How to estimate the pressure under a bolt flange?

What do you mean?

• Pressure due just to bolt tightening? This should be estimated by dividing the bolting force by the surface carrying the load.
• Force due to bolt tightening? This can be calculated if you know the applied torque, by dividing the torque by the "thread factor" which depends on the thread geometry (flank angle, mean diameter, pitch and helix angle) and the friction factor between bolt and nut. This is the main problem for estimating bolting force: the friction factor is usually unknown and just estimated by the lubrication status, etc. But keep in mind that variations of friction factors within "normal" values may result in changes in force in ratios 1:2 or even more. So it´s quite difficult to determine with some accuracy the bolting force just by calculations. For approximation, the "thread factor" formula can be found in many mechanical literature (i.e Roark,...). If you want I can give you the formula (I don't keep it in my memory and have to look for it).

Best regards

The nut will also encounter friction with the flange surface. If you only consider the friction bolt-nut you neglect more than half of total friction. The pre-load at tightening depends on whole friction resistances met at assembly.

In reality friction coefficients between bolt and nut and between nut and flange are not the same but usually to simplify they are considered equal.

Under this assumption the equation is:

T= F*( 0.16*P+µ*(0.5773*d2+0.5*Dm)) where

T= tightening torque in your units Nm or ft-lb

F= pre load in N or lbs

P= thread pitch same length units as the other values

µ= friction coefficient assumed same for the 2 sliding surfaces

d2= mean diameter from tables or computed

Dm= mean diameter of contact area between nut and flange or bolt head and flange.

When computing Dm the chamfer has to be taken into consideration.

Values for µ depend on several factors you have to make the choice using tables either for bolted assemblies or in the tribology chapter of wikipedia or bolt /flange manufactures.

Thank you nick name for your pointing, I missed the nut (or bolt head) to flange friction. I was thinking in a valve stem thread/driving nut assembly because I'm just specifying some valve actuators.

I have to add a detail the factor 0.5773 is valid for a flank angle of 30° (thread angle 60°) if your thread has an angle of 55° the factor will be 0.5637.

I too accustomed to metric threads so that I neglected this slight difference.

I was just coming in here to add to the discussions but it looks like everything has been covered. The equations given above would give approximately the values you are looking for however there are calculations which delve deeper into the world of the bolted joint...

I actually use the equations above while doing lubrication testing to determine the CoF of various lubricants from a given torque and a measured bolt load.

I work for Hydratight in England (bolting specialists for the oil and gas industry). There is a basic bolting package on our website "Bolt-up" which you can use free of charge. However, this program gives out bolt load and torque from a given set of inputs for bolt, flange, gasket etc etc so some trial and error might be needed to get to where you need to be.

There are other factors to look at further to the equation given above such as:

Bolt (length, diameter, thread size etc)

Bolt material (Youngs modulus, thermal expansion etc)

Flange material (youngs modulus and thermal expansion)

Gasket material and type (Spiral wound gasket, full face, ring type joint. Non-asbestos filled or asbestos filled, iron, SS, etc etc)

Assembly conditions such as temperature, and miss-alignment (which would create axial mis-alignment or rotational forces to be overcome).

Working conditions (temperature would possibly be higher and there would be extra forces to overcome from the medium within the pipe).

Coefficient of Friction of the lubricant used.

Use of washers if any.

Standards such as ASME VIII - Div 2 - Appendix 3 covers the above in great detail and further.

I am currently looking at EN1591 and EN13445. These look at the actual tightening process and the deformations that the gasket goes through during the tightening process. This is a new area of the bolted joint and contains a high level of maths in the calculation process.

Another big factor (which again is looked at in EN1591 and EN13445) is the scatter of the bolting up method. This can be +/- 15% at times and can greatly affect the final bolt load.

