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# Bolt load capacity after tightening15

## Bolt load capacity after tightening

(OP)
Hi all,

I hope its not a stupid question, or if it is then maybe someone can point towards that "simple and obvious" answer that I'm failing to see here! Here goes:

I haven't got much experience with bolted joints, so far simple guidelines such as VDI2230 have helped me out just fine.

However, now I was trying to use VDI2230 for determining the tightening torques for a bolted flange and came across something that I fail to make sense of.

I'll give you a simplified description. It's a pipe with a flange, and an end cap bolted onto it to seal it off. Lets say it has 4 bolts that are evenly spread along the diameter, or 90degrees apart from each other. The holes in the flanges are not threaded, just bolts through and and nuts on the other side.

I'll use the VDI2230 method for calculating these bolts, following the procedure I found in a Würth publication.

Based on the diameter of the pipe and maximum working pressure I have determined that the maximum force on the cap will be 9.2 kN, that makes 2.3 kN per each of the 4 bolts. Therefore the axial operating force Fa = 2.3 kN.

As I have no shear forces to consider, the assembly preload force Fm = Fa = 2.3 kN. This will be my starting point.

Let's say I want to use grade 8.8 bolts. Looking at the VDI2230 table, the next closest load there is 2.5 kN -> size M4 is specified for 8.8 bolts.
Add one step for static concentric load -> 4.0 kN -> M5
Add one step for tightening with a torque wrench -> 6.3 kN -> M6

So the bolts that I need are grade 8.8 size M6.

I will estimate the coefficient of friction to be 0.11. The next closest step in the guidelines I have is 0.10, so lets got with that.

Based on all this, VDI2230 advises me that the tightening torque would be Ma = 9.0 Nm, which would create a 10.4 kN preload force in the bolt. It is said to utilize 90% of the screws yield strength.

Based on my calculation, the breaking load of a M6 8.8 coarse thread bolt at yield strength (640 MPa) is 11.29 kN.
10.4 / 11.29 = 92%, so that's just about right.

But... the assembly is not pressurized when I'm tightening those bolts. By just tightening them, I've already used up 92% of the bolts' reserve, not much left for when I will actually pressurize it.

If i will now calculate how much pressure this assembly can take after tightening the bolts, then I can only use the reserve left in the bolts (8 percent to yield strength) as in my calculation? That's not much...

Or lets give you another really simple example just to illustrate the point I'm trying to make here:
Lets say you have an M6 eye bolt, you insert it through a hole in a rigid steel plate in the ceiling, and screw a nut on the other side. If the nut is not tightened, then you can hang 11.29 kN load on your eye bolt before it breaks, but after you've tightened the nut according to VDI2230, you can only hang 11.29 kN x 8% = 0.9 kN off it before it snaps!.

I'm kinda confused here. What am I missing? All the example calculations I have seen for pressurized flanges, lids, end caps on pressure vessels etc just use the full capacity of the bolts in their strength calculations. But how can I do that if I've already used up 9/10 of it???

Could I tighten the nuts to a lesser torque than specified? But wouldn't the flange then leak, and would the bolts rattle loose / become undone too easily?

Thanks for any feedback (or for proving me stupid, it that happens to be the case :)

J.

### RE: Bolt load capacity after tightening

3
Hi Nordic8

I think I see where you are confused, I think you are assuming that all the load when your vessel is pressurised is carried by the bolts and that is not correct.
When you tighten the end cap on the vessel you tension the bolts but at the same time, the end flange compresses slightly against the end of the vessel, now when you pressurise the vessel the load is actually shared by both the bolts and the mating flange, the flanges are trying to release the compressive stress they are under which in order to do so must absorb some of the load and the remainder of the load is shared be the bolts. See this link https://www.boltscience.com/pages/basics2.htm
I should of also said that the majority of the external load on a bolted joint is carried by the clamped members due to the fact that clamped members are usually much stiffer than the bolts.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

You need to calculate bolt stress considering both preload and working load.

Now the yielding factor of safety is S_p/sigma_b, S_p is bolt proof stress.

### RE: Bolt load capacity after tightening

#### Quote (desertfox)

I think you are assuming that all the load when your vessel is pressurised is carried by the bolts and that is not correct.
I am going to have to disagree with this statement. The load is most definitely carried by the bolts, there is no other load path. However Preload of a bolt is an internal force and the application of an external force is not additive to that internal force.

The confusion lies in not considering the change in the internal forces of the joint. When you torque the bolts, you develop a tension, or preload, in the bolt by clamping the flanges together. This clamping force results in the flange and end cap pushing on each other with a force that is equal and opposite and is in direct relation to the tension in the bolt. So, your entire joint is in equilibrium but there are all sorts of internal stresses. Now, you apply pressure to the end cap, this results in the compression force between the flange end endcap decreasing by the same amount that your external pressure applies a force. See the picture below to see what I mean:

### RE: Bolt load capacity after tightening

dauwerds

The bolts do not see all the external load that is not incorrect, the external load is shared between the clamped parts and the bolts and that’s what I have explained. If the bolt sees all the load the joint will be on the verge of separation.

#### Quote (dauwards)

Now, you apply pressure to the end cap, this results in the compression force between the flange end endcap decreasing by the same amount that your external pressure applies a force.

the above statement by you is actually incorrect because the bolt stretches to accommodate a slight increase in tension as the compressive stresses are relieved between the clamped end cap and vessel, what you are implying the bolt sees no additional load due to the external force and that is incorect. its also a contradiction because you state the bolts see all the load.

#### Quote (dauwards)

The load is most definitely carried by the bolts, there is no other load path

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

#### Quote (desertfox)

If the bolt sees all the load the joint will be on the verge of separation.
That depends on how large the external load is. If it is less than the preload than there is still a clamping force (equal to the initial clamping force minus the external load). If the external load is equal to the preload, the clamping force is zero (i.e. on the verge of separation). If the external force is greater than the preload, then yes, the joint will absolutely separate.

Draw a free body diagram of the joint and show me how there is any situation where the bolts are not resisting the full pressure.

### RE: Bolt load capacity after tightening

you guys realise you're both saying the same thing ?

when the joint is clamped together the external load is shared between the joint faces (compression) and the bolt
when the joint is gapped, all the eternal load is reacted by the bolt.

### RE: Bolt load capacity after tightening

Hi rb1957

Well clearly dauwerda doesn't see it like that but now his post is misleading because in one post he is saying the bolts take all the load but in his text as quoted by dauwerda he states the whole external load is taken by the end cap and vessel releasing some compressive stress.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

No rb1957, we are not saying the same thing. In fact, your first statement, "when the joint is clamped together the external load is shared between the joint faces (compression) and the bolt" is also incorrect.

The external load applied on the cap is only ever resisted by the bolt tension, there is no sharing this tension with the joint faces.
You could say that the tension in the bolt is resisted by both the external force and the clamping force. That is, as the external force is increased, the clamping force decreases so that the tension in the bolt remains constant.

