I think that many engineers, especially in the structural field, start FEA to calculate complex connections. There are few traps on such problems, and one of them is preloading bolts! This is why I’ve created a tutorial to do just that in Femap! I hope you will like it!

There are several ways in which you can preload bolts in your model. It’s possible to simply “set” a bolt preload as a type of load, but things are a bit more complicated if you want to have a 3D meshed bolt!

Your approach will depend on what your software possibilities you have access to, and how your model looks. Firstly, let’s look at why you may want to preload a bolt. Later we will see how you can do it depending on the situation!

Bolt preloading is a pretty straight forward procedure, but it has some tricks to it. General idea is, that you want to tighten the nut of the bolt so much… that the bolt will start to elongate. This, of course, increases the tensile force in the bolt itself. You can measure this load, but measuring how difficult it is to tighten the nut. This is usually done by measuring the torque. There are tables for tightening torque giving you the force in the bolt depending on the grease you use. This is more or less how it works:

Without a doubt bolt preloading is a “premium procedure”. By this, I mean that it is easier not to preload the bolt than to do that! This leads to a situation where people usually think about those connections as “better”, and rightfully so. But there is a big problem with preloaded connections!

Let’s think about a shear connection of two plates (a bit similar as the one above). It will be loaded in horizontal direction (top plate goes right while bottom plate goes left on the drawing above). This is a typical “shear” connection, and it’s quite a popular thing.

A funny observation is, that bolts have the capacity due to shear almost equal to capacity due to tension. Normally you would expect the shear capacity to be lower (0.58 is the factor thanks to von Mises criterion). But in bolts shear happens usually where there is no thread in the bolt (so area is higher). On the other hand tension always fail at the thread (higher capacity but lower cross-section area). Those two effects even each other out leading to almost equal shear and tension capacity of a typical bolt.

Now the twist!

Imagine a bolt with around 100kN of shear and tensile capacity. In a non-preloaded connection shear capacity of the bolt is 100kN. While in a preloaded connections it’s the preload force times friction coefficient. In Poland we preload bolts for 70% of their tension capacity. I know however, that in some countries even 100% of the bolt capacity is ok. Let’s say it’s 80% of the load “on average” so 80kN. A good friction coefficient would be 0.3. Sure… you could try to go higher, but that would require some serious skills and effort. So the shear capacity of the preloaded bolt is… 80kN*0.3 = 24kN.

In essence you need around 4 preloaded bolts to carry shear of 1 “normal” not preloaded bolt!

Sure, after the friction “breaks” there is still some “extra” capacity when bolt starts to be in shear. But, codes universally assume that when the slippage happen, this should be treated as failure!

In other words… it takes effort to preload the bolts, and their capacity due to shear is lower when we do this! There must be a reason why people still want to do this anyway, right?!

I don’t want to overdo the intro here, so I will try to keep this short and sweet!

There are several reasons why you would like to have preloaded bolts:

• Fatigue! I don’t know how things looked like at your Uni, but here the strongest emphasis was on fatigue. When you preload the bolts in a connection, then the force in the bolts is constant. This is true even when the forces in the connection change. This is super important since the thread of the bolt has some super-bad geometry shape that really concentrates stress. In the case of fatigue, this would be a nightmare! Prestressing bolts clearly solves that for you!
• Rigidity! Slippage in bolted connections can be a real mess (more about it here!). If you preload bolts there will be no movement possible due to friction, so the connection is much more rigid.
• Reduced deformations! This comes with the rigidity I guess. If you have shear connections, increasing their rigidity and not allowing slippage will reduce deformations of your structure.

There are some other reasons as well. I get a feeling that preloaded connections are done with more care (always a good thing). You can also connect something to the existing structure without welding and drilling holes in it. All you need to do is put something around it, and pretension it so the friction will carry the vertical force.

The above, in some cases seriously “outweigh” the fact, that shear capacity of such connections is lower than the non-preloaded ones. And this is why we often use them! Without any doubt, they are needed if fatigue is a risk. But preventing slippage is also very important (but a bit more subtle!).

Since you know what, and we know why… it’s time for the how!

I will use Femap here, but of course, bolts preload can be done in all FEA systems. While not every single one allows simply to “define” the preload force you can work around this pretty easily.

