Bolt connection with pretension


from my job i have to understand a bolt connectin with pretension.
So i want to understand these calc. and diagramm:

Is it possible to get these result with a simple 2-D plane strain model / calc.?
maybe with a half (red) or a quarter (blue) of the model for beginning?

contact - prestress - and so on!?

Maybe an axis-symmetric model? I’m not sure if P.Strain/Stress would be appropriate to get the clamp loads. I haven’t tested the pretension option on 2D models, but I know it works for 3D. I would start with a 3D model, maybe a coarse mesh, and see if the numbers make sense with the analytical values. I tried to do a similar test a few months ago but could not finish my validation plan.

Yes, you can get those from 2D with the option:

*El file, Output=3D
S, E
*Contact file, Last iterations

You may even start with a simplified beam model (single B31 element representing the bolt) since *PRE-TENSION SECTION should work in such a case as well. However, I would use a simple 3D model, for example, something like this:

By the way, it would be great if such a bolt preload test model could be included in the CalculiX examples repository created by @mkraska.


yes, a test example would be very helpful.
maybe we can help / inspire him.
sequel follows,
please hold the line !



This Prepromax tutorial should help you as models a pretension bolt + nut and add preload. I followed this tutorial and works quite well. Generating inp from this tutorial should help you a lot, I hope this helps

it has been a while but to my recollection thermal shrinkage could be a way to mime pretension. give the bolt a high thermal coefficient and chill it.
That way it is a load condition thing, not a model thing. You can change the effect easily and investigate what happens in the case of creep or loss of pretension from other sources.

That may work fine if you don’t have a thermal load case after your pretension/installing loads. However, I recall a study I had to perform where the thermal load case was the critical case for failure after applying pretension and duty cycle loads. Thus, a non-realistic coefficient of thermal expansion could lead to problems correlating.

Some time ago I did a version for calculix of this Abaqus example: Abaqus Example Problems Guide (6.13) ( 1.1.1 Axisymmetric analysis of bolted pipe flange connections)
Please, check as well the original paper with test results so you can compare FEM, hand methods and tests.
You can download the ccx inp file from here boltpipe4_calculix.inp - Google Drive


Great, thank you for sharing this :slight_smile:

I’m looking for an example for hand calculation.
Has someone a very or the most simplest calc. for bolt with pretension?


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I’m also looking for that. So far I didn’t have enough time to further investigate this topic but I think that I will go back to it soon.

There are many formulas for hand calculations of bolts in books such as “Shigley’s Mechanical Engineering Design” but one would need to study them carefully in order to use them for direct comparison with FEA. Thus, I was looking for some ready-made examples where FEA is verified using an analytical approach but it’s hard to find such resources (not only for bolted joints but in general - concrete examples of analytical vs numerical calculation are very rare).

Anyway, here’s the best article that I’ve found on this topic:

Check this link : MITcalc - Design and strength check of bolt connection

As a textbook reference I’d recommend Bickford

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Microsoft PowerPoint - Bolt Preload - White Paper Rev-0.pptx (

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I added a bolt example to my collection. Yet, it uses thermal shrinkage for pre-tension.

Alternatives would be usage of the pre-tension feature as discussed here in the thread. This would require additional modelling effort (cutting plane)

Also, you could use an initial contact penetration (like a shrink fit), this is the only way it can be done in Autodesk inventor stress analysis module.