### RE: Bolt load capacity after tightening

We are clearly having some disconnect here.

#### Quote (desertfox)

Well clearly dauwerda doesn't see it like that but now his post is misleading because in one post he is saying the bolts take all the load but in his text as quoted by dauwerda he states the whole external load is taken by the end cap
I am not trying to be misleading. The pressure is applied to the end cap. The reason the end cap doesn't blow away is that the bolts resist that force. The bolts transfer the full force of the external pressure that is applied to the endcap. This is true whether they are preloaded or not.

Again, I believe this is a very misleading statement:

#### Quote (desertfox)

I think you are assuming that all the load when your vessel is pressurised is carried by the bolts and that is not correct.
I interpret that as somehow meaning there is some other mechanism in place (other than the bolts) that resists the load applied to the end cap. All of the load is absolutely carried by the bolts.

The confusion the OP had was that he/she was trying to add the tension force due to the pressure to the preload tension of the bolt. This is not the correct approach. Rather than being additive, The tension in the bolt remains the same, as the external load increases the clamping force between the parts decrease. The external force applied on the end cap is still however, only resisted by the bolts.

### RE: Bolt load capacity after tightening

"You could say that the tension in the bolt is resisted by both the external force and the clamping force. That is, as the external force is increased, the clamping force decreases so that the tension in the bolt remains constant." ... that is exactly, exactly, what I am saying ... "the external load is shared between the joint faces (compression) and the bolt" Possibly my "(compression)" is clouding the statement ... external tension load will increase the bolt tension and reduce the joint compression; until the joint compression is zero (the joint is gapped) and all the external load is in the bolt.

### RE: Bolt load capacity after tightening

I think that we need to think about the problem conceptually. This is not simple static determinacy problem but a statically indeterminate problem where the displacement compatibility(flange faces move together as long as joint is tight) to be ensured.
Now we take initial position of flange faces as 0 after applying preload. Now due to external load a increase of length delta takes place in bolt. This is also the increase in thickness of flanges considered together(reduction in strain).

From the above it is apparent that external load P is shared between bolts and flanges.

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

### RE: Bolt load capacity after tightening

I'm off to the pub ...

### RE: Bolt load capacity after tightening

#### Quote (rb1957)

that is exactly, exactly, what I am saying
It's not though.

#### Quote (rb1957)

"the external load is shared between the joint faces (compression) and the bolt"

We all agree that the external load is the pressure that is on the end cap, correct?

The compression on the joint faces is due to an internal load (bolt pretension), it is not due to an external load (pressure in vessel).
Stating that the load is shared between the joint faces and the bolt is very misleading. The joint faces are not resisting the external load. The joint faces are resisting the internal load that is caused by the clamping force due to bolt pretension. As an external load is applied to the endcap, it is only resisted by the bolts (no sharing). However, as stated before, this results in the internal clamping force (caused by the bolts) to decrease.

#### Quote (rb1957)

external tension load will increase the bolt tension and reduce the joint compression;
No. The external tension load (again, this is the pressure on the end cap) will reduce the joint compression and the bolt tension will remain the same.

#### Quote (rb1957)

until the joint compression is zero (the joint is gapped) and all the external load is in the bolt.
Yes. Except that all of the external load was always in the bolt. The change is that there is no longer any load in the bolt due to the resistance of the clamped parts.

### RE: Bolt load capacity after tightening

My absolute agreement with you rb1957

I stated this in my first post but it seems to have been ignored by dauwerda

#### Quote (desertfox)

now when you pressurise the vessel the load is actually shared by both the bolts and the mating flange,

My reference to all the load being carried by the bolts was that the external load on the vessel due to the internal pressure plus the bolt preload was the total load in the bolt and that is not correct but I believe thats what the OP thinks.
example two plates 10mm thick clamped together with an M16 bolt and a bolt preload of 40KN which is then subject to a external load of 30KN what is the total tension in the bolt dauwerda?

No dauwerda the bolt tension won't remain the same.

#### Quote (dauwerda)

The external tension load (again, this is the pressure on the end cap) will reduce the joint compression and the bolt tension will remain the same.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

#### Quote (desertfox)

example two plates 10mm thick clamped together with an M16 bolt and a bolt preload of 40KN which is then subject to a external load of 30KN what is the total tension in the bolt dauwerda?
The tension in the bolt is 40kN
You start with a tension in the bolt that is 40kN, this is resisted by the compression between the two faces of the joint, also equal to 40kN.
You apply an external load of 30kN. The bolt still has a tension force of 40kN, however to maintain equilibrium, this means the compression force between the faces of the plates is now only 10kN.

#### Quote (desertfox)

No dauwerda the bolt tension won't remain the same.
Unless you disagree with my answer above, yes it does remain the same.

Please go back and look at the initial picture that I posted (actually, I'll repost it). For the OP's example the red spring is the bolt, the yellow box holding the spring scale is the flange and the block that is in inserted would be the endcap. The external load applied to the hook would be the pressure applied to the endcap.

As can be seen in that image, the external force is only resisted by the bolt tension. The the block or endcap does not magically stick to the flange without the bolt (this is what load sharing would imply). The clamping force is a function of both the bolt preload and the external load. i.e. the clamping force changes when the external load changes, but this does not mean that the flange faces "share" the external load with the bolt.

### RE: Bolt load capacity after tightening

#### Quote (goutam_freelance)

In which country pubs are open? Curious...

I could be wrong, but I believe rb1957 was referring to this forum, https://www.eng-tips.com/threadminder.cfm?pid=1088

### RE: Bolt load capacity after tightening

yes dauwerda I disagree I will post shortly

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

nope ... I meant the literal pubs, rather than the unsatisfying virtual pubs

### RE: Bolt load capacity after tightening

#### Quote (rb1957)

nope ... I meant the literal pubs, rather than the unsatisfying virtual pubs
Well color me jealous, please enjoy a drink for me.

### RE: Bolt load capacity after tightening

Here you go the bolt tension increases slightly with the external load applied it doesn’t stay constant as quoted by dauwerda

Quote (desertfox)
No dauwerda the bolt tension won't remain the same.

#### Quote (dauwerda)

Unless you disagree with my answer above, yes it does remain the same.

quote from one of the site links below:-

The preload elongates the bolt and compresses the clamped parts. When a tensile load is applied to the joint, some portion of the applied load acts to relieve the compression in the clamped parts and the other portion further elongates the bolt. The portion of the applied load that is carried by the bolt is dependent on the relative stiffness of the bolt and the clamped parts. This relative stiffness is known as the joint constant, C:

The following is a representative diagram of bolt load as a function of the applied joint load:

These are the links I used for the calculations:-
https://mechanicalc.com/reference/bolted-joint-ana...

https://prod-ng.sandia.gov/techlib-noauth/access-c...

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

This bolt joint diagram may also help.

Ted

### RE: Bolt load capacity after tightening

I think the doubt still remains and also there is demand for free body diagram.