Normally, you won’t have “free space” between plates that are connected with preloaded bolts. But just for a demonstration, I’ve made a model of a Rectangular Hollow Section (RHS). I will preload a bolt going through the pipe. This way, the deformation of the pipe sides will show us, that something is indeed happening. Normally there are almost no deformations since it’s only one plate pressing into the other plate!

This may not be the best technical solution (preloading bolts like on our example isn’t the best idea). But I think it will be a great test of how preloading works!

As I mentioned there are several possibilities. The first thing we have to decide on is if we want to have a bolt modeled with a beam or with a solid body! Let’s start there!

Bolt: Beam or Solid?

This is a very important choice, but somehow I get a feeling that you already know what you will use! This strongly depends on what you want to do of course!

If I do a 2D plate model of a relatively big structure (so, stuff that I normally do!) modeling bolts with solid elements is simply impossible! The size of the job would be so big, that waiting for outcomes wouldn’t make any sense! In such cases, I usually use beams as bolts.

If I have a small detail to analyze, and this happens to be meshed with 3D elements, I would instantly assume that 3D elements for bolts should be used as well.

Let’s take a look at the choice in a bit more details:

Bolt as a Beam is great in big tasks. It’s “light” on elements (since I’m using beam elements in red above), and usually, you can use it without contact. It’s a natural choice in plate structures. But of course, nothing is for free. I will have to rigidly connect my bolt to the plate (blue rigid elements above). This is “cheating” in how such a connection carries shear forces. They are applied to the entire circumference of the opening, and they shouldn’t! This is a price I’m usually willing to pay. I will simply analyze those regions manually later. But without a doubt, this is a drawback for sure! Hint: if you want to learn how this “cheating” works, sign up for free sample lessons from my FEA course here (it’s in lesson 2)!

Bolt with Solids allows modeling stuff more accurately. I even did a nut and a washer as you can see above! Since you can make contact from bolt to opening “inner surface” (Nastran doesn’t fancy edge to surface contact) you won’t cheat in shear loads. Here, I’ve decided to leave the RHS as plate elements. It reduces the size of the model, and there will be no shear forces anyway. You can also include slippage, friction between everything and all the jazz. All in all, this is a fun thing to do! The problem is, that this is super computing-intensive! Not only you need to have a 3D mesh marked in blue above, but there is contact involved (washer and RHS wall have contact defined between them). This all makes the model more time consuming to calculate!

For now, let’s assume we want to have a bolt modeled as a beam. This is an example quite close to my heart!

I think, that most FEA packages have a simple “bolt preload” load type. You can see how this looks in Femap in the video below:

As you can see, this is a rather simple thing. You just define the preload and move along. Of course, there are several things to consider. Depending on the FEA package you use, bolt preload may mean different things. What you want to achieve is, that the preload happens in full, before other loads appear in your model. Usually, this is how it works when you define “bolt preload”. However, you may have to create 2 step analysis of your model in nonlinear analysis to get this effect. In step 1, you apply bolt preload, and in step 2 you apply the rest (and bolt preload should still be there of course!). This will depend on the software you are using.

The problem is, that you don’t want to apply bolt preload at the same time as “everything else” in nonlinear analysis. This is because solver “takes” all the loads and divide it into increments. Let’s say that we will use 1% of the load per increment. In the first increment, you have 1% of all the loads in such a case. But in most problems, you want to have 100% of preload on the bolts from the start! This is why defining bolt preload as an initial condition (or the first step in analysis) makes sense.

There is a second part of this as well. In the example above you can see, that I used a rather simple approach. That is, I have ab RBE2 element filling the opening, with a bolt modeled later. But let’s say we want to carry shear force due to friction. The above model won’t work, because there is nothing to have friction with. In such a case, it’s a good practice to define a washer and a nut. You will attach the bolt to them of course (instead of RHS). Then you define contact between washer and the connecting plate:

Notice that the RBE2 (rigid element in blue) looks the same, but this time it’s attached to the opening in the washer, not in the RHS plate. The washer is either 3mm thick (for the normal washer, in green), or much thicker (including the nut thickness) in yellow. Perhaps this is too pedantic, but since I wanted to make this as nice as possible I went that route!

