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

Overview of VDI 2230Overview of VDI 2230

An Introduction to the Calculation An Introduction to the Calculation Method for Determining the Stress in Method for Determining the Stress in

a Bolted Jointa Bolted Joint

Important NoteImportant Note

This summary of the VDI 2230 Standard is intended This summary of the VDI 2230 Standard is intended to provide a basic understanding of the method. to provide a basic understanding of the method. Readers who wish to put the standard to use are Readers who wish to put the standard to use are urged to refer to the complete standard that contains urged to refer to the complete standard that contains all information, figures, etc.all information, figures, etc.

DefinitionsDefinitions

• Covers high-duty bolted joints with Covers high-duty bolted joints with constant or alternating loadsconstant or alternating loads

• Bolted joints are separable joints between Bolted joints are separable joints between two or more components using one or more two or more components using one or more boltsbolts

• Joint must fulfill its function and withstand Joint must fulfill its function and withstand working loadworking load

Aim of CalculationAim of Calculation

Determine bolt dimension allowing for:Determine bolt dimension allowing for:

• Strength grade of the boltStrength grade of the bolt

• Reduction of preload by working loadReduction of preload by working load

• Reduction of preload by embeddingReduction of preload by embedding

• Scatter of preload during tighteningScatter of preload during tightening

• Fatigue strength under an alternating loadFatigue strength under an alternating load

• Compressive stress on clamped partsCompressive stress on clamped parts

1. Range of Validity1. Range of Validity

• Steel BoltsSteel Bolts

• M4 to M39M4 to M39

• Room TemperatureRoom Temperature

2. Choice of Calculation 2. Choice of Calculation ApproachApproach

• Dependent upon geometryDependent upon geometry– Cylindrical single bolted jointCylindrical single bolted joint– Beam connectionBeam connection– Circular plateCircular plate– Rotation of flangesRotation of flanges– Flanged joint with plane bearing faceFlanged joint with plane bearing face

Cylindrical Single Bolted Cylindrical Single Bolted JointJoint

• Axial force, Axial force, FFAA

• Transverse force, Transverse force, FFQQ

• Bending moment, Bending moment, MMBB

Beam Geometry, Ex. 1Beam Geometry, Ex. 1

• Axial force, Axial force, FFAA

• Transverse force, Transverse force, FFQQ

• Moment of the plane of the beam, Moment of the plane of the beam, MMZZ

Beam Geometry, Ex. 2Beam Geometry, Ex. 2

• Axial force, Axial force, FFAA

• Transverse force, Transverse force, FFQQ

• Moment of the plane of the beam, Moment of the plane of the beam, MMZZ

Rotation of FlangesRotation of Flanges

• Axial force, Axial force, FFAA (pipe force)(pipe force)

• Bending moment, Bending moment, MMBB

• Internal pressure, Internal pressure, pp

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

• Axial force, Axial force, FFAA (pipe force)(pipe force)

• Torsional moment, Torsional moment, MMTT

• Moment, Moment, MMBB

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

• Axial force, Axial force, FFAA (pipe force)(pipe force)

• Transverse force, Transverse force, FFQQ

• Torsional moment, Torsional moment, MMTT

• Moment, Moment, MMBB

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

• Axial force, Axial force, FFAA (pipe force)(pipe force)

• Transverse force, Transverse force, FFQQ

• Torsional moment, Torsional moment, MMTT

• Moment, Moment, MMBB

3. Analysis of Force and 3. Analysis of Force and DeformationDeformation

• Optimized by means of thorough and exact Optimized by means of thorough and exact consideration of forces and deformations consideration of forces and deformations including:including:– Elastic resilience of bolt and partsElastic resilience of bolt and parts– Load and deformation ratio for parts in Load and deformation ratio for parts in

assembled state and operating stateassembled state and operating state

4. Calculation Steps4. Calculation Steps

• Begins with external working load, Begins with external working load, FFBB

• Working load and elastic deformations may Working load and elastic deformations may cause:cause:– Axial force, Axial force, FFAA

– Transverse force,Transverse force, F FQQ

– Bending Moment, Bending Moment, MMBB

– Torque moment, Torque moment, MMTT

Determining Bolt Determining Bolt DimensionsDimensions

• Once working load conditions are known Once working load conditions are known allow for:allow for:– Loss of preload to embeddingLoss of preload to embedding– Assembly preload reduced by proportion of Assembly preload reduced by proportion of

axial bolt forceaxial bolt force– Necessary minimum clamp load in the jointNecessary minimum clamp load in the joint– Preload scatter due to assembly methodPreload scatter due to assembly method