So here are a few FBDs with different scenarios.

2. With internal load assuming all internal load is taken by bolt (hypothetical)

So the flange load remains same as for only preload case. But this is impossible as bolt has extended due to extra load and there will be flange gap if the flange does not expand.
3. With load sharing between bolt and flange

So the distribution of internal load is nicely defined.
Sorry for long post !

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

### RE: Bolt load capacity after tightening

To summarize for the benefit of the OP and I take it now we are all in agreement that the external load applied to the joint is shared between the clamped flanges and the bolt as shown by several posts above.

Both the statments below are incorrect

#### Quote (duwerda)

That is, as the external force is increased, the clamping force decreases so that the tension in the bolt remains constant.

#### Quote (dauwerda)

The load is most definitely carried by the bolts, there is no other load path

Take the first quote, if the clamping force decreases and the flanges start to return to there unstressed condition, then the tension in the bolts cannot remain constant because equilibrium will not be maintained, the bolts have to stretch to allow the flange to expand.

in the second statement it says the load is carried by the bolts which appears to conflict with the first statement which states the bolt tension remains constant.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

(OP)
Thanks for the great response everyone!

Yeah, I can clearly see where my original logical error was. The theory of how it actually works (which is really clearly explained in the link in desertfox’s original response) does seem counterintuitive at first glance but makes perfect sense when I think about.

Preload basically determines how much capacity for an external load there is in a joint before a gap bevelops between joined parts (shortly after which the bolt fails – given that it’s tightened properly and preload value is close to proof load value of the bolt, or 90% of the yield stress)
.
Basically it’s like a credit card – the preload is the credit limit and you can have your card charged for any amount of dollars, as long as that amount is less than the credit limit. Your remaining account balance will be the remaining clamp load.

In a real-life case you would need to consider joint stiffness. Looking at the calculation desertfox did:

Joint constant C = 0.2566

So, when applying 30kN external load to the bolt, the portion of that load that goes into relieving clamp load / pretension will be (1 – 0.2566) * 30kN = 22.302kN

Therefore the remaining clamp load will be 40 – 22.302 = 17.698kN

The remaining part of the external load is 0.2566 * 30kN = 7.698kN, that will go into increasing the tension in the bolt. As a result, the tension in the bolt will be (as desertfox already showed) T = 47.698 kN.

Now, lets assume that the bolt was tightened to approx 90% of the bolt’s yield load. The bolt would then reach it’s yield point at 40kN / 90% = 44.444kN. It means that with 30kN external load applied, this particular bolt would snap as 47.698 > 44.444

Yes, I know that 90% is not a precise figure and in reality there is a lot of variation. But for the sake of argument, lets say that its precise. In that case, the external load capacity of that joint would be (40kN – 44.444kN) / 0.2566 = 17.319kN

When the external load P = 17.319kN, the tension in the bolt T = 44.444kN

So the safe amount external load value (P = 17.319kN) is still far less than pretension. It’s only 43.3% of pretension.

What are the real-life solutions for improving that figure? Using a bit less pretension? Or perhaps spring washers?

Enjoy the pub guys, I’m stuck self isolating for another four days!

### RE: Bolt load capacity after tightening

Hi Nordic8

You’re welcome.

I will look further into your post in a little while, I’m just doing something at present👍

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

You need to design the bolt properly. Fi is not an arbitrarily high value. It has been provided as a protection against joint separation and hence leakage. Refer excerpts from Shigley.

You need to define a reasonable Po and n_o and calculate Fi accordingly.

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

### RE: Bolt load capacity after tightening

I think dauwerda and desertfox are talking the same issue with two different premises, both are true then. While dauwerda considers no-slip condition after locking the preload (plate is very stiff that deflection is negligible), desertfox considers slip will occur due to the difference in flexibility of the bolt and the plate. The bolt internal stress varies as well as the clamping stress, both are reduced after an external load applied to the pre-tensioned bolt. I will try to draw a sketch to demonstrate my thought and come back later.

However, I think the OP made a mistake in saying,

#### Quote:

The remaining part of the external load is 0.2566 * 30kN = 7.698kN, that will go into increasing the tension in the bolt. As a result, the tension in the bolt will be (as desertfox already showed) T = 47.698 kN.
IMO, the tension in the bolt shall be 40-7.698=32.302 kN - the external load reduces the bolt pre-tension, not increase.

### RE: Bolt load capacity after tightening

Ok, now I understand one disconnect. I was assuming the stiffness of the flanges was much greater than that of the bolt as alluded to in the second example in the OP. If that is true the increase in the tension of the bolt is negligible (which your equations show). That was never what I was taking issue with however, I'm taking issue with the idea that the bolts aren't transferring the full load of the external load. They are. As Nordic8 summarized nicely, the reason you don't see the tension in the bolt increase equal to the applied load is because as it does increase (at a rate depending on relative stiffness between bolt and flanges), the clamping force decreases. That is, tension in the bolt that had previously been caused by clamping is now being caused by the external load.

I stand by this statement,
Quote (dauwerda)
"The load is most definitely carried by the bolts, there is no other load path."
And everything that has been shown above only reinforces it.

### RE: Bolt load capacity after tightening

you are entitled to your opinion and we can leave it at that however you took issue with the fact that I and several others stated that the external load was shared between the bolt and flange faces and not just the statement in your last post regarding the bolts load path. See all quotes below.

#### Quote (9/01/21 dauwerda)

If that is true the increase in the tension of the bolt is negligible (which your equations show). That was never what I was taking issue with however, I'm taking issue with the idea that the bolts aren't transferring the full load of the external load

[/quote]8/01/21 dauwerda]No rb1957, we are not saying the same thing. In fact, your first statement, "when the joint is clamped together the external load is shared between the joint faces (compression) and the bolt" is also incorrect.[/quote]

#### Quote (8/01/21 dauwerda)

The external load applied on the cap is only ever resisted by the bolt tension, there is no sharing this tension with the joint faces.

My issue was you stated the bolt tension remained constant but then stated the bolt took all the load which it clearly doesn't. In fact even your diagram is incorrect because the spring representing the bolt doesn't move until the external force exceeds the preload, the calculation example and the bolt diagram also show that also to be incorrect.
The increased tension in the bolt in the example I posted is almost 20% of the external load I wouldn't call that marginal.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

Hi Nordic8

Below is an extract from one of the links in my post with the calculations, it shows joint seperation to be a criteria for bolted joint failure and gives a formula for working out the seperation force:-

Joint Separation
The knee in the curve in the bolt load diagram above shows the point where the joint separates. At this point, the applied load is sufficient to separate the parts in the joint (all of the compression in the clamped parts has been relieved), and after this point any load applied to the joint is taken entirely by the bolt. The force that will result in separation of the joint is found by:

Fsep = Fpl/(1-C)

where Fsep = seperation force
Fpl = 90% proof load of fastener

Note that the separation force will always be somewhat higher than the preload force.

