Overview of VDI 2230 An Introduction to the

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

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.

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

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

1. Range of Validity • Steel Bolts • M 4 to M 39 • Room Temperature

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

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

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

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

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

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

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

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

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

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

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

Calculation Step R 1 • Estimation of bolt diameter, d • Estimation of clamping length ratio, l. K/d • Estimation of mean surface pressure under bolt head or nut area, p. G • If p. G is exceeded, joint must be modified and l. K/d re-determined

Calculation Step R 2 • Determination of tightening factor, a. A, allowing for: – Assembly method – State of lubrication – Surface condition

Calculation Step R 3 • 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

Calculation Step R 4 • Determination of load factor, F, including: – Determination of elastic resilience of bolt, d. S – Evaluation of the position of load introduction, n*l. K – Determination of elastic resilience of clamped parts, d. P – Calculation of required substitutional crosssection, Aers

Calculation Step R 5 • Determination of loss of preload, FZ, due to embedding • Determination of total embedding

Calculation Step R 6 • 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

Calculation Step R 7 • If changes in bolt or clamping length ratio, l. K/d, are necessary, repeat Steps R 4 through R 6

Calculation Step R 8 • Check that maximum permissible bolt force is not exceeded

Calculation Step R 9 • 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

Calculation Step R 10 • 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

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

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

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

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

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

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

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

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, a. A, reflects amount of required “over-design”

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

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

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

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

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