Bolt-up can be found on our website at: http://www.boltup.com/

Gasket information can usually be found from Flexitallic or similar manufacturers: http://www.flexitallic.co.uk/

A lot of bolt information can be found from bolt science: http://www.boltscience.com/pages/info.htm

Useful unit conversion site: http://www.unitconversion.org/index.html

Hope this all helps.

Kind Regards

Kev Brown

(P.S. Hope nobody above thinks I am stepping on their toe's or anything there and correct me if I am wrong on any of the above please - only been in this line of engineering for about 10 months.)

I tried to reply to Kev but as i noticed several times i do not know why it does not work. So that I have to type again the whole.

Dear Kev,

The question was the relationship between Pre load and Torque. I consider that when a question is asked we have to answer it and not give too many informations which could disturb the questioner and make him/her feeling unsafe. We have not always to shaw all what we know but give to the "client" what he asks for.

Of course there are a lot of factors to be considered but not for the function F=f(T). According to a very thorough research the NASA did there are 76 factors. Did you know that? Imagine we start to tell the guy all about those factors how will he feel?

The research you do is very interesting and since I make myself seminars in bolting technology (there are others too not only Bolt Science active) I am interested in the results you can give free. I am also asking if your measurements concern the equivalent global CoF or are you equipped for the separate determination of the 2 CoF? If yes it is ok if not I can suggest you the best equipment for it, the company making the rigs developed different sizes from M3 up to M60 which covers your domain. Let me know if you are interested.

Do you also analyse the effect of sliding velocity on the CoF or do you always work at same speed?

Why is this needed? Of what £/$ value is it?

This is a messy topic!! The amount of friction is quite variable; galvanizing is a lubricant. The state of lubrication may be poorly known. Some look at the amount of bolt/stud elongation/stretch; but are you stretching the threaded portion or the shank? With the bigger studs we worked with before I retired (mostly 2.25") they used turn-of-the-nut tightening often with a sledge wrench. This can make your head hurt!

After 16+ years I doubt if the OP is still interested!

But it's not clear to me what he meant by flange. Is it the bolt head? If so he could divide the bolt load by the contact area, which depends on the diameter of the clearance hole.

A common formula for bolt load is

Load (N) = 5000*torque (N.m)/bolt nominal dia (mm).

I know it's possible to go into it with lot more detail, wrt lubrication etc, but no point in the absence of more information.

Can somebody explain, in "normal" language, why it is necessary to know this particular factor?
Normally when tightning a Nut and Bolt there is a Torque figure given, based on a table using various factors and I also would have thought that the Position / Weight / Movement / Size would also have an impact ?
In addition the choice of material would also be a factor, for example, tightning two pieces of plastic together... one being POM or PA6 and the other say PMMA or PC, one will hold up to the pressure, the other will shatter after a certain amount of pressure whereas two identical pieces of steel will be equally under pressure.
Example, A Street Lampost bolted to a concrete foundation, there would be the static weight of the Lampost pressing down on the Joint but in the case of say a Nut being torqued up on the end of a Driveshaft in a car which rotates in both directions and also carries unsprung weight would have different requirements, as the weight factor would not be relevant.

To estimate the pressure under a bolt flange when the torque is known, you can use the formula Pressure = (Bolt Force / Bolt Area) = (Torque / (k * d)) / (π * (bolt radius)^2), where 'k' is the nut factor (accounting for friction), 'd' is the bolt diameter, and 'bolt radius' is half the bolt diameter. Here's a more detailed breakdown: 1. Understanding the Concepts:

• Torque: The twisting force applied to tighten the bolt.
• Bolt Force (Preload): The tensile force exerted by the bolt after tightening, which creates the clamping force on the flange.
• Nut Factor (k): A dimensionless factor that accounts for friction between the bolt threads and nut, and is typically between 0.15 and 0.2.
• Bolt Diameter (d): The nominal diameter of the bolt.
• Bolt Area (π * (bolt radius)^2): The cross-sectional area of the bolt where the force is applied.
• Pressure: The force per unit area, in this case, the pressure exerted by the bolt on the flange.