Separation of the joint is a failure criteria, and a joint should be designed such that it will not separate during service. The factor of safety on separation is found by:-

FSsep = Fsep/Ftapp where Ftapp is the external force applied to the joint.

The only way to increase joint strength is add more bolts or use bigger bolts either way you have to calculate them.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

#### Quote (desertfox)

Note that the separation force will always be somewhat higher than the preload force.

Exact. Before the applied load exceeds the preload, the joint will not move, but the stress on bolt and fittings (plate and nut) is reduced.

In further review, I think it is really depends the manner how the external load is applied. If it is applied directly to the bolt, the bolt will feel 100% of the applied load; if the load is applied through the plate, then the plate will take the force proportional to the relative stiffness of the bolt and the plate. The reason for my conclusion is the fact that the plate is loosely placed over the bolt, the tightening/clamping is done by the nut pushing the plate. After locking, the nut and the plate receive passive force passed by the bolt, which is in an effort to return to the original state, but can't because of the presence of nut and plate. At this stage, the force in the embedded bolt is reversed from tension to compression (tension on the portion inside the nut), which is the so called "preload", or "pre-tension".

### RE: Bolt load capacity after tightening

Hi Nordic8

I found this website which might interest you

https://www.instarengineering.com/pdf/Instar_DABJ_...

Also I took a snap shot of the last two pages shown below;- it clearly states that once a bolt is preloaded that it is no longer the main load path on the first page and on the second page shows how the major part of the load is transferred through the clamped components, just to clear any further confusion from dauwerda’s incorrect statements.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

Please note the words "under tensile loading"...and note the load path (thru tension wall) in the sketch. That's exactly I've pointed out - the tension load is applied to parts connected to the clamping plate, not the bolt.

### RE: Bolt load capacity after tightening

I can think of these two cases below can cause the applied load get directly to the bolt(s). The fittings do not involve in these applications.

### RE: Bolt load capacity after tightening

(OP)

#### Quote (r13)

IMO, the tension in the bolt shall be 40-7.698=32.302 kN - the external load reduces the bolt pre-tension, not increase.

No, I think I got that right. It seems that when external load P is applied, part of it (C * P) goes into relieving clamp force and the rest ((1 - C) * P) will go into increasing the tension in the bolt. This slide from desertfox's link seems to illustrate is as well:

See how the bolt tensile load keeps creeping up as applied tensile load increases - right up to separation point (or if the bolt reaches the yield point - whichever happens first).

### RE: Bolt load capacity after tightening

It is very interesting, but contrary to my training. I'll keep to investigate, at the meantime, I can give you an example to think about.

Let's compress a spring inside a tube, with force P that cause x amount of shortening, then plug the tube and remove the load, at this stage, what is the force in the spring - compression, or tension? Next, we move the plug back to half of the displacement distance x, what is the force required to move the plug in terms of P, and what is the force in the spring? Note that the case of pretension is just the reverse of this exercise. I could be wrong though.

### RE: Bolt load capacity after tightening

(OP)
Thanks goutam_freelance and desertfox for those formulas for calculating FOS against joint separation. You've both described the same thing and both of those methods will give the same results.

So, in the example of that bolt with 40 kN pretension and 30 kN external load applied to it:

Separation force (Po, or Fsep) would be Po = Fi / (1 - C) = 40 / (1 - 0.2566) = 53.807 kN
FOS against separation would then be n_o = 53.087 / 30 = 1.794

But how about the capacity of the bolt against yield?

As I calculated earlier, if the bolt is tightened to 90% of it's yield load (as VDI2230 suggests) then the yield point would be reached when external load is 40kN / 90% = 44.444kN

I decided to check how that Applied Load vs Bolt Load graph would look like in this case.

The tension in the bolt equals external load times joint constant: T = P * C. Thats one of the sloped lines on the graph.
The other line is Slope = 1.
The separation point is where those lines cross. The graph seems to confirm my calculations, its somewhere around 53.8 kN
However, the bolt's yield limit is at 44.4 kN... so there's an issue here!

After the external load has exceeded 44.4 kN, the tension inside the bolt will not grow along that straight line anymore, but instead it will go ductile and would probably be more like the curve that I added to the sketch. There would actually be less than 53.8 kN external load required now to separate the joint.

And my drawing also confirms another one of my earlier calculations - the external load that the bolt can take before hitting the yield point is about P_yield = 17.3 kN.

I'm guessing that the situation on those sample graphs that I posted before is more desireable that the situation that I drew up. You don't want the bolts to reach yield point BEFORE separation point, right?

Or actually - does it really matter? It should be alright as far the external force that the joint has been designed to is less than the for that will get it past the yield point: P_design < P_yield

### RE: Bolt load capacity after tightening

Hello
The question of Bolt load capacity after tightening is not simple and it is really helpful. Thanks to this topic, I have learned a lot more useful information

### RE: Bolt load capacity after tightening

The yield factor of safety is given by

As can be seen n_o reduced with increasing P.
So you need to know your P and design bolt such that n_o is never less than 1.
So there is no alternative for a proper design.
By the way if your load is variable or alternating you need to consider fatigue criteria instead of yield criteria.

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

### RE: Bolt load capacity after tightening

Confirmed what I thought I knew, and added a little frosting on top... thanks gentlement/ladies (I never know which).

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

### RE: Bolt load capacity after tightening

fox... the article by Instar on the 'design and analysis of bolted joints' is great. Thanks for the info.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

### RE: Bolt load capacity after tightening

Hi r13

If you look at my example calculation,I have assumed the load is applied to the clamped plates which is actually a similar scenario which occurs with the pressure vessel, that Nordic8 is referring to.
The vessel is pressured after the bolts have been preloaded so this force is directed onto the end cap; provided the bolt preload is sufficient to prevent separation occurring, the following sequence takes place:- the compressive stress between the clamped flange faces is relieved as the faces now try to expand to their unloaded state under the action of the external force, the bolt also has to extend by the same amount to accommodate this expansion and maintain equilibrium. The forces both in the flange faces and the bolt which are generated by the external force are proportional to their relative stiffness. Referring to my example calculation you can see the stiffness for both the bolt and the clamped plates have been estimated but it is clear that the clamped plates have a much higher stiffness when compared to the bolt by almost a factor of 3. The clamped faces being much stiffer than the bolt and the main load path carries a bigger proportion of the external load when compared to the bolt and is the main load path, so the force in the clamped plates is 22.3KN and that in the bolt is 7.698KN

Deflection of the joint
Under external force = force in joint/ stiffness of joint = 22.3*10^3/ 4.696*10^6

= 4.748*10^-3 mm

Deflection of bolt. = force in bolt/ stiffness of bolt = 7.698*10^3/ 1.6214*10^-6

= 4.748*10^-3 mm

Equilibrium is maintained because the expansion of the joint equals the expansion of the bolt.

