Bolts CALc

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:
– 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