2. Formula and Calculation:

• Step 1: Calculate Bolt Force (Preload):
• The formula for bolt force is: Bolt Force = Torque / (k * d).
• You'll need to know the applied torque, the bolt diameter (d), and estimate the nut factor (k).
• Step 2: Calculate Bolt Area:
• The formula for bolt area is: Bolt Area = π * (bolt radius)^2.
• Where 'bolt radius' is half of the bolt diameter (d/2).
• Step 3: Calculate Pressure:
• The formula for pressure is: Pressure = Bolt Force / Bolt Area.
• Substitute the calculated bolt force and bolt area into this formula to get the pressure.

3. Example:

• Let's assume:
• Torque = 100 Nm.
• Bolt diameter (d) = 16 mm (0.016 m).
• Nut factor (k) = 0.2.
• Step 1: Bolt Force:
• Bolt Force = 100 Nm / (0.2 * 0.016 m) = 31250 N.
• Step 2: Bolt Area:
• Bolt radius = 0.016 m / 2 = 0.008 m.
• Bolt Area = π * (0.008 m)^2 = 0.000201 m^2.
• Step 3: Pressure:
• Pressure = 31250 N / 0.000201 m^2 = 155,373,000 Pa (or 155.373 MPa).

4. Important Considerations:

• Nut Factor (k): The nut factor is crucial and can vary depending on the lubrication, thread type, and other factors. Use a value appropriate for your specific application.
• Bolt Material and Strength: Ensure the bolt material and strength are adequate for the calculated pressure and clamping force.
• Gasket Material and Thickness: The gasket material and thickness must be compatible with the calculated pressure and the application.
• Flange Rigidity: The rigidity of the flange also plays a role in how the pressure is distributed.

@ Solar Eagle.. I have a question to your Formular above: Section 2 Calculate Bolt Area... how do you calculate the following.. a Bolt has a diameter of 20mm but has a washer under it of 30mm ?
Also assuming the Nut (which does not have the same value as the Bolt Head as the middle value is missing ) also uses a Washer ?
Would it not be correct to say that only the area of the Bolt Head minus the value of the actual Bolt itself should be calculated / measured just like the Nut's area ( with or without a washer? as the clamping force of the bolt as the area of the bolt itself is not bearing on any surface area ? Example being a Threaded Rod using a Nut at both ends, where only the Nut's surface area is in contact with the parts being held together.

In

2. Formula and Calculation:

• Step 3: Calculate Pressure:

• The formula for pressure is: Pressure = Bolt Force / Bolt Area.
• Substitute the calculated bolt force and bolt area into this formula to get the pressure.

It's misleading to call it pressure. This gives the bolt tensile stress (same units as pressure but still...)

To work out pressure, need to decide what area the bolt load is taken over, as I said in #11.

Incidentally, my formula agrees with

Bolt Force = 100 Nm / (0.2 * 0.016 m) = 31250 N.

..."When tightening the fastener, the amount of friction created depends on multiple factors. Lubrication, like engine oil, applied to the threads and underneath the bolt head drastically decreases the amount of friction created compared to dry components. Using a moly lubricant can drastically change this value as well. The engineers at Automotive Racing Products (ARP) have found that when using engine oil, the amount of friction changes as the fastener is torqued through several cycles.

It’s critical to understand that only 10 to 15 percent of torque applied to a bolt is used to create the expected clamp load. The rest (roughly 85 percent) is required to overcome friction. This is a shocking percentage. In real world terms, if a head bolt needs 65 ft.-lbs. of torque to apply the proper load to the head gasket, then only 10 ft.-lbs. is really needed to pre-load the bolt. The rest (55 ft.-lbs.) is used to overcome friction. What this really points out is that using different lubricants will cause uncontrolled variables when attempting to create a stable load – which is counter-productive. If there was a way to eliminate friction, we’d only need to torque head bolts to 10 ft.-lbs. and the head gasket would seal no problem. That should get your attention.