Now Nordic8 is correct because the bolt has to stretch to accommodate the expansion of the clamped flanges and therefore this results in additional bolt tension of 7.698KN adding to the preload of 40KN making the bolt tension 47.698KN.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

Hi dik,

You’re welcome

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

Hi Nordic8

The calculation is only for a single bolt imagine if you put four bolts in the joint and tightened each one to 90% yield and then apply the 30KN external load, the external load now would be spread over four bolts. So to find the proportion of the external load in the bolt you would divide the external load by four and then repeat the calculation like my example. At the end of the day yes you would want the bolts to stay below yield although there is a school of thought that says tightening bolts into yield isn’t an issue but I would increase the number of bolts or size and run the calculation till the bolts were below yield.
https://www.boltscience.com/pages/glorimermorethou...

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

3
Mechanical engineers talking about bolted connections is nearly always a mess (I think it's because of Shigley's).

If doing a pressure retaining bolted joint you need to follow a pressure vessel/ piping code.

If doing a structural connection, refer to a structural code.

For structural connections the preload is not additive; as in preload does not effect the strength of the bolted joint. This is stated in the Research Council on Structural Connections' Specification for Structural Joints Using High-Strength Bolts. They provide an explanation with references. https://boltcouncil.org/files/2014RCSCSpecificatio...

A pressure retaining connection is more complicated, with a gasket, a leak criteria and the potential for a temperature gradient. The best approach is of course to use a standard flange. If you must use a custom flange then you need to do calculations in accordance with a code such as EN 1591-1.

Any calculations which do not follow a recognised code should be ignored.

### RE: Bolt load capacity after tightening

Hi SScon

I agree with you about following the appropriate code but as you can see from the posts the OP was confusing preload and external load, so the thread went general specifically looking at bolted joints, preload, joint stiffness etc whilst we got the concept across. I assume that Nordic8 would be following some pressure vessel code for the project he was discussing.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

#### Quote (If doing a pressure retaining bolted joint you need to follow a pressure vessel/ piping code. If doing a structural connection, refer to a structural code.)

I've occasionally done reports for court where you reference code related issues as well as 'the real' issue.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

### RE: Bolt load capacity after tightening

SSCon has cleared my confusion. Thanks.

### RE: Bolt load capacity after tightening

#### Quote (SSCon)

A pressure retaining connection is more complicated, with a gasket, a leak criteria and the potential for a temperature gradient. The best approach is of course to use a standard flange. If you must use a custom flange then you need to do calculations in accordance with a code such as EN 1591-1.
A structural joint is no less complicated as the emphasis is on shear failure.

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

### RE: Bolt load capacity after tightening

Mechanical engineers talking about bolted connections is nearly always a mess (I think it's because of Shigley's).

If doing a pressure retaining bolted joint you need to follow a pressure vessel/ piping code.

If doing a structural connection, refer to a structural code.

For structural connections the preload is not additive; as in preload does not effect the strength of the bolted joint. This is stated in the Research Council on Structural Connections' Specification for Structural Joints Using High-Strength Bolts. They provide an explanation with references. https://boltcouncil.org/files/2014RCSCSpecificatio...

A pressure retaining connection is more complicated, with a gasket, a leak criteria and the potential for a temperature gradient. The best approach is of course to use a standard flange. If you must use a custom flange then you need to do calculations in accordance with a code such as EN 1591-1.

Any calculations which do not follow a recognised code should be ignored.

amen brother, but it's important to understand the concept more than the calculation, then the calc's. . but yes the specification or code unless it does not cover it.
code is written by humans. god bless

### RE: Bolt load capacity after tightening

(OP)
Yeah, I know the load will get spread between a number of bolts. Just focusing on one bolt now to understand the theory.

I did a few calculations and actually in my case the "plate" is really thick and bolts are skinny, so the joint constant is only C = 0.07 (I found this online tool for quick calculation: https://www.tribology-abc.com/calculators/e3_6h.ht...)

Which means that when I tighten the bolts to the values given in VDI2230 tables, I wont be reaching the yield point.
But yes, otherwise I would have needed to specify a lower tightening torque or change the number and size of bolts. As it appears, you can play around with the joint constant - you'll get it to go down by using skinnier bolts (just need increase the number of the bolts - if that's possible in a given situation, of course).

And some other interesting info...
I also found this thread that dates exactly 20 years back:

(The thread ID is 1002, whereas this thread is 477945... so it means the forum must have been only about a thousand threads old that time :D )

Anyway, I found this quote in that thread:

#### Quote (Anthonyr)

And here's a tightening torque calculator that I found (I think I found that link in this forum, somewhere...):
http://www.online-iso-calculator.com/online-bolt-t...

### RE: Bolt load capacity after tightening

(OP)
The info in this thread is great!
I have a collection of resources now, I've saved some links from here and I'll bookmark this thread as well.

I've also set up a simple Excel file for myself which allows me to enter the bolt properties, suggested tightening torque values (VDI2230), joint constant and external loads and it will calculate the FOS against separation and FOS against yield. I reckon it'll come handy in the future!

### RE: Bolt load capacity after tightening

Hi Nordic8

You found some interesting stuff there👍. I agree with the quote you posted by Anthony in regard to the preload being 150 to 200% of the external load however the cycling stress bit is not quite in line with the calculation I provided. Consider my calculation with the 30KN external load we calculated that the bolt sees an increase of 7.69KN so if you divide that by the bolt area that’s gives you the increased stress, so an M16 has a stress area of about 156mm^2, therefore giving a stress increase in the bolt of 49N/mm^2 which in the greater scheme of things is about 19% of the stress due to preload however it is not zero as per the quote by Anthony.
I have archived the thread too, there is some good stuff here.👍

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

#### Quote (desertfox)

You found some interesting stuff there👍. I agree with the quote you posted by Anthony in regard to the preload being 150 to 200% of the external load however the cycling stress bit is not quite in line with the calculation I provided. Consider my calculation with the 30KN external load we calculated that the bolt sees an increase of 7.69KN so if you divide that by the bolt area that’s gives you the increased stress, so an M16 has a stress area of about 156mm^2, therefore giving a stress increase in the bolt of 49N/mm^2 which in the greater scheme of things is about 19% of the stress due to preload however it is not zero as per the quote by Anthony.

### RE: Bolt load capacity after tightening

Hi r13

I went through the thread and all the posters seemed to agree that after the joint was preloaded any external force was shared between the bolt and clamped parts, it was only in this thread that dauwerda believed there was no load sharing and that the bolt was the main load path.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

I think there is a confusion between mechanical and structural joints.
1.Bolts in mechanical joints take primarily tension load and used for leak tight joints which we are discussing here. Here both bolt and member share the load.
2. Structural joints primarily take shear loads where the bolt(and the member too) has to take the full external load while experiencing the preload.

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

### RE: Bolt load capacity after tightening

desertfox,

I don't mean the load sharing, I was pointing to the effect of tension applied after the bolt was tightened. See requote below.

