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# Overview of VDI 2230 by mifei

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```									 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
• Bolted joints are separable joints between
two or more components using one or more
bolts
• Joint must fulfill its function and withstand
Aim of Calculation
Determine bolt dimension allowing for:
• Strength grade of the bolt
• 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
• M4 to M39
• 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 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
Calculation Step R2
• Determination of tightening factor, aA,
allowing for:
– Assembly method
– State of lubrication
– Surface condition
Calculation Step R3
• Determination of required average clamping
– 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 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
Calculation Step R5
• Determination of loss of preload, FZ, due to
embedding
• Determination of total embedding
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
Calculation Step R7
• If changes in bolt or clamping length ratio,
lK/d, are necessary, repeat Steps R4 through
R6
Calculation Step R8
• Check that maximum permissible bolt force
is not exceeded
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
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
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
• Should not exceed yield load
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
• 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
• Considers:
– Dimensional values (tensile cross-section of
– Thread form & nut form
– Bolt clearance hole
• Ensures that failure will occur in free loaded
thread section or in the shank
• Highest tensile stress in thread < Highest
Surface Pressure at Bolt
• Calculation determines surface pressure
capable of causing creep resulting in loss of
• 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
uncertainty in level of tensile and torsional
stress
• Tightening factor, aA, reflects amount of
required “over-design”
Fatigue Strength
• Design modifications to improve endurance
limit of joint
–   Reduce pitch of screw thread
–   Reduction of modulus of nut material elasticity
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
– 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