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Bolt Preload Calculation Procedure

Question: How is bolt installation preload calculated?

Answer: Bolt pretension, also called preload or pre-stress, comes from the installation torque T

you apply when you install the bolt. The inclined plane of the bolt thread helix converts torque to bolt pretension. Bolt preload is computed as follows.

i ! T"#$ %& #'q. (&

where i ! bolt preload #called ) i in *hi+ley&.

T ! bolt installation torque.$ ! torque coefficient.

% ! bolt nominal shan diameter #i.e., bolt nominal sie&.

Torque coefficient $ is a function of thread +eometry, thread coefficient of friction µt, and collar 

coefficient of friction µc. oo up $ for your specific thread interface and collar #bolt head or nut

annulus& interface materials, surface condition, and lubricant #if any&. #/Torque specs for screws,/ *hi+ley, and various other sources discuss various $ value estimates.& 0f you cannot

find or obtain $ from credible references or sources for your specific interfaces, then you would

need to research to try to find the coefficients of friction for your specific interfaces, thencalculate $ yourself usin+ one of the followin+ two formulas listed below #*hi+ley,  Mechanical 

 Engineering Design, 1 ed., 2c3raw-Hill, (454, p. 678, 'q. 5-(4, and 20-H%B$-89, (449,

*ect. (99.1.(, p. 8, 'q. (99.1.(, respectively&, the latter bein+ far simpler.

$ ! ;<#9.1 d p&#tan λ = µt sec β&"#( > µt tan λ sec β& = <9.81 µc %@"% #'q. &

$ ! ;<9.1 p"π = <9.1 µt #% > 9.A1 p sin α&"sin α = <9.81 µc %@"% #'q. 6&

where % ! bolt nominal shan diameter. p ! thread pitch #bolt lon+itudinal distance per thread&.

α ! thread profile an+le ! 89 #for 2, 2C, DE, DEF, and DEC thread profiles&.

β ! thread profile half an+le ! 89" ! 69.

tan λ ! thread helix an+le tan ! p"#π d p&.

d p ! bolt pitch diameter.

µt ! thread coefficient of friction.

µc ! collar coefficient of friction.

% and  p  can be obtained from bolt tables such as *tandard 2etric and D*G Bolt *han 

%imensions.

The three terms in 'q. 6 are axial load component #coefficient& of torque resistance due to #(&

thread helix inclined plane normal force, #& thread helix inclined plane tan+ential #thread

friction& force, and #6& bolt head or nut washer face friction force, respectively.

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However, whether you loo up $ in references or calculate it yourself, the en+ineer must

understand that usin+ theoretical equations and typical values for $ and coefficients of friction

merely +ives a preload estimate. oefficient of friction data in published tables vary widely, areoften tenuous, and are often not specific to your specific interface combinations and lubricants.

*uch thin+s as unacnowled+ed surface condition variations and ignored dirt   in the internal

thread can sew the results and produce a false indication of preload.

The en+ineer and technician must understand that published $ values apply to perfectly cleaninterfaces and lubricants #if any&. 0f, for example, the threads of a steel, inc-plated, $ ! 9.,

/dry/ installation fastener were not clean, this mi+ht cause $ to increase to a value of 9.6 or 

even hi+her. Ine should also note that published $ values are intended to be used when applyin+the torque to the nut. The $ values will chan+e in relation to fastener len+th and assembly

runnin+ torque if the torque is bein+ read from the bolt head.

Ine should measure the nut or assembly /runnin+/ torque with an accurate, small-scale torque

wrench. #/Funnin+/ torque, also called prevailin+ torque, is defined as the torque when all

threads are fully en+a+ed, fastener is in motion, and washer face has not yet made contact.& Theonly torque that +enerates bolt preload is the torque you apply above runnin+ torque.

G few more thin+s to be aware of are as follows. Bolt proof stren+th * p is the maximum tensile

stress the bolt material can withstand without encounterin+ permanent deformation. ublished bolt yield stren+ths are determined at room temperature. Heat will lower the yield stren+th #and

 proof stren+th& of a fastener. 'specially in critical situations, you should never reuse a fastener 

unless you are certain the fastener has never been yielded.

1.1 Bolt Preload Measurement

0f a more accurate answer for bolt preload is needed than discussed above, the specificcombination and lubricant would have to be measured   instead of calculated. 2easurementmethods are +enerally involved, time-consumin+, and expensive, and are beyond the scope of 

this article. But perhaps one of the simplest and least expensive methods, to test specific

combinations and lubricants, is to measure the installed fastener with a micrometer, if possible,and compute torque coefficient $ as follows, per *hi+ley, op. cit., p. 671, para. .

$ ! T "#' G delta %& #'q. 7&

where T ! bolt installation torque, ! bolt +rip len+th, ' ! bolt modulus of elasticity, G ! bolt

cross-sectional area, % ! bolt nominal shan diameter, and delta ! measured bolt elon+ation in

units of len+th.