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13 December 2016

# Slippage in bolted connections

Slippage in connections is often neglected in the design of steel structures. I have seen its importance when I was working in the team investigating the structural failure. Just as easily I could learn about it when it was my design under investigation! It is incredible how easy it is to discard slippage from calculations, and how terrible outcomes this may bring!

## What is slippage

Slippage is a possibility of the connection to deform, before it starts to transmit forces. It has nothing to do with capacity of the connection, only with its rigidity. This makes omitting this phenomenon easy, as engineers tend to think that if capacity is ok, everything will be fine.

Screwed connections with long holes (without pre-tensioning) are the best example of slippage:

This connection will not carry any force at the beginning. First, the movement (slippage) has to happen in order for the screw to reach the sides of holes in both elements. Then the shear force will be transmitted as can be seen below:

After the screws are in contact with the sides of the holes, forces are transmitted as normal. So what is the problem you might ask… the problem is with the movement itself!

In the above example connection can easily slip more than 30mm (depending on the long hole length of course) – it is obvious that the designer’s intention was to allow such movement. But in a “normal” screwed connection this movement is usually restricted to around 2mm (holes tend to have a diameter 2mm higher than bolts). Seems like very little right… I will show you the effect of such 2mm slippage on 2 examples below.

Please note, that as Peter pointed out below you should never use slotted holes on both sides of the connection. The above example looks like this, as I was afraid that on small screens (like your smartphone) people won’t be able to see the movement otherwise. Thank you, Peter, for pointing this out!

## Simple slippage example

Sometimes slippage only causes additional deformations – i.e. if a table has 4 legs screwed with slippage it will end up being shorter than originally assumed. Such shortening in itself does not have to be critical. If the structure is not overrigid this will only cause additional deformations. If those deformations are acceptable, then everything is fine.

Most structures, however, are overrigid, and in those structures, additional deformation actually causes force redistribution. This means that some parts of the structure will take less load than they “should” and other elements will be overloaded.

Let’s try with a simple truss first – I will compare the outcomes from a truss with no slippage connections, and the one with 2 slippage connections in the middle:

I have defined the slippage in the nonlinear tab of connection properties with the following chart. You can see that at the beginning deformation (u) rises without any force (P) appearing, and then after a certain value of slippage (here 2mm) connection start to  rigidly transmit normal forces:

Outcomes for both trusses, of course, are quite different. Take a look at the deformation below:

You can easily see that the truss with the slippage has much higher deformations (4 times higher to be precise). Notice that the model with slippage software actually shows slippage (bottom chords are drawn as “not continuous” while the top chord is overlapping). I should also mention that those additional deformations are almost 10 times higher than the slippage value – slippage is in the horizontal direction, while we measure the vertical deflection.

In truss with slippage, some additional forces appeared, but overall the biggest change is in the deflection. Let’s see now how many additional deformations can drastically influence some structures.

## Slippage in complex overrigid structures

In overrigid structures, additional deformations of certain elements can greatly influence the force distribution in the structure. As long as everything deforms together, things tend to be better than if some elements move more than others (this is why uneven foundation settlements are considered far worse than even settlements).

I will use a relatively small model to show you how incredible this influence can be. The model consists of  6 trusses (with circumferential truss) intersecting each other as shown in the picture below (it actually uses the same trusses as the one in the first example):

The intention of the designer of this structure is clear – trusses in both directions should carry the load evenly. This allows the structure to carry a relatively high load (when compared to trusses in one or the other direction working “alone”). However, there is a problem with structures like this one. While in one direction trusses can be “continuous” (the red ones below) in the other direction (the green ones) they will have a connection on both sides of perpendicular trusses (black rectangles). This means that the top view will look like this:

If the rigidity of the marked connections will be sufficient, nothing wrong will happen. Trusses in both directions will work evenly resulting in capacity usage shown below:

However if the connections will have slippage (for instance shear screwed connections without pre-stressing), force distribution changes greatly.

Let’s get back to the simple truss in the first example for a moment. The one without slippage was able to take a lot of load without much deformation, but the one with the slippage had to deform in order to carry the same load. Both could safely carry the load, but since here they will cooperate they will deform together…

Since a continuous truss will deform only “a little”, the truss with the slippage will never reach the deformation needed for it to carry the load. It may “close” the gaps in the connections (there are far more here than in the first example) but even then continuous trusses will be greatly overloaded. This effect called redistribution of forces can be seen in the drawing below, showing capacity ratios in the model with slippages:

As you can see above the continuous trusses are clearly overloaded (the capacity ratio is twice as high as in the first example). Such redistribution is why slippage is so dangerous. If the connections would be evenly spaced in both directions (not a very practical solution to be honest), then such effect will be smaller. Sure, deformations would be higher, and some additional forces would appear, but the redistribution of forces wouldn’t be as drastic.

