1. Overview of VDI 2230
An Introduction to the Calculation Method for Determining the Stress in a Bolted Joint

2. Important Note
This summary of the VDI 2230 Standard is intended to provide a basic understanding of the method. Readers who wish to put the standard to use are urged to refer to the complete standard that contains all information, figures, etc.

3. Definitions
Covers high-duty bolted joints with constant or alternating loads
Bolted joints are separable joints between two or more components using one or more bolts
Joint must fulfill its function and withstand working load

4. Aim of Calculation Determine bolt dimension allowing for:
Strength grade of the bolt
Reduction of preload by working load
Reduction of preload by embedding
Scatter of preload during tightening
Fatigue strength under an alternating load
Compressive stress on clamped parts

5. 1. Range of Validity
Steel Bolts
M4 to M39
Room Temperature

6. 2. Choice of Calculation Approach
Dependent upon geometry
Cylindrical single bolted joint
Beam connection
Circular plate
Rotation of flanges
Flanged joint with plane bearing face

7. Cylindrical Single Bolted Joint
Axial force, FA
Transverse force, FQ
Bending moment, MB

8. Beam Geometry, Ex. 1 Axial force, FA Transverse force, FQ
Moment of the plane of the beam, MZ

9. Beam Geometry, Ex. 2 Axial force, FA Transverse force, FQ
Moment of the plane of the beam, MZ

10. Rotation of Flanges Axial force, FA (pipe force) Bending moment, MB
Internal pressure, p

11. Flanged Joint with Plane Bearing Face, Ex. 1
Axial force, FA (pipe force)
Torsional moment, MT
Moment, MB

12. Flanged Joint with Plane Bearing Face, Ex. 2
Axial force, FA (pipe force)
Transverse force, FQ
Torsional moment, MT
Moment, MB

13. Flanged Joint with Plane Bearing Face, Ex. 3
Axial force, FA (pipe force)
Transverse force, FQ
Torsional moment, MT
Moment, MB

14. 3. Analysis of Force and Deformation
Optimized by means of thorough and exact consideration of forces and deformations including:
Elastic resilience of bolt and parts
Load and deformation ratio for parts in assembled state and operating state

15. 4. Calculation Steps Begins with external working load, FB
Working load and elastic deformations may cause:
Axial force, FA
Transverse force, FQ
Bending Moment, MB
Torque moment, MT

16. Determining Bolt Dimensions
Once working load conditions are known allow for:
Loss of preload to embedding
Assembly preload reduced by proportion of axial bolt force
Necessary minimum clamp load in the joint
Preload scatter due to assembly method

17. Calculation Step R1 Estimation of bolt diameter, d
Estimation of clamping length ratio, lK/d
Estimation of mean surface pressure under bolt head or nut area, pG
If pG is exceeded, joint must be modified and lK/d re-determined

18. Calculation Step R2
Determination of tightening factor, aA, allowing for:
Assembly method
State of lubrication
Surface condition

19. Calculation Step R3
Determination of required average clamping load, Fkerf, as either:
Clamping force on the opening edge with eccentrically acting axial force, FA Or
Clamping force to absorb moment MT or transverse force component, FQ

20. Calculation Step R4 Determination of load factor, F, including:
Determination of elastic resilience of bolt, dS
Evaluation of the position of load introduction, n*lK
Determination of elastic resilience of clamped parts, dP
Calculation of required substitutional cross-section, Aers

21. Calculation Step R5
Determination of loss of preload, FZ, due to embedding
Determination of total embedding

22. Calculation Step R6 Determination of bolt size and grade
For tightening within the elastic range, select bolt for which initial clamping load is equal to or greater than maximum initial clamping load due to scatter in assembly process
For tightening to yield, select bolt for which 90% of initial clamping load is equal to or greater than minimum initial clamping load due to scatter in assembly process

23. Calculation Step R7
If changes in bolt or clamping length ratio, lK/d, are necessary, repeat Steps R4 through R6

24. Calculation Step R8
Check that maximum permissible bolt force is not exceeded

25. Calculation Step R9 Determine alternating stress endurance of bolt
Allow for bending stress in eccentric load applications
Obtain approximate value for permissible stress deviation from tables
If not satisfactory, use bolt with larger diameter or greater endurance limit
Consider bending stress for eccentric loading

26. Calculation Step R10
Check surface pressure under bolt head and nut bearing area
Allow for chamfering of hole in determining bearing area
Tables provide recommendations for maximum allowable surface pressure
If using tightening to or beyond yield, modify calculation

27. 5. Influencing Factors Allow for factors depending upon:
Material and surface design of clamped parts
Shape of selected bolts and nuts
Assembly conditions

28. Strength of the Bolt Stress caused by: Should not exceed yield load
Torsional and axial stresses during tightening
Working load
Should not exceed yield load

29. Minimum Thread Engagement
Depends upon:
Thread form, pitch, tolerance, and diameter
Form of the nut (wrenching width)
Bolt hole
Strength and ductility of bolt and nut materials
Type of stress (tensile, torsional, bending)
Friction coefficients
Number of tightenings

30. Thread Shear Strength Bolt-Nut Strength Matching
Number for strength grade of nut is equivalent to first number of strength grade of bolt

31. Calculation of Required Nut Height
Allows for geometry and mechanical properties of joint elements
Predicts type of failure caused by overloading
Considers:
Dimensional values (tensile cross-section of bolt thread, thread engagement length, etc.)
Thread form & nut form
Bolt clearance hole

32. Bolt Head Height
Ensures that failure will occur in free loaded thread section or in the shank
Highest tensile stress in thread < Highest tensile stress in bolt head

33. Surface Pressure at Bolt Head & Nut Bearing Areas
Calculation determines surface pressure capable of causing creep resulting in loss of preload
Surface pressure due to maximum load should not exceed compressive yield point of clamped material

34. Tightening Factor, Alpha A
Allowance must be made for torsional stress caused by pitch and thread friction, and axial tensile stress
Scatter in friction coefficients and errors in method of controlling preload create uncertainty in level of tensile and torsional stress
Tightening factor, aA, reflects amount of required “over-design”

35. Fatigue Strength
Design modifications to improve endurance limit of joint
Increase preload
Reduce pitch of screw thread
Reduction of modulus of nut material elasticity
Increase thread engagement

36. Fatigue Strength -Continued
Design modifications to improve endurance limit of joint
Change form of nut
Reduce strength of nut material
Increase elastic resilience of bolt, lower elastic resilience of parts
Shift introduction of load toward interface

37. Embedding Caused by flattening of surface irregularities
Affects forces in joint
Reduces elastic deformation and preload

38. Self-Loosening and Prevention
Preload drops due to:
Relaxation as a result of embedment or creep
Rotational loosening due to relative movements between mating surfaces

39. 6. Calculation Examples
Ex. 1, Concentric Clamping and Concentric Loading
Ex. 2, Transverse Shearing Force
Ex. 3, Torsional Shearing Load
Ex. 4, Eccentric Clamping and Eccentric Loading
Ex. 5, Eccentric Clamping and Loading