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- 1. Overview of VDI2230 An Introduction to the Calculation Method for Determining the Stress in a Bolted Joint
- 2. Important Note This summaryof 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-dutybolted 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 Determinebolt 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 ofValidity • Steel Bolts • M4 to M39 • Room Temperature
- 6. 2. Choice ofCalculation 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 withPlane Bearing Face, Ex. 1 • Axial force, FA (pipe force) • Torsional moment, MT • Moment, MB
- 12. Flanged Joint withPlane Bearing Face, Ex. 2 • Axial force, FA (pipe force) • Transverse force, FQ • Torsional moment, MT • Moment, MB
- 13. Flanged Joint withPlane Bearing Face, Ex. 3 • Axial force, FA (pipe force) • Transverse force, FQ • Torsional moment, MT • Moment, MB
- 14. 3. Analysis ofForce 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 • Onceworking 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 theBolt • Stress caused by: – Torsional and axial stresses during tightening – Working load • Should not exceed yield load
- 29. Minimum Thread Engagement • Dependsupon: – 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 RequiredNut 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 atBolt 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, AlphaA • 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 • Designmodifications 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 byflattening of surface irregularities • Affects forces in joint • Reduces elastic deformation and preload
- 38. Self-Loosening and Prevention • Preloaddrops 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