To check this EXPERIMENTALLY (not analytically) there are load indicating films that can be clamped in your joint.  A link to one manufacturer's product is: http://www.sensorprod.com/bjoint.html.

Thank you for your response, butelja.  I used Sensor Products' Micro (2-20 psi) pressure indicating film, but I found that the repeatability of this low pressure film is questionable.  I think that the angle at which the layer is torn off is a factor.  Analytically, anyone?

More so than because of the uncertainty regarding repeatability, I'd rather use an analytical solution than the film because parameters (e.g., clamping load, plate materials and dimensions, and ideally bolt locations) could then quickly be varied.  I realize that this is a nonlinear (contact) problem, but maybe a ballpark general solution exists.

I do not know if this helps or not.  We often
bolt split rings in bearings and want to know
how the clearance is effected by the clamping.
We simply take the cross section of the total
number of bolts and ratio it against the cross
section of the interfaces and then use this factor
times the stress.  I think you can determine how
much the bolts stretch by the clamping force verses
the length, and assume the material below it will
compress according to the above guideline.

I may not be picturing your problem correctly, but if it is similar to the analysis of bolted joints in a structural steel connection, with plates etc bolted together and transmitting axial, shear and bending forces across the connection, then there are many software packages that will analyse the bolt loads.

The calculation is based on simple statics, taking moments about a point and solving equations for force at equilibrium.  This is assuming that all the parts operate within the elastic range and that the plates are fairly stiff.  For inelastic conditions or ultimate limit state it can get a bit more complicated.

Thank you, both.  I'm not clear on your reply, diamondjim.  Can you provide a sample calculation?  I am interested in the pressure or force BETWEEN bolts, not AT each bolt.  RiBeneke, I thought that the problem is nonlinear even for elastic plates because of the interface contact...

I usually assume a pressure cone of 45 degrees starting from under the head of the bolt. This come continues until the joint split line. So Unless you have either very thick joint members or your bolts are very close together then there will be negligible contact pressure between bolts. See Mech. eng. Design by Shigley for more info. I have confirmed this by FEA.

Good luck
Derek
WWW.fea-uk.co.uk

Thank you, Deeko!  I will borrow a copy of Shigley's book.  The joint in my case has neither stiff plates nor closely spaced bolts.  In the interface there is a pad, whose thermal resistance is very dependent at low pressures, that fills the bow air gap, flatness deviations, and micro roughness.  Although the contact pressure between bolts is negligible compared to the pressure under the bolt head, it is still important to know what the value is.  Pressure film gives some idea.  Is FEA of a bolted joint (with or without an interface material) to solve for the pressure distribution (and get thermal resistance or conductance) as complicated as I suspect?

In any case a tight joint will depend on one compressible material to which the stiffness of the flanges result in overall uniform pressure distribution. Otherwise bolted joints would be nonsense to tightness purpose.

Thank you, ishvaaag.  I had trouble with your phrasing, but I think that I understand.  Doesn't a tight joint depend not only on the interface material but also the stiffness of the members/flanges and the bolt pattern?  In my case, there are no bolts in the interior of the interface area.

Certainly, EcoMan.

For bending strength only we may allow some gap happen somewhere where the bolts are subject to tensile action.

Contrarily, where tightness need be imparted by the mechanical devices operating on some softer sealeant material, such rubber or neoprene, there must be some differential of stiffness between what compresses and what is compressed... and whatever causes the tightness through compression in the softer material needs deliver a pressure regular enough on the softer material, that only can be attained but through some minimum stiffness of the flanges for every pattern of the bolts.

Economy in the connection itself and the need to limit secondary stresses in pipes etc further describe how to tackle the design of the joints.

I think ISHVAAG's point can be though of as this:

Consider the flange clamping the gasket to be analogous to a beam on an elastic foundation with individual point loads caused by the bolts.  The stiffer the beam (flange) is compared to the elastic foundation (gasket), the less variation in foundation (gasket) loading between bolts.  It is not so much the absolute stiffness of either the gasket or the flange that matters as much as the ratio of flange to gasket stiffness.