## Takeaway notes

Some ideas I have described today, you might want to remember:

• Slippage can appear in all shear screw connections if pre-stressing isn’t used
• Slippage does not depend on connection capacity. It will appear even if capacity of the connection is sufficient (or even far to high!)
• Slippage will always cause additional deformations of the structure
• Slippage may lead to drastic redistribution of forces if some elements deform more than others. This can be fatal to the structure

Thank you for reading! I hope you will find it useful : ) Also I have a surprise for you : ) If you are interested you can subscribe below to get my free FEA essentials course. If you have any questions you can always leave them in the comments!

#### Author:Łukasz Skotny Ph.D.

I have over 10 years of practical FEA experience (I'm running my own Engineering Consultancy), and I've been an academic teacher for a decade. Here, I gladly share my engineering knowledge through courses, and on the blog!

### Join the discussion

Joss - 2021-02-12 09:13:26

Hey Lukas,

Very nice article as usual :)

I am sizing some bolted joints and I am struggling in finding a proper way to solve it.

My joints show always between 0,1 and 0,3mm slippage (FEA with contact enabled), if I follow strictly Eurocode 3 1-8 then the joints fail the requirements. My question is, what is acceptable and is Eurocode taking FEA level of accuracy into account?

Maybe I do not do it properly but I would extract the axial and total shear force from the bolts (beam elements) to check against the requirements. I also check the sliding distance at the contact region and pressure surface distribution and values.

Thank you for your help.

Best regards,

Joss

Łukasz Skotny Ph.D. - 2021-02-12 18:36:36

Hey Joss!

So nice to hear from you!

Well, I think I will disappoint you - EN 1993-1-8 is not suited for FEA calculation :( There are no rules for that in the code - or at least I didn't find any!

Technically you should divide the force in the bolts "by hand" and then use formulas. And slippage in the pre-stressed connections is verified by the "friction capacity" of the joint. There are no limits to how much slippage is "still ok" because the assumption is, that if the capacity of the pre-stressed connection is sufficient... there will be no slippage!

I think that there are no conditions for non-pre-stressed connections in that regard as well.

I think that your approach (taking the forces from FEA and checking the code conditions) isn't a bad one. In fact, I do this myself with complex connections (although often enough I do the "by hand" force division in the simple connections since it is way quicker!). Of course, a lot depends on how you model your FEA stuff, but you seem like a pretty competent guy, so I have no reason to think that you would do something "weird" :)

Well, that's about it - I hope that it will be at least a bit helpful, and do not hesitate to follow up with additional questions if you will have any!

See you around!
Ł

Kenneth Cabacungan - 2019-09-01 10:52:28

I was actually in the middle of a study of a retrofit design of deflected cantilever slabs using steel plates on the top surface connected by anchor bolts. We had a previous design for the retrofit but never had we considered the slippage in the connections. The path of the load transfer seems to be more of a bearing-type in my case. So, I guess even if slippage is not a concern, the pretensioning of the bolts should be concerned.

Nonetheless, this article is a good read for starters when designing shear connections involving steel elements. Thank you for this!

Łukasz Skotny Ph.D. - 2019-09-01 17:23:12

Hey Kenneth!

I'm really glad that you like the article :)
It's amazing how complex engineering is, isn't it?

All the best
Ł

GANESH - 2019-01-13 02:28:56

hello Sir, Recently i am facing bolt slippage issue , where joinery design is bolted through tapping . in this there is no slot in bracket ,hole is there having 2mm diametrical clearance and meeting part is tapping threads. but this assembly is under high vibration .....my question is there any ways to avoid bolt slippage e.g by adding spring or split washer , Noard lock washer or nylon washer etc

Łukasz Skotny Ph.D. - 2019-01-13 19:37:10

Hey!

I'm not sure if I understand everything you wrote correctly. But maybe you can pre-stress bolts? That would sort out slippage completely. Washers won't really help with that, but some types help with nuts being loosened by vibrations (still I would be more happy with the counter-nut). That said this wouldn't really help with slippage - I would go with prestressing.

Hope this helps!
Ł

Ganesh - 2019-01-15 07:13:07

Thank you for the valuable comment.

Łukasz Skotny Ph.D. - 2019-01-15 07:36:18

I'm glad that I could help even if just a little bit :)

All the best
Ł

Peter Placzek - 2016-12-18 22:30:53

Yes, you understand what I mean by interference correctly. Keeping in mind that we are designing to limit state it is totally acceptable for some bolts to be loaded earlier. It does not effect the connection ultimate capacity or SF against failure. What it however means is that for the 1st 2 mm :"travel" you assume 0 load in your model when in reality the loads starts to develop immediately... possibly at flatter rate initially.

