Overview of VDI 2230

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,
  nlK
• 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 lt 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