#### Quote (Anthonyr)

If the initial bolt pre-load is higher than the external load, then the bolt should not see any alternating stress when the external load is applied.

Actually I don't fully agree with Anthonr on the text in bold, IMO, the bolt preload is negate/changed by the external load, but you and OP seem do not agree either. So, for now, I think the different application and focus point between disciplines is the divider between us.

### RE: Bolt load capacity after tightening

Hi r13

Yes there is some alternating stress post pre-load of bolt as we have calculated above, it certainly isn't zero, however the higher the pre-load the less the range of cyclic stress but if the pre-loads too high then the bolts can fail as the additional stress can take it above yield.
I see what you are saying though

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

desertfox,

The quote below indicates your correctness in describing this matter for mechanical fastening practices. What Dauwerda and I have described are civil engineering practices, that concerning pretension a bolt embedded in a solid medium, such as concrete, or rocks. As you can see these are two set of completely different applications that do not relate to each other, but the similarity in preload the bolt. The similarity ends there, as after the pretension, the manner of load distribution is, again, different. Sorry for my poor writing, hope you understand.

"When a load (weight) is placed on a bolt, it is limited to the amount of load the bolt can handle before failing. However, when a bolt is tightened against a material, it allows the bolt to distribute the force through the material, so the bolt itself only holds a portion of the load. This means that a bolt can hold a significantly higher load when the correct amount of tension is applied. That tension is known as preload.

Load – The amount of force acting on a fastener assembly

Preload – The amount of tension (compression) needed to distribute a load’s force throughout a fastener assembly

Bolt Preload – The tension created when the nut is screwed onto a bolt to hold two materials together. When the tension reaches the optimal preload, the working load (load added after creating the assembly) placed on a bolt will be distributed into the installation materials, so the bolt does not take the entire load."

### RE: Bolt load capacity after tightening

Hi r13

I am sorry I cannot understand your last post.
However the original question by Nordic3 was purely mechanical and nothing to do with civil engineering practice, so if civil engineering practice was being discussed then it had no place here, giving information that doesn’t relate to the question serves no purpose.😀

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

"This means that a bolt can hold a significantly higher load when the correct amount of tension is applied."

well, I disagree with that statement. Preload does not increase the failure load of the bolt, since most joints will gap before failure.
I guess you could have a very very high preload with a very very flexible bolt and then possibly maybe the external load could exceed the bolt allowable, but this would be a very tricky joint to design and would need very tight control on the preload (not the typical +-1/3 with a torque wrench).

I concur.

### RE: Bolt load capacity after tightening

rb,

IMO, that author was indicating the bolt only share a portion of the external load applied after pretension, thus the load can go much higher, if the preload is at the optimum level.

### RE: Bolt load capacity after tightening

yeah, but that's not what (IMHO) the words say. the load the bolt can hold is not "significantly higher" because some preload is applied. The allowable load of the bolt (Ftu*A) is unchanged (for the vast majority of cases) by preload, as the joint will gap before the allowable load is applied.

I speculated that it may be possible to apply a very high preload (95% allowable) and to have a very high joint stiffness so that the load increase in the bolt is very low to that the joint may be able to support a load higher than the bolt allowable ... but I think it's unlikely.

rb, I agree.

### RE: Bolt load capacity after tightening

I too appreciate this discussion and everything that desertfox (and others) have posted.
I am going to once again try to clarify what my stance has been.

#### Quote (desertfox)

In fact even your diagram is incorrect because the spring representing the bolt doesn't move until the external force exceeds the preload,

This is the disconnect I was talking about in my previous post.
This is not incorrect with the assumptions that were made (and noted in the diagram). The assumption is that the block is many times stiffer than the bolt or spring. That is, in the calculation you posted, the stiffness of the steel plates Kp is taken as infinity. If it is, your joint constant C becomes 0, the increase of force in the bolt is therefore 0, and the decrease in the clamp force is equal to the full external load. That does not mean that the bolt is not carrying the load of the external force. It means that as the bolt takes the load of the external force, it releases some of the clamping force that is causing load in the bolt, so that the clamping force is no longer causing a stress in the bolt. With an infinitely rigid plate this is a 1:1 relationship.
This is the point I have been trying to make regarding the load path.
To me, stating that the load is shared between the bolt and the clamped plates indicates a belief/understanding that tension is somehow transferred between the plates, when clearly it is not (maybe I'm the only one who interprets it that way?). The load path for any tension must be through the bolt, there is nothing else in the joint providing resistance to tension. The external load causes tension in the bolt, so does the plates resistance to compression (clamp force). The clamp force between the plates decreases when an external load is applied because the stress/force in the bolt that was previously causing clamping action is now resisting the external force and is no longer developing that clamp force. A decrease in compression between the plates (which is caused by the tension in bolt) due to an external force being applied is not the same thing as load sharing between the bolt and the plates (again, to me, and how I interpret that statement).

I also understand/recognize that in reality the clamped plates are not infinitely stiff. But starting at that point can help with understanding what is actually happening in the joint before complicating the issue more.

To determine how much an externally applied load will increase the tension in the bolt and at the same time decrease the clamp force in the joint is really a simple strain compatibility issue. As the bolt takes on more load it will elongate, as the bolt elongates it will release clamp load, at the same time the plates will expand as they are now under less compression. As long as the joint hasn't gapped, we know that the deformation in the plates is equal to the deformation in the bolt and can use that to determine actual forces. However, finding the actual strain in the clamped plates is not so simple, as the area that is engaged is not uniform through the thickness or clearly defined. desertfox presented a method that is used for determining this. As hit on above, this is something that is typically ignored in structural joints but is considered in mechanical pressure vessel type joints. Prior to this thread, I did not know that it was considered in mechanical joints and I appreciate the education and information provided by desertfox.

### RE: Bolt load capacity after tightening

maybe you'd be right ... if we could find an infinitely rigid plate. But damn'it we're stuck with these finite stiffness plates.

Yes, the joint clamp-up is much stiffer than the bolt and the change in bolt load whilst clamped is small (as I said a not unreasonable approximation is no change in bolt load) but we're trying to be precise. Once the joint is gapped, all the external load is carried by the bolt.

### RE: Bolt load capacity after tightening

Even in pressure vessel work they consider the elasticity of the bolt and that of the gasket , it is not assumed that the load in the bolt remains constant and they consider the joint and bolt stiffness similar to the calculations shown here.

#### Quote (08/01/2021 desertfox)

When you tighten the end cap on the vessel you tension the bolts but at the same time, the end flange compresses slightly against the end of the vessel, now when you pressurise the vessel the load is actually shared by both the bolts and the mating flange, the flanges are trying to release the compressive stress they are under which in order to do so must absorb some of the load and the remainder of the load is shared be the bolts. See this link https://www.boltscience.com/pages/basics2.htm
I should of also said that the majority of the external load on a bolted joint is carried by the clamped members due to the fact that clamped members are usually much stiffer than the bolts.