Łukasz Skotny Ph.D. - 2016-12-19 08:15:08

Hi Peter,

Thanks for writing back :)

I agree to some extent. Sometimes those gaps will be closed simply by the self-weight, but that doesn't have to be the case. In the 3D model I have shown that wouldn't happen for instance. It is as I wrote in the post: if entire structure can move similarly than deformations will be higher and rest will have smaller impact. However if you have elements that won't deform or deform significantly less (like the continuous trusses in my example) they will keep the other elements "undeformed" (for the connections to close gaps in my model the "noncontinuous" trusses would have to deflect in vertical direction far more that what the continuous trusses allow!). This leads to a situation where when "real" load comes, continuous trusses deflect more, but still not enough for the "noncontinuous" trusses to take any significant part in load transfer.

Have a great day!
Łukasz

Peter Placzek - 2016-12-17 04:51:27

Assuming 2 mm movement is extremely conservative. Multi bolt connection achieves significant interference reducing the actual slippage to a fraction of millimeter. It is OK only as a theoretical exercise.

Łukasz Skotny Ph.D. - 2016-12-17 10:13:53

Hi Peter,

Thank you for the comment :)

I wouldn't say its all that much conservative really. I assume that by interference you mean that some holes would be "less closed" and others will be "more closed" meaning that some screws will start to work sooner than others, and thus reducing slippage? (I'm not sure if I have understood you here)

If that is the case, I think that if only few screws will work (from many), that would reduce the initial slippage, but also would lead to a complete overload of those screws! In reality bolt holes would yield a little, to allow other screws to take part in load transfer.

Perhaps initially with small loads, slippage is reduced due to such mechanism, but under full load slippage will still occur in my opinion.

As a proof I can say that the structure I have investigated had around 20 bolts in a typical shear connection - and still it failed with slippage involvement.

I would love to hear your thought about this, perhaps there is something I'm missing here.

Have a great day
Łukasz

Fatih - 2016-12-14 04:06:05

as long as i know, bolted connections itself are very unforgiving against transverse slippage and related bending... I would never design a bolted connectiin which might slip. shear joints have clearance values of 2-3 mils only (less than 1 mm to allow assembly without hammering). clearance holes on the other side ensure the non slippage by the friction force and enough clamp. to me, if the joint is slipping, it is already failed. but your approach looks to be a good check against ultinate loads which might occur once through the life of the connection. by the way, are you performing a nonlinear analysis? with a nonlinear spring ? I wonder how u dealt with the nonlinearity of the slipping connection.

Łukasz Skotny Ph.D. - 2016-12-14 10:04:28

Hey Fatih,

Thank you for comment!

I don't know about codes in your country, but in Eurocodes (European Union civil engineering codes) you can easily design a shear connection without pre-stressing. I'm not claiming it makes sense, but obviously is allowed :)

Code of course states that you have to take nonlinearities into account but engineers rarely do so... and this is why I have come up with this post idea. Sure there are ways to prevent slippage (mentioned pre-stress for instance), but there are many connections that are not pre-stressed (I really did took part in investigation why a big steel structure failed, and slippage was one of the main reasons - so it is happening).

If you are using means to prevent slippage that it is awesome - I hope that this post will convince people to do so... or at least take slippage into account in design.

All the examples in this post are made with 2mm slippage - this is a value for a normal 20mm diameter screws (holes would be 22mm each) - assuming that one hole "moves left" 1mm and the second one "moves right" 1mm you get total of 2mm slippage. As you can see even in seemingly small displacements this effect may be really big.

I have used nonlinear analysis. As I shown in the post I have used a nonlinear chart of displacement - force in selected nodes on the direction of a normal force. It basically made the node move 2mm without "doing anything", and then started carrying loads normally. Convergence takes a while, but it works as can be seen on screens from results :) Someday I will make an online course on nonlinear static design... it will take time however :)

Hope that helped - if you have any questions feel free to ask!
Cheers
Łukasz

peter panozzo - 2016-12-13 22:01:32

I note that slotted holes side by side are a NO NO , First why would you have slotted holes without pretension ? Second you can have only one side of the connection slotted , the other plate will have a normal diameter hole , this would be in compliance with AS4100 .

When applying pretension the surfaces in contact would need to be prepared for a friction grip connection.

Also what is generally missed is that a plate washer would need to cover the whole slotted hole otherwise you will not be able to apply the pre-tension load on the bolt.

Łukasz Skotny Ph.D. - 2016-12-14 10:09:53

Hey Peter!

Thank you for the comment!

Sure the "double-slotted" holes like that are a bad idea - I just wanted to have something where you can easily see that both plates are moving (one to the left and other to the right) even if you are looking at a small picture on your smartphone. This is why I used such example - in normal design I would never used it... perhaps I should add a short description in the text about this fact.

Also as I mentioned in the other comment all the examples in this post are for slippage in normal holes (not the long ones) - obviously long holes are made to allow slippage - that is beside the point. Seems I have chosen the first example to show slippage poorly... it is a bit confusing I admit...

I agree with all your comments about pre-tensioned connections - it was not the topic of this post, but the remarks you make are all valid.

Thank you for writing, I hope that reply have cleared things out. If you have any more questions I will do my best to help out!

Cheers
Łukasz