Calculation Step R1Calculation Step R1

• Estimation of bolt diameter, Estimation of bolt diameter, dd

• Estimation of clamping length ratio, Estimation of clamping length ratio, llKK/d/d

• Estimation of mean surface pressure under Estimation of mean surface pressure under bolt head or nut area, bolt head or nut area, ppGG

• If If ppGG is exceeded, joint must be modified is exceeded, joint must be modified

and and llKK/d/d re-determined re-determined

Calculation Step R2Calculation Step R2

• Determination of tightening factor, Determination of tightening factor, AA, ,

allowing for:allowing for:– Assembly methodAssembly method– State of lubricationState of lubrication– Surface conditionSurface condition

Calculation Step R3Calculation Step R3

• Determination of required average Determination of required average clamping load, clamping load, FFkerfkerf, as either:, as either:

– Clamping force on the opening edge with Clamping force on the opening edge with eccentrically acting axial force, eccentrically acting axial force, FFAA

OrOr– Clamping force to absorb moment Clamping force to absorb moment MMTT or or

transverse force component, transverse force component, FFQQ

Calculation Step R4Calculation Step R4

• Determination of load factor, Determination of load factor, including:including:– Determination of elastic resilience of bolt, Determination of elastic resilience of bolt, SS

– Evaluation of the position of load introduction, Evaluation of the position of load introduction, n*ln*lKK

– Determination of elastic resilience of clamped Determination of elastic resilience of clamped parts, parts, PP

– Calculation of required substitutional cross-Calculation of required substitutional cross-section, section, AAersers

Calculation Step R5Calculation Step R5

• Determination of loss of preload, Determination of loss of preload, FFZZ, due to , due to

embeddingembedding

• Determination of total embeddingDetermination of total embedding

Calculation Step R6Calculation Step R6

• Determination of bolt size and gradeDetermination of bolt size and grade– For tightening within the elastic range, select For tightening within the elastic range, select

bolt for which initial clamping load is equal to bolt for which initial clamping load is equal to or greater than maximum initial clamping load or greater than maximum initial clamping load due to scatter in assembly processdue to scatter in assembly process

– For tightening to yield, select bolt for which For tightening to yield, select bolt for which 90% of initial clamping load is equal to or 90% of initial clamping load is equal to or greater than minimum initial clamping load due greater than minimum initial clamping load due to scatter in assembly processto scatter in assembly process

Calculation Step R7Calculation Step R7

• If changes in bolt or clamping length ratio, If changes in bolt or clamping length ratio, llKK/d/d, are necessary, repeat Steps R4 through , are necessary, repeat Steps R4 through

R6R6

Calculation Step R8Calculation Step R8

• Check that maximum permissible bolt force Check that maximum permissible bolt force is not exceededis not exceeded

Calculation Step R9Calculation Step R9

• Determine alternating stress endurance of boltDetermine alternating stress endurance of bolt• Allow for bending stress in eccentric load Allow for bending stress in eccentric load

applicationsapplications• Obtain approximate value for permissible Obtain approximate value for permissible

stress deviation from tablesstress deviation from tables• If not satisfactory, use bolt with larger If not satisfactory, use bolt with larger

diameter or greater endurance limitdiameter or greater endurance limit• Consider bending stress for eccentric loadingConsider bending stress for eccentric loading

Calculation Step R10Calculation Step R10

• Check surface pressure under bolt head and Check surface pressure under bolt head and nut bearing areanut bearing area

• Allow for chamfering of hole in Allow for chamfering of hole in determining bearing areadetermining bearing area

• Tables provide recommendations for Tables provide recommendations for maximum allowable surface pressuremaximum allowable surface pressure

• If using tightening to or beyond yield, If using tightening to or beyond yield, modify calculationmodify calculation

5. Influencing Factors5. Influencing Factors

• Allow for factors depending upon:Allow for factors depending upon:– Material and surface design of clamped partsMaterial and surface design of clamped parts– Shape of selected bolts and nutsShape of selected bolts and nuts– Assembly conditionsAssembly conditions

Strength of the BoltStrength of the Bolt

• Stress caused by:Stress caused by:– Torsional and axial stresses during tighteningTorsional and axial stresses during tightening– Working loadWorking load

