Transcript Overview of VDI 2230

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
• M4 to M39
• Room Temperature
2. Choice of Calculation
Approach
• Dependent upon geometry
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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
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Axial force, FA (pipe force)
Transverse force, FQ
Torsional moment, MT
Moment, MB
Flanged Joint with Plane
Bearing Face, Ex. 3
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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:
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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
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 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 crosssection, 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
loading
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
– Working load
• Should not exceed yield load
Minimum Thread
Engagement
• Depends upon:
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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, aA, reflects amount of
required “over-design”
Fatigue Strength
• Design modifications to improve endurance
limit of joint
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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