The desired bolt pre-load is very important and is a value created by the bolt manufacturer. For any bolt, the combination of the strength of its material, diameter, thread, and length all play important roles in establishing the proper fastener stretch. This desired stretch is the amount of pre-load that the bolt is designed to accommodate and still return to its original length without compromising its strength. You can think of a bolt like a spring. As long as you don’t over-stretch the spring, it will always return to its original shape. If the bolt is over-torqued and stretched beyond its limit, this exceeds its yield strength which means it can no longer maintain the needed clamp load and must be replaced.

One way to overcome the huge variable of friction when tightening fasteners like head bolts is to use a technique called torque angle. This differs from applying a simple torque. In torque angle, the first step is to establish an accurate starting point by applying a light torque to the bolt. With an LS engine inboard main cap bolt, for example, the first step is to torque each bolt to 15 ft.-lbs. At this low level, friction is not a major factor so the error induced by different lubes is minimal.

The second step is to use a torque-angle gauge that employs a small arm connected to a gauge stop. With the stop resting against a solid portion of the engine so it won’t move, the dial that can then be easily set at 0 degrees. Finally, using a breaker bar, the bolt is tightened, which moves the dial to the specified angle – hence the term torque-angle. In the case of the LS main cap bolt, with a preload of 15 ft.-lbs., the torque-angle for the inner bolt is 80 degrees. The number of degrees establishes the clamp load by ignoring the actual torque required to overcome friction.

So torque-angle is not affected by the amount of friction created by the under-head bolt thread friction. Of course, if you change fasteners like converting to ARP bolts, then that torque angle spec cannot be used since the ARP’s fasteners are made from a much stronger steel. ARP supplies a specific torque to use instead while also specifying its own ARP Ultra-Torque thread lubricant. Using this lubricant creates a much more accurate and repeatable amount of friction. This creates a much more accurate clamp load.

Another variable that directly affects normal torque values is accuracy of the torque wrench. It’s typical for a torque wrench to only be most accurate in one particular torque range. This is exactly how a torque wrench is calibrated. It’s easy to see how big problems could be created by a wrench that under-torques fasteners by perhaps 8 to 10 ft.-lbs. when the spec calls for 65 ft.-lbs.

Torque-to-yield (TTY) fasteners are a completely different style of fastener that have come into vogue with 21st Century engines. These fasteners are commonly torqued into place using a torque-angle method, but that’s where the similarities end. TTY fasteners are designed to stretch to a certain yield point and not exceed this clamp load limit. This tends to stabilize the load for a head gasket, as an example, when the engine is both cold and then as it warms up – especially it the engine is all aluminum where material growth is a concern."....

Being a Layman in this area, how would somebody calculate the "Bolting" force if a Rivet was used instead of a nut and bolt??
And how does one compensate for the Bolt stretching, which happens quite a lot in automotive Cylinder Head Bolts. How would you work out the Bolt Force where you have a Bolt, a Cylinder Head, a compressible Gasket and a solid Engine Block ?

I don't know much about rivets, but I doubt if "Bolting" force is a criterion, rivets likely to be loaded in tension or shear.

I haven't checked, but I'd assume the specified torque for cylinder head bolts is similar to the recommended torque for the bolts, which is the torque to give 85% proof load stress, proof load stress being 90% yield stress, (which depends on grade of bolt).

The average pressure on the head gasket is of course much lower than the bolt stress, being over a larger area. I doubt if the head gasket is significantly compressible, but I remember years ago it was recommended to check bolt tightness after a period of running. Don't know if that's still the case.

https://www.portlandbolt.com/technical/bolt-torque-chart/

https://boltdepot.com/Fastener-Information/Materials-and-Grades/Bolt-Grade-Chart?srsltid=AfmBOooyZ2IcKgFEL-LD0z275o6c3yVX12hHsZSnRYMA1z1zXEz_em0e

https://www.almabolt.com/pages/catalog/bolts/tighteningtorque.htm