• Should not exceed yield loadShould not exceed yield load

Minimum Thread Minimum Thread EngagementEngagement

• Depends upon:Depends upon:– Thread form, pitch, tolerance, and diameterThread form, pitch, tolerance, and diameter– Form of the nut (wrenching width)Form of the nut (wrenching width)– Bolt holeBolt hole– Strength and ductility of bolt and nut materialsStrength and ductility of bolt and nut materials– Type of stress (tensile, torsional, bending)Type of stress (tensile, torsional, bending)– Friction coefficientsFriction coefficients– Number of tighteningsNumber of tightenings

Thread Shear StrengthThread Shear Strength

• Bolt-Nut Strength MatchingBolt-Nut Strength Matching

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

Calculation of Required Nut Calculation of Required Nut HeightHeight

• Allows for geometry and mechanical Allows for geometry and mechanical properties of joint elementsproperties of joint elements

• Predicts type of failure caused by Predicts type of failure caused by overloadingoverloading

• Considers:Considers:– Dimensional values (tensile cross-section of Dimensional values (tensile cross-section of

bolt thread, thread engagement length, etc.)bolt thread, thread engagement length, etc.)– Thread form & nut formThread form & nut form– Bolt clearance holeBolt clearance hole

Bolt Head HeightBolt Head Height

• Ensures that failure will occur in free Ensures that failure will occur in free loaded thread section or in the shankloaded thread section or in the shank

• Highest tensile stress in thread < Highest Highest tensile stress in thread < Highest tensile stress in bolt headtensile stress in bolt head

Surface Pressure at Bolt Surface Pressure at Bolt Head & Nut Bearing AreasHead & Nut Bearing Areas

• Calculation determines surface pressure Calculation determines surface pressure capable of causing creep resulting in loss of capable of causing creep resulting in loss of preloadpreload

• Surface pressure due to maximum load Surface pressure due to maximum load should not exceed compressive yield point should not exceed compressive yield point of clamped material of clamped material

Tightening Factor, Alpha ATightening Factor, Alpha A

• Allowance must be made for torsional Allowance must be made for torsional stress caused by pitch and thread friction, stress caused by pitch and thread friction, and axial tensile stressand axial tensile stress

• Scatter in friction coefficients and errors in Scatter in friction coefficients and errors in method of controlling preload create method of controlling preload create uncertainty in level of tensile and torsional uncertainty in level of tensile and torsional stressstress

• Tightening factor, Tightening factor, AA, reflects amount of , reflects amount of

required “over-design”required “over-design”

Fatigue StrengthFatigue Strength

• Design modifications to improve endurance Design modifications to improve endurance limit of jointlimit of joint– Increase preloadIncrease preload– Reduce pitch of screw threadReduce pitch of screw thread– Reduction of modulus of nut material elasticityReduction of modulus of nut material elasticity– Increase thread engagementIncrease thread engagement

Fatigue Strength -ContinuedFatigue Strength -Continued

• Design modifications to improve endurance Design modifications to improve endurance limit of jointlimit of joint– Change form of nutChange form of nut– Reduce strength of nut materialReduce strength of nut material– Increase elastic resilience of bolt, lower elastic Increase elastic resilience of bolt, lower elastic

resilience of partsresilience of parts– Shift introduction of load toward interfaceShift introduction of load toward interface

EmbeddingEmbedding

• Caused by flattening of surface Caused by flattening of surface irregularitiesirregularities

• Affects forces in jointAffects forces in joint

• Reduces elastic deformation and preloadReduces elastic deformation and preload

Self-Loosening and Self-Loosening and PreventionPrevention

• Preload drops due to:Preload drops due to:– Relaxation as a result of embedment or creepRelaxation as a result of embedment or creep– Rotational loosening due to relative movements Rotational loosening due to relative movements

between mating surfacesbetween mating surfaces

6. Calculation Examples6. Calculation Examples

• Ex. 1, Concentric Clamping and Concentric Ex. 1, Concentric Clamping and Concentric LoadingLoading

• Ex. 2, Transverse Shearing ForceEx. 2, Transverse Shearing Force

• Ex. 3, Torsional Shearing LoadEx. 3, Torsional Shearing Load

• Ex. 4, Eccentric Clamping and Eccentric Ex. 4, Eccentric Clamping and Eccentric LoadingLoading

• Ex. 5, Eccentric Clamping and LoadingEx. 5, Eccentric Clamping and Loading