How exactly does a fastener elongate when tightened? 1

[CamJPete]

I am trying to calculate the stiffness of a custom screw using K = EA/L, but while specifying the length, I'm having a hard time visualizing how a fastener elongates along its length when preloaded into various plate configurations.

As a simple example, suppose you have two plates that are 0.5 inches thick each. Both plates have unthreaded through holes. A bolt is installed and tightened with a nut. It seems straightforward that the fastener will elongate only over 1 inch.

Now suppose both holes are tapped and no nut is used. It seems the compressive deflection of the plate threads will fight against the tensile deflection of the bolt threads. Do the threads just plastically deform or does the system just bind up before you can generate appreciable preload? Or something else? What effective length would be used to calculate the bolt stiffness here?

Now suppose the top plate is a through hole and the bottom plate tapped. Same questions here. Does it bind up a little in the bottom plate? What is the effective length for the stiffness calculation? Does the fastener within the tapped hole portion elongate? Is this elongation non-uniform along the fastener? I know that's a lot of questions, but these are just all kind of floating around in my mind and I can't resolve them.

Cameron

 

[3DDave]

Check the Bolt Science website for answers to most of these questions.

 

[BrianE22]

Do a free-body diagram of the threaded portion of the screw. I think you'll see that even in the threaded portion the bolt elongates. It's non uniform along the length of the thread though. To figure it out you would have to know how the load is distributed along the length of the thread. I think most people agree that the first few threads react most of the load.

 

[Compositepro]

If both plates are tapped, you cannot develop any clamping force between the plates, unless you rotate the plates. In that case the bolt elongates only within one or two thread pitches. If only one plate is threaded, then the bolt elongates over one plate thickness.

 

[CamJPete]

Thank you for your responses.

BrianE22, that is a good point. That reminds me of free body diagrams I've seen of a bolt that shows the distribution of the force spread out among the the first few threads. The first few take the majority of the load. Of course. Had you asked me that I would've known that.

Compositepro, I mostly agree with you, now that I've consulted my machine design book (should've done that earlier). I've read this section before, but it didn't really stick until now. Norton states that the bolt stiffness (when used on one unthreaded plate and one threaded plate) is found using a length equal to the thickness of the first plate plus half the diameter of the bolt (if the thickness of the second plate is greater than or equal to the bolt diameter.) Compactly, lm = t1 + d/2 (if t2 >or= d). The shape of the frustum cone when the second plate only is tapped does extend the compression zone into the second plate, but Norton is modeling it as only extending down into the engaged threads by d/2, then truncating the cone at that point.

I feel comfortable assuming that the bolt elongates only up to the end of the first few engaged threads, and will model it with Norton's approach. Thanks for the insight everybody!

 

[Scuka]

How do you expect to put a bolt through two threaded bolts?

 

[kingnero]

How do you expect to put a bolt through two threaded bolts?

That would be difficult, but I'm sure a properly skilled magician would be able to do just that...

As for the example of putting a bolt through two threaded plates, the second/bottom plate would basically do nothing, and all preload would be achieved in the theoretical part between the bottom of the bolt head and the top of the first plate, meaning over ~ zero distance, ignoring the practical elongation in the first few threads.

I guess in reality nobody takes into account the elongation in the first few threads but only the "measurable" distance upto the top of the nut/threaded hole.

 

[CWB1]

As for the example of putting a bolt through two threaded plates, the second/bottom plate would basically do nothing, and all preload would be achieved in the theoretical part between the bottom of the bolt head and the top of the first plate, meaning over ~ zero distance, ignoring the practical elongation in the first few threads.

Incorrect. Assuming zero distance between two flat plates, the two plates function as one thick plate.

 

[kingnero]

I disagree, because in reality the threaded holes can be tapped separately. This is where your "assuming..." comes into play.
Your theory only works when both plates were tapped at the same time, clamped together.

Further, almost all load transfer happens almost immediately (I should take my theory books, but from memory I'd say 60-70 % goes into the first two/three threads).

 

[Scuka]

^ reply to few posts above...


First of all, how does a nut tighten two plates with holes without a thread in the first place?
The thread is basically an inclined plane, and rotating the nut on a bolt makes the nut travel along the plane upwards (or bolt travels down the inclined plane), and the clamping force is created when the nut wants to travel up, but the plate doesn't allow it to anymore, forcing the bolt to elongate.

What happens when you've got a nut through two threaded holes on two plates? Both plates travel up the inclined plane together until they hit the bolt head. And then what? There's nothing that would force the bottom plate to clamp against the top plate because they both tend to travel along the thread together. They're tightened or released together, however you turn the bolt.
And that's assuming you even manage to put the bolt through two plates (how do you expect to align the threads short of clamping both plates together in an exact position in a jig and tapping the two holes together?)


TLDR - there's a reason why 1 plate max has a thread on it.
Joints with multiple tapped holes are just not done, because it makes no sense.

 

[CWB1]

I disagree, because in reality the threaded holes can be tapped separately. This is where your "assuming..." comes into play.
Your theory only works when both plates were tapped at the same time, clamped together.

Unless there is another unmentioned constraint then the plates can be tapped independently and simply rotated then locked into position to align the two threads. Many anti-backlash assemblies and other mechanisms do exactly that via a single screw and multiple parts tapped with female threads.

Load transfer does begin at the first thread however it doesnt end there, hence why the minimum engagement length is a critical output to any bolted joint calc. Low strength materials, loose thread engagement (% thread-thread), and bad rules of thumb have gotten many engineers into trouble over minor details.

 

[kingnero]

Weird line of thinking of rotating the parts in order to accomodate full thread engagement. But indeed, having lost quite some sleep over the VDI 2230, I agree that good engineering goes a long way. Lets agree that the hypothetical case that the OP suggested (a bolt in two threaded plates) doesn't fall under that.

 

[3DDave]

I did a plate-plate screw engagement once. It was to place two cameras base-to-base for stereographic photography; I ended up creating a precision spacer plate to ensure the correct tension at the point the cameras were pointing the same way.

 

[XL83NL]

Has no one mentioned Bickford yet?

 

[hydtools]

The two threaded plate case sounds akin to double nutting a through bolt or threaded stud.

Ted

 

[3DDave]

Typically nuts have a chamfer which leaves at least one thread of the fastener exposed below the mating surface, so a double nut should have nearly two threads worth to extend. Whether or not a plate is ground flush without lead-in chamfer or not would make some difference.

I think the detailed analysis depends very much on a number of factors not mentioned and would require a sophisticated FEA to see the entire distribution of strains throughout all the parts; this would include friction, small variations in form that will close under stress, slight differences in elastic modulus between the fastener and the surrounding material, et al.

Even a slight counterbore could increase the deformation in the thread by a factor of 10 to 100 over the ground-flat case.

 

[CWB1]

Weird line of thinking of rotating the parts in order to accomodate full thread engagement...

That's actually one of the "more normal" designs in my world. I specialize in 3d parametric design for the auto industry, particularly packaging challenges that nobody else wants.