Though there are many standards and guidelines (ISO, DIN, BS) and handbooks, theoretically it is not a simple matter. It depends on how a threaded fastener sustains loading, that is, if (a) a single bolt or a large number of bolts (pattern) is concerned to work together, (b) the tensile force is acting in a static or dynamic situation, (c) the coupled 'plates' are rigid or flexible, (d) the load is repetitive over a longer time period, (e) the kind of loosening to be considered (inside, outside, mixed), and (f) there are thermal and/or chemical effects. The standards cover these uncertainties with sufficient-enough safety factors. To consider all the above factors in an analytical way, I suggest you to use a finite element model/analysis to find the optimal pretension by a series of virtual experiments. Please visit: http://www.boltscience.com/pages/preloadrequirementcharts.htm

Many Thanks to Ariadne Tsambani and Imre Horvath for your help.

I am using analytical method to calculate tightening torque using stiffness calculations.

Regards,

Mahesha

did you get answer? Please share any analytical formula if you have any. Even I faced the same problem