Bolts in FEA [4]: Simple Bolt Model
We already covered what can fail in a bolted connection, and what you should pay attention to while modeling…
24 September 2024Bolts in FEA [5]: Complex Bolt Model
13 minutes read
This is the 5th installment of the “bolt series”. In this article we will discuss:
An Advanced Model of Bolts, you can use in complex situations. How to model it, what problems you may encounter and when it will be useful to you.
In case you missed the previous articles, you can find them here:
Also, I’ve prepared a free PDF Guide on dealing with Lap Joint Connections in FEA. You can download it, using the button below:
Get for Free:
Bolted Joints PDF Guide
Bolted Joints PDF Guide
Simplify Your FEA Models, Maintain Design Accuracy!
Advanced Bolt Model
Firstly, let me start with something important:
This is an advanced model…
Setting it up takes extra effort! But what is even more important your analysis (with bolts modeled this way) will be more tricky to converge as well.
This means, that you will have to put extra effort to make this work!
Just make sure, your case needs such an accurate bolt modeling before you use it. In many cases, you may get just as good results with simple bolt model (and it takes much less work from you!).
Still, if you need to solve a more complex connection – this will save your life!
Let’s take a look at the model itself!
This model consists of quite a few elements. Let’s take a look at them one by one:
- Plates have an opening modeled (and meshed around). In the simplified version of bolt modeling we were discussing what diameter this opening should have. Here, there is very little choice, as I would aim for the opening diameter (this is where the contact will happen).
Sure, bolt diameter is almost the same, so you can use those as well. Although most models comes with opening diameters already there, so I don’t think you will ever do that really!
- GAP Elements (compression only elements). Those will connect the bolt to the plates (in the plate plane). Thanks to the fact that those are compression only, we will get contact between the bolt and the opening only on the “correct side” (where shear will really cause contact).
If you feel brave, you can even play with actual gap (say 0.5 to 1mm) which will represent the opening having diameter a bit higher than bolt. But this will make the convergence even mode demanding, and this 0.5-1mm may not be worth an effort (but if you need it, definitely you can do it!).
- Washer model. To be honest with you, there are many ways you can do this. I think the most popular would be a Rigid Element (RBE2) on a diameter of the opening (so the same diameter as the GAP elements “below”) and then the rest modeled as plate. Just be aware, that I would not use the “washer thickness” here, but more a “washer+nut” thickness as this will way better represent the real rigidity.
You could of course use only plate elements (perhaps with relatively high rigidity). I also saw people using GAP elements instead of contact for the washers (although they should transfer shear in such a case, and for some reason this never worked for me in Femap).
- Beam element. This time our beam model consists of several parts – it starts at the “top” washer, then has a node to connect the “top” GAP elements, then another node to connect “bottom” GAP elements and finally ends in “bottom” washer. But I would still simply use a beam with cross-section representing the bolt nominal diameter (or re-calculated actual diameter acknowledging thread if you wish for some reason).
- Contact… everywhere! This one is rough. Of course, you need the contact between connected plates, but you also need contact between washers and plates (otherwise you won’t be able to transfer tension from the bolt). And there is more! The contact between washers and plates should transfer friction… to prevent Rigid Body Motion (more on this later).
To be honest, I really don’t like “stacking contact” (where there are layers of plates one on another with contact between each neighboring plates). This usually converges a bit worse than “normal” contact – but it works – no worries!
In the simplified bolt model I wrote, that you may want 8 elements along the circumference of the opening. Here, this may not be enough.
Sure, if rough estimate will suffice, this will be ok. But if you want to design the plate in FEA, I would say that you should have more elements.
Remember that each GAP element is basically a “fancy beam”. It will apply the load to the node on the circumference, just like a point load. You want to have more than 2-3 “closed GAPs” I guess! This means that 16 or even more elements around the circumference will be a better call.
Bolted Joints PDF Guide
Simplify Your FEA Models, Maintain Design Accuracy!