Of course, you need to define contact between the washer (both green and yellow parts) and the RHS plate (here in gray). If you want to carry shear force, you need to define the friction coefficient for this contact as well. How this works is, that you press both washers toward them (thanks for the bolt preload). Since there is contact between washer and RHS this means that those elements “push” into each other. This means that friction is possible, so you can carry the shear load. Nice… maybe apart from the fact that you need to converge contact in the analysis (so computing takes longer).

There is also a slight difference in outcomes. While the preload is the same, it is applied to a bigger area with the washer. This reduces the max deformations of the RHS slightly (along with reducing stresses as well!):

I’m not sure if such a difference is so important to model washer for every bolt. Personally, I don’t do it. But I’m also aware, that I have a bit of margin modeling the bolts without the washers (when the bending of the plate is involved of course!).

I think you can easily imagine how this is done with solid bolts. Firstly let’s take a look at Femap possibilities in the video below:

Just as previously, there are several possibilities. As you could see in the video, the easiest way is to apply bolt preload on a “solid region”. However, I’m not sure if all pre-post processors allow this. This is why sometimes a “creative” approach to things helps! Cutting part of the solid bolt out, and changing it to a single beam element may do the trick. This way, you can simply apply the pretension to that beam element, and be done with it!

But there is one thing that’s “left”! Let’s compare outcomes from different methods! Firstly, let’s see if we got the same, from both approaches to solid bolts preloading:

As you can see above the difference is minuscule at best (0.2%). Obviously, both methods work! But there is also something else we should pay attention to! This solid bolt is almost precisely the same thing, as the Beam bolt with washer we used before. Since it is the same head and washer, just modeled differently, we should get similar outcomes right?

And we did! In the previous case, it was 979 MPa, now its 990 MPa. This means that the difference is only around 1%! We were expecting this of course! After all, it would be sweet to get the same outcomes regardless of the approach right?!

## Summary!

In this post, I covered the best ways to apply bolt preload in FEA. Let’s wrap up what we have learned here!

• Preloading bolts make sense! It can help you with fatigue problems (since force in the bolt is constant, so no fatigue!). Preloading also helps with the rigidity of some connections. All in all, a useful trick!
• Preloading has costs! This is something people often forget! Since you carry shear force via friction, shear capacity of each bolt is much lower than in a “classical” connection! Don’t forget that!
• How you approach preloading depends on your model! In big models made mostly with 2D elements (plates), it’s better to model bolts as beams. In smaller, solid models you will most likely model the bolts as 3D solids with 3D mesh.
• Bolts modeled as beams are simpler! You can simply select a special load type called “preload”. As you saw in the video, there isn’t a lot you have to do to set this up! The problem is, that you “cheat” when the shear load is involved. Since the bolt is connected with the opening via rigid elements, the shear load is applied to the entire circumference. Not the best thing for sure, but a useful simplification!
• Help the beam! You can resolve the problem, by modeling a washer and connecting the bolt to the washer instead. Then shear loads are properly transferred via friction. The problem is, that this requires contact between the washer and the plate in the connection. For a few bolts this may not be an issue, but for hundreds of them in a single model… this should be carefully considered!
• About the accuracy! It is true, that when you use a washer, the plate in the connection is loaded more accurately (on bigger area etc.). This means that the stresses will be slightly lower. This is, of course, great, but with a lot of bolts in the model, you are “buying” the accuracy with a lot of computing!
• Solid bolts are also a solution! In some cases, you may want to model bolts as solid bodies meshed with 3D elements. The biggest advantage is, you can have contact between bolt “side” and opening “side” on the plate. This would allow transferring shear force more accurately in the case without preloading. But since with preload you transfer shear loads with friction anyway, this is not the biggest issue!
• 2 solid approaches! In Femap, you can define a bolt region and apply preload on the solid bolt directly. But if this is not doable in your FEA package, you can always cut out part of the thread, and replace it with a short beam element (you just need to connect its ends to all the nodes in the bolt cross-section at each end). This way, you can apply bolt preload easily!
• It’s all the same! Funny enough, solid modeling leads to super similar outcomes that beam + 2D washer (for bolts). While all of those require contact, with bolt and 2D washer there are far fewer elements at least. This is something definitely worth thinking about!