cap screw?
Is the installation torque greater than the torque for a conventional hex head cap screw with your hex size?

Will you have some control over What installation tools are going to be used ?

I can't imagine the hex being the weak link unless it is quite puny compared to the thread size.
Kind of the opposite of this -

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

TM, those small heads aren't hex, they are 12 point with with full engagement. They are very stout, we used them in some very high strength tight clearance applications.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

RE: G.S. Case "Stresses on Bolts: Nut Dimensions: Wrench Design" 1926

For a medical screw, just change to Torx drive and be done with it. The failure will be much higher than is possible with a hex.

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