You don’t have to model every Bolted Lap-Joint in FEA! Thanks to this guide, you will learn:
- What outcomes to read from your FEA model
- Using those outcomes to calculate needed forces
- Calculating bolt capacity and bearing plate capacity
- Checking if the connection is designed well!
Bolted Joints PDF Guide
Simplify Your FEA Models, Maintain Design Accuracy!
How this works?
I wish to quickly address how this works. This is important, as it will also show you where potential problems may lie.
Shear Transfer
This is actually pretty straight forward. Shear basically means that one plate wishes to move against the other along the plane of their contact.
This will simply “close” GAP elements on the side marked in red above (depending on the movement direction). Those GAP elements transfer compression – just as a real bolt that would press into the opening side.
Since there is an eccentricity in the connection, there will be some contact pressure between the washer and the plates on both ends to make a “counter moment”. This is nothing “too serious”. Not only it really does happen in real connections (although a bit less, since we have an exaggerated eccentricity, as we are moving mid-surfaces here).
Tension Transfer
This mechanism is rather simple. If the two plates want to move apart, each of them will try to get closer to the corresponding washer. This in turn means, that the contact will start working, and in result bolt will be in tension – just as it suppose to be!
There is even a nice practical bonus to this. In the simple bolt modeling we were wondering what diameter we should use for the rigid element. The argument for bigger diameter was, that for thin plates, washers and nuts really strengthen the plate bending. Thanks to this model, you don’t need to wonder at all – it considers this effect automatically.
Things this Model Does Well (and not so well)
This section will be similar to what we did for a simplified model from the previous article. Let’s wonder here, what our advanced model handles better!
Correct Stress Distribution in Tension
Of course this model works great in tension.
Argument could be made however, that it’s worse than the simple model here. Not because it does something “wrongly” – far from it! In fact, it will automatically consider potential strengthening effects in bending of thin plates… so it works better.
The thing is, that it’s way more complicated, so you spend more time setting up the model, and playing with convergence… without much gain.
Correct Stress Distribution in Shear
This is of course, where the magic happens. Sure, for a good stress distribution you will need a significant amount of elements along the opening circumference, which is not very practical. But even with a reasonable amount of elements, this give a WAY better idea on how the stress will be distributed to the plate!
I would still check the plate bearing stress by hand (call me conservative!). But if I would feel that this bearing stress would impact other stresses in the model and “add up”, I would say that my analysis considers this.
Nice Weakening of the Plate
This model really nicely deals with weakening of the plate. GAP elements can’t transfer tension, so there is no way for this setup to strengthen the plate in tension (if it would fail as shown above).
They would however strengthen the plate in compression (GAPs on both sides will be compressed and will transfer load). This is not an issue however, as Eurocode actually allow this!
Not the Best Distribution of Forces inside the Bolt
This is the same problem as in the case of the simplified model. Sure, the tension and shear forces in the bolt will be calculated ok – and this is what you need to check the bolts capacity by the code.
But as previously, bending in the bolt will be funky, as we are using a mid-surface model so eccentricities are artificially higher (and will lead to higher bending than would be observed in reality).
Still, all you need to do is to check the bolt capacity by hand, using the forces from your FEA model. And you will be fine!
A Nice Step Forward!
As you can see, this model really handles a lot of things decently.
Realistically, the only thing you should NOT count on, is bolt design. And to be honest with you… this will never change!
It doesn’t really matter what you are calculating – modeling a bolt accurately enough to derive it’s capacity directly from FEA is an insane task. It will take a LOT of resources… simply to get a check you can do simply comparing the force to the value in a table!
But apart from direct bolt design (that is simple to do by the code) this model really does a good job to allow you to realistically consider bolts.
In comparison with the simplified model we already discussed using this advanced model allows you to decently capture shear and plate weakening. This is of course great, but if you don’t expect issues with those, remember that using a simplified model will save you a lot of work (and headaches with convergence!).
