# Detailed Bolted Joint Calculations.xls

### Description

Purpose of calculation:

Determine force distribution in a bolted joint.

Calculation Reference

Machine Design Juvinall

Scahum's Machine Design

http://www.mech.uwa.edu.au/DANotes/threads/mechanics/mechanics.html

http://em-ntserver.unl.edu/Negahban/em223/note16/note16.htm

http://en.wikipedia.org/wiki/Bolted_joint

http://www.boltscience.com/

Use 'Torque Pretension' worksheet also consult with the following references

https://roymech.org/Useful_Tables/Screws/Preloading.html#Initial_Bolt_Tension

https://roymech.org/Useful_Tables/Screws/Screw_loads.html

Calculation Validation

http://ocw.mit.edu/OcwWeb/Mechanical-Engineering/2-007Spring-2005/Tools/detail/spreadsheet.htm

1) Material and basic geometry geometry

Young's modulus of bolt

Poisson ratio of bolt

Young's modulus of clamped plate

Poisson ratio of clamped plate

upper clamped plate thickness

lower clamped plate thickness

total clamped plate thickness

2) Bolting details

bolt diameter

bolt thread root diameter

bolt clearance hole

bolt head diameter

(note: could be increased using a flanged headed bolt or a washer)

thickness of bolt head

nut thickness

(note: enter 0 if threaded into flange)

bolt length assumed equal total clamped plate thickness + hnut

3) Torque Tightening and Bolt PreLoad Calculation

Method of torque tightening determines accuracy of bolt preload obtained.

It is not unusual to increase bolt size because the torque tightening method cannot guarentee a minimum preload.

The effects of the torque tightening method are shown on the joint diagram below.

Variation in preload (+ and -)

Tightening Torque (to yield bolt see Eqn. 37)

Bolt head dimension across flats

Thread pitch

outer thread radius

inner thread radius

mean thread radius

Effective radius of rubbing surface against which head/nut bears

Coefficient of friction between screw and nut thread

Coefficient of friction at head/nut bearing collar

Thread Lead (equals thread pitch for single thread screws)

Angle of thread at mean radius

Thread angle at bearing surface

Angle between tangent to tooth profile (on the loaded side) and a radial line

Thread Constant

Bolt preload (load parallel to screw axis)

Efficiency of the screw mechanism (ratio of useful work out to work in)

Torque to stretch Bolt

Thread Torque (torsional load in the bolt to stretch the bolt and overcome thread friction)

Torque to overcome thread friction

Torque to overcome collar friction

Joint pretension constants to compare with other threads

Typical K factors for comparison purposes

Steel Thread Condition

0.30 as received, stainless on mild or alloy

0.20 as received, mild or alloy on same

0.16 cadmium plated

0.14 molybdenum-disulphide grease

0.12 PTFE lubrication

Off Torque - torque required to loosen the nut (if negative then torque needs to be applied to hold nut still)

Bolt Pretension and material properties

Bolt ultimate tensile strength

Bolt yield stress

Force on joint at which bolt yields (ignoring torsional effects)

% of bolt yield stress used by bolt preload

4) Stiffness of tensile loadpath

Tensile stiffness of a bolt shaft

Shear stiffness of a bolt head

Shear stiffness of a nut

Total stiffness of bolt

5) Stiffness of compressive loadpath

cone angle (normally 45° dispersion from bolt head/nut)

Compressive stiffness of clamped plates (in series)

Shear stiffness of clamped plates

Total stiffness of all compressive loadpath elements under bolt

6) Calculate Basic Joint Forces

Force in bolt when preload is lost (joint separates and contact force between clamped plates = 0)

Fbreak/Fleak: resulting safety factor

7) Calculate bolt loads for a particular external load applied to the joint

External load applied to the bolted joint

Load in the bolt

External shear load applied to the bolted joint

Contact force between clamped plates

Coefficient of friction between clamped plates

Shear capacity of joint

8) Graphical Representation of Results

9) Bolt Stress Analysis

Direct stress in the bolt

Shear stress in bolt (using torsion in circular shaft formula)

maximum principle stress

minimum principle stress

Von Mises Stress (note s3=0 for biaxial stress system)

Possible increase in preload

10) Bearing stress under head of bolt

Note excessive bearing stresses lead to creep effects which will result in a loss of preload over time.

This relaxation is a function of:

Typically the bearing stress should not exceed the clamped plate yield stress.

Maximum bearing Stress

11) Joint deflections and nut rotation.

Bolt extension

Flange compression

Angle turned to extend the bolt

12) Losses at Clamped Surfaces

Paint compression factor

Maximum paint thickness (specification)

Number of painted surfaces

Preload after paint compression

Maximum paint thickness (specification)

Preload after paint compression

A simpler version of this calculation is available here.

**Calculation Reference**

Handbook of bolts and bolted joints

American Machinists' Handbook and Dictionary of Shop Terms

Basic Principles for Construction, Cengage Learning

Machinery's Handbook

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kf = kf1.kf2/(kf1+kf2)

A separate calc for d1 and d2 with hf1 and hf2 in the equations and with the initial 2 deleted in each equation. A separate calc for kf1 and kf2 based on d1 and d2 ( and possible using separate E values (Ef2 and Ef2 ) although I do not think this is important.

kf = kf1+kf2 /(kf1.kf2).

I have created a modified version of the spreadsheet if John Doyle wants a copy.

1) Add fine thread sizes.

2) Add screw joint, that is, bolt through clearance material into tapped hole.

However I was unsure of the derivation of the formula and decided to include simpler terms. Now that I have taken a look at the stiffness derivation on your site I feel much more confortable using your formulae.

Thank you very much for the comment and I update the calculation shortly.

uses the stiffness of a cylinder with OD = dia of bottom of cone frustrum. Other

sources including roymech,co.uk use the actual stiffness of the frustrum.

The method used may be acceptable from a practical point of view but the resulting stiffness factors are very low compared to the other sources.

Please could John comment on this.

Note this is an excellent highly visible set of calcs.