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

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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.

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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

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**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

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

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**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

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**Cylindrical Single Bolted Joint**

Axial force, FA Transverse force, FQ Bending moment, MB

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**Beam Geometry, Ex. 1 Axial force, FA Transverse force, FQ**

Moment of the plane of the beam, MZ

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**Beam Geometry, Ex. 2 Axial force, FA Transverse force, FQ**

Moment of the plane of the beam, MZ

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**Rotation of Flanges Axial force, FA (pipe force) Bending moment, MB**

Internal pressure, p

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**Flanged Joint with Plane Bearing Face, Ex. 1**

Axial force, FA (pipe force) Torsional moment, MT Moment, MB

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**Flanged Joint with Plane Bearing Face, Ex. 2**

Axial force, FA (pipe force) Transverse force, FQ Torsional moment, MT Moment, MB

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**Flanged Joint with Plane Bearing Face, Ex. 3**

Axial force, FA (pipe force) Transverse force, FQ Torsional moment, MT Moment, MB

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**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

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**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

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**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

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**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

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

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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

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**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

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

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**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

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

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

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**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

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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

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**5. Influencing Factors Allow for factors depending upon:**

Material and surface design of clamped parts Shape of selected bolts and nuts Assembly conditions

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**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

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**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

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**Thread Shear Strength Bolt-Nut Strength Matching**

Number for strength grade of nut is equivalent to first number of strength grade of bolt

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**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

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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

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**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

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**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”

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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

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**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

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**Embedding Caused by flattening of surface irregularities**

Affects forces in joint Reduces elastic deformation and preload

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**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

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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

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