The issue with this model
As we discussed, this model will allow you to cover most failure modes (basically besides direct bolt failure). But there is one thing, that I feel I should mention.
Please take a look at the model once more:
Note, that this model consists realistically of 3 elements:
- Plate 1: Doesn’t matter if it’s the top or the bottom plate – we assume it’s connected to something else, that is supported somewhere – it should be stable (in static sense, i.e. no Rigid Body Motions).
- Plate 2: Just as in the case of Plate 1 I’m assuming this is a part of a bigger model (or that it’s at least supported somehow). So again it should be stable (so no Rigid Body Motions).
Of course, you may have a situation, that the model is unstable without the connection (I mean, this is why you have it, right?). So the plates may not be sufficiently supported if you would take the connection away. But since you have the connection, I’m assuming that the model is stable.
- The problem lies in the Bolt + Washers: Note, that the bolt (beam elements) and washers (RBE2 + Shell elements or however you modeled those) are a single body. They are rigidly connected together, and that is great.
But the bolt is not supported at all… it kind of “floats” in the air!
Sure, under load some Gaps will start transferring shear as compression, and in tension contact will close. Thanks to the fact that the contact also should have friction defined, this will prevent the bolt from rotation around it’s own axis… making it stable!
So on the first glance, everything seems fine with those 3 parts above. Even the Bolt +Washers works nicely, as long as there is some load in he model.
But let’s remember one thing: analysis has to start somewhere! And at the beginning there is zero load… making this tricky to converge (ha!).
But what is even worse… think about this connection under pure compression!
In such conditions, contact between plates is closed (but not between washers and plates) and all GAPs are open. The bolt can simply rotate around it’s own axis.
But solver will also see that the bolt can move in any direction, as nothing is holding it! Sure, as soon as it moves some Contacts and GAPs will close. But this is a very difficult step for the analysis.
This is why sometimes it’s just needed to add “soft springs” between the washers and the plates. Simply to keep them “in place”. You don’t really want to support the bolt. The reason is, that your structure will deform and drag the bolt with it. This makes supporting the bolt (even with low rigidity supports) quite awkward.
The best solution is to add weak springs with small rigidity, between washer and corresponding plate.
FREE Bolts in FEA Guide
Simplify your FEA, maintain accuracy!
Bolted Joints PDF Guide
Simplify Your FEA Models, Maintain Design Accuracy!
Summary
Without a doubt this is an advanced model. It takes time to set up, and sometimes gives headaches with convergence. But if you are reasonable about it, the benefits you get are great! This is which failure modes you can cover (you can read more about failure modes here):
- Get Internal Shear and Tension in Bolts. But you still have to check bolts capacity outside of FEA by the code.
- Endplate Failure due to Tension. You can get the capacity directly from your Nonlinear FEA analysis. Sure, punching shear is checked as well… but I would check it by the code anyway – especially since it’s just a single simple equation, and you are checking the bolt in tension/shear anyway!
- Plate Failure due to Shear in Bolts. I admit, that I would check bearing (contact) capacity of the plate by the code anyway. But weakened plate will be checked nicely. This is especially great if various effects (i.e. punching shear, bearing stress and tension in the plate) would add up – there is no simple way to do this “by the code”, and your FEA model will be a best bet!
- Buckling of the Plate Between Bolts. Your model will detect this failure mode for you. And it will even behave reasonably with it.
As you can see, there are a lot of advantages in using the advanced model. Just don’t forget that it has a serious downside:
Converging an analysis with a lot of those bolts may be a bit more difficult than normal!
This is why, if you are mostly worried about tension in the bolts (and bending of the end plate resulting from this tension), I would recommend the simplified bolt model.
But if you have a more complex case (and let’s face it, those happen more often than you would like!) this is your friend!
I really hope that you enjoyed this article!
Ł
Categories:
- FEA Fundamentals
Share
Join the discussion