According to your first post, my statement above was incorrect (which I took exception too)but you only cherry picked one line of the paragraph but I went on to say about relieving compressive stress between the joint faces and I have never stated that tension was shared between joint and bolt, what I have said is the the external force is shared between joint and bolt.
So if you are now saying you were considering the flanges to be rigid why did you not state this several days ago? because you argued with several posters here that the load was not shared. further to this you state:-

[08/01/2021 quote dauwerda]The tension in the bolt is 40kN
You start with a tension in the bolt that is 40kN, this is resisted by the compression between the two faces of the joint, also equal to 40kN.
You apply an external load of 30kN. The bolt still has a tension force of 40kN, however to maintain equilibrium, this means the compression force between the faces of the plates is now only 10kN.[/quote]

Reading your statement it seems very similar to what I said originally but you said I was wrong??

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

Are you even reading what I am writing? Are you trying to understand it at all?

Your first paragraph is repeating what I just said in my post, not sure why it is written like I said something different than that.

I didn't state that I was assuming a rigid plate because the op did it for me (as I pointed out earlier.)

I really don't understand what your sticking point here is? Once we cleared up the rigid issue the only other thing we disagreed about (and the only thing we disagreed about initially), was the statement:
"I think you are assuming that all the load when your vessel is pressurised is carried by the bolts and that is not correct."
I didn't disagree with anything else in your initial post (which you just quoted above), I don't understand why you think that I did or do disagree with it.

Yes! Exactly! I cherry picked the statement that I believe is misleading! I didn't quote anything else because I agreed with it!

You keep quoting me like I have been changing my tune on things, meanwhile I feel like I just keep repeating myself over and over. The only issue I had with your original post was the issue I brought up. I have explained why I believe it to be misleading multiple times above. If that statement works for people and helps them understand how the joint works, great. It doesn't work for me, and that is all I have tried to explain/bring light to.

### RE: Bolt load capacity after tightening

#### Quote (rb1957 )

Once the joint is gapped, all the external load is carried by the bolt.

Unless there's prying. Then load in bolt is higher than the external load. But let's not go there in this post....

### RE: Bolt load capacity after tightening

Dauwerda
Am I trying to understand it ???
Remember I wasn’t the one charging in to this thread copying a part of someone else’s post and then stating that they were wrong, you managed that by yourself, but then you actually realised that, it was you who was wrong. This followed several days of silence whilst you try to justify your position and then returning and posting claiming that “oh I was assuming the vessel flanges were rigid”. Next we also have your statement “the bolt is the only load path” again totally wrong. There is nothing in the OP’s post that states the flanges were rigid.
I wrote that Nordic8’s confusion I believed was generated by the fact, that when the external load was applied, he thought the bolts took the full amount of the external load and that is not correct,I then stated most of the external load goes into reducing the compressive stress generated at the flanges and smaller amount goes into stretching the bolt to accommodate the relaxation of the flange faces, it
appears that everybody else except you,understood that.
In my opinion you have changed your story on one hand you are saying the bolts took all the load then in the next minute you are saying some of the external load relieves compressive stress at the flange interface.
Rb1957 even, put in a post saying you guy’s are saying they same thing but you even argued against that, so I suggest that you reread the posts and understand what people were saying to you.

Finally it might pay in the future before cherry picking peoples paragraphs and claiming they are wrong to get the full facts before posting, as this saves valuable time and doesn’t get people’s backs up.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

#### Quote (desertfox)

Remember I wasn’t the one charging in to this thread copying a part of someone else’s post and then stating that they were wrong, you managed that by yourself,
I didn't state that you were wrong. I stated that I disagreed with one of your statements. This leaves it open for me to be wrong just as much as it does for you to be wrong.

#### Quote:

but then you actually realised that, it was you who was wrong. This followed several days of silence whilst you try to justify your position and then returning and posting claiming that “oh I was assuming the vessel flanges were rigid”.
I actually pointed out the rigid assumption disconnect in my post that is time stamped,9 Jan 21 13:41. This was simply the following morning after my previous post. Here is what I said, "Ok, now I understand one disconnect. I was assuming the stiffness of the flanges was much greater than that of the bolt as alluded to in the second example in the OP. If that is true the increase in the tension of the bolt is negligible (which your equations show)." Sorry if this didn't clearly depict the rigid assumption, I thought that it did.

#### Quote:

Next we also have your statement “the bolt is the only load path” again totally wrong.
No, this is not wrong. This is our sticking point. Please take a look at the FBD below (initially provided by, goutam_freelance) and show me where or how there is any load path for the external load other than through the bolt.

#### Quote:

There is nothing in the OP’s post that states the flanges were rigid.
Here is the statement in the OP that I am referring to (highlight is from me):
"Or lets give you another really simple example just to illustrate the point I'm trying to make here:
Lets say you have an M6 eye bolt, you insert it through a hole in a rigid steel plate in the ceiling, and screw a nut on the other side. If the nut is not tightened, then you can hang 11.29 kN load on your eye bolt before it breaks, but after you've tightened the nut according to VDI2230, you can only hang 11.29 kN x 8% = 0.9 kN off it before it snaps!."
So yes, the OP did include this assumption to help with the overall concept.

#### Quote:

I wrote that Nordic8’s confusion I believed was generated by the fact, that when the external load was applied, he thought the bolts took the full amount of the external load and that is not correct
Yes, and this is the statement that I disagree with. It implies that there is some other load path for the force to take. There is not, see above.

#### Quote:

I then stated most of the external load goes into reducing the compressive stress generated at the flanges and smaller amount goes into stretching the bolt to accommodate the relaxation of the flange faces, it
appears that everybody else except you,understood that.
I did not disagree with this statement. I disagreed with your first statement. This statement does not support your first statement, here is why:
What is causing the compressive stresses generated at the flanges? The bolt is.
Why does the bolt stop generating these compressive stresses? Because the bolt is now resisting the external load.
That is, some of the stress in the bolt is now being caused by 100% of the external load and the rest is still being caused by the remaining clamping force.

#### Quote:

In my opinion you have changed your story on one hand you are saying the bolts took all the load then in the next minute you are saying some of the external load relieves compressive stress at the flange interface.
That's just it, this is the same story. The bolt is no longer providing those compressive stresses because it must resist 100% of the load. The bolt stiffness constant is not assigning a percentage of the external load to the bolt and a percentage of the external load to the flange. It is determining how much excess stress is created in the bolt based on relative stiffness's compared to the initial unloaded condition. Or, if you go back and look at your example, you determined the final condition has 47.698 kips of tension in the bolt. 30 of those kips is because it is transferring the external load. That means the clamping force between the plates is now only 17.698 kips as opposed to the initial 40 kips.

So, in summary, The bolt does resist 100% of the load, but in doing so it stops creating as much of a clamping force between the plates. The increase in force due to external load and decrease in force due to the release of clamping combine to form an overall net gain of tension in the bolt that is determined from the bolt constant, which is based on the ratio of the stiffness of the bolt to the stiffness of the bolt plus the stiffness of the plates.

#### Quote:

Finally it might pay in the future before cherry picking peoples paragraphs and claiming they are wrong to get the full facts before posting, as this saves valuable time and doesn’t get people’s backs up.
Again, I did not claim that you were wrong. I stated my disagreement, leaving it open for discussion to be hashed out.

### RE: Bolt load capacity after tightening

I've been following this thread, and I think this whole disagreement is just based on confusion regarding terms. Someone, at some point, said something to the effect of 'the mating flange and bolt share the applied load' which seemed to start this giant discussion.

'Share' is the problematic term. The load experienced by the bolt and the load experienced by the flange are related, but the aren't 'shared'- they have opposite signs. Two bolts on the same flange DO 'share' load- in that the load applied to the flange is split 50-50 (in a perfect world) between the two bolts. Ultimately the bolt/flange interaction is really not that complicated if you look at the interaction in terms of balancing the forces.

Say we have a flange clamped by a bolt. The bolt applies (for easy math) a load of 10,000 kgf to the flange (10,000 kgf of preload); the bolt stretches 1mm to apply this load (so the bolt has a spring constant of 10,000 kgf/mm), and the flange compresses 0.01mm due to compressive stress from the bolt preload. (So the flange has a stiffness in compression of 1,000,000 kgf/mm) Other than bolt preload, initial load on the flange is zero.

Assume the flange is compressible but infinitely stiff in bending (flange bending makes this much more complicated).

Say we then apply pressure to the back of the flange sufficient to create 1000 kgf of load on the flange.

This reduces preload on the flange to 9,000 kgf. The stiffness of the flange in compression is 1,000,000 kgf/mm, so the strain of the flange due to compression load is now 0.009mm

In order to maintain equilibrium, the increase in strain in the bolt must match the reduction in strain in the flange- so the strain in tension of the bolt shank must be 1.001mm; knowing what we know about the bolt, this gives us a bolt tension of 10,010 kgf.

This tells us a lot of things that as engineers we already know; namely, that the ratio of stiffness between the flange and bolt matters, a lot. It also tells us something that structural engineers know well, but that mechanical engineers often forget, which is that the less stiff something is, the less load it will attract. If we reduced the stiffness of the bolt (by, say, extending the grip length by any arbitrary amount)we would actually reduce the magnitude of the increase in tension in the bolt shank, without affecting the performance of the joint at all (because we would still be providing 9000 kgf of tension on the flange in the loaded condition).

Say we take the same imaginary scenario, but we increase the stiffness of the bolt by a factor of 10:

-Bolt stiffness: 100,000 kgf/mm
-Bolt strain due to preload: 0.1mm
-Flange stiffness: 1,000,000 kgf/mm
-Flange strain due to preload: 0.01mm

-Applied load: 1,000 kgf (no change)
-Remaining bolt preload: 9,000 kgf (no change)
-Flange strain due to remaining preload: 0.009 mm (no change)

-Bolt strain in loaded condition: 0.101mm
-Bolt tension in loaded condition: 10,100 kgf

By making the bolt 10 times stiffer we've made it attract 10 times more load. In most cases bolt/flange stiffness ration doesn't matter that much, but it's easy to see that in certain edge cases it can make the difference between joints that are robust and joints that aren't.

### RE: Bolt load capacity after tightening

Well that's what makes the world go a round. it's very informative with all of the comments, if this is the right terminology, the stiffness & the flanges or what ever is as or maybe more important than the bolts or as important to equally work as well. lol I personally have more understanding. Bolt and other fasteners has been around since the beginning of time and some are to this day are functional. it amazes me with the controversy of the subject. is it getting to be a lost science or art.

### RE: Bolt load capacity after tightening

On the 8th Jan at 21:19 time stamp I clarified my statement regarding my comment about the bolts seeing all the load, it clearly states that adding the external load and pre-load together is not correct which is in line with what everyone else said as far as I can see, see copy of quotes below.

#### Quote (desertfox)

My absolute agreement with you rb1957

I stated this in my first post but it seems to have been ignored by dauwerda

Quote (desertfox)
now when you pressurise the vessel the load is actually shared by both the bolts and the mating flange,

[color ]My reference to all the load being carried by the bolts was that the external load on the vessel due to the internal pressure plus the bolt preload was the total load in the bolt and that is not correct but I believe thats what the OP thinks.[/color]
example two plates 10mm thick clamped together with an M16 bolt and a bolt preload of 40KN which is then subject to a external load of 30KN what is the total tension in the bolt dauwerda?

No dauwerda the bolt tension won't remain the same.
Quote (dauwerda)
The external tension load (again, this is the pressure on the end cap) will reduce the joint compression and the bolt tension will remain the same.

So really that should of been the end of the matter but when then have this statement from dauwerda:-

#### Quote (dauwerda)

Quote (dauwards)
The load is most definitely carried by the bolts, there is no other load path

However on my post the 10th Jan I posted a diagram from Instar which clearly shows two load paths on a pre-loaded joint under a tensile external force, it goes on to say that the main load path is in the clamped parts and that the bolt is not the main load path.

I would suggest dauwerda that if you want to continue this discussion we start another thread rather than clutter this one any further.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

### RE: Bolt load capacity after tightening

"By making the bolt 10 times stiffer we've made it attract 10 times more load." ... I don't think so. the load portioning (if sharing is a bad word) between the bolt and the joint depends on the ratio of the bolt stiffness to the joint stiffness.

so in the first case we have kb/(kb+kj) and kj/(kb+kj), and in the 2nd it'd be (10*kb)/(10*kb+kj) .NE. 10*kb/(kb+kj)

### RE: Bolt load capacity after tightening

#### Quote (rb1957)

I don't think so. the load portioning (if sharing is a bad word) between the bolt and the joint depends on the ratio of the bolt stiffness to the joint stiffness.

Yes- but as long as the joint stiffness is much larger than the bolt stiffness (which it should always be), the total change in ratio is near the multiplier on the bolt stiffness. As bolt stiffness and joint stiffness converge the magnitude of the total change approaches 1, but if you're operating near that limit, most of the time that means you're building a very bad joint design.

Ultimately my point was at attempt at speaking in generalities- if you calc out this stuff using Shigley there's more nuance.

### RE: Bolt load capacity after tightening

Here's a good site for bolt analysis:-
https://www.xceed-eng.com/bolted-connections/

#### Quote (dauwerda)

No rb1957, we are not saying the same thing. In fact, your first statement, "when the joint is clamped together the external load is shared between the joint faces (compression) and the bolt" is also incorrect.

Note also they use the term the load is shared between the members and the bolt itself which appears to in error according to dauwerda:- see extract below

Why Can The External Load Be So Big?
For a given joint in tension, the amount of load that the bolt takes is only a portion of the load for the joint. This makes sense because we just figured out that the load is shared with the members and the bolt itself. The amount of load that the bolt takes is simple to calculate.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

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