This document summarizes an analysis project that models the static structural behavior of a bolted connection between a bolt and nut. It includes the axisymmetric model geometry, mesh, materials defined as structural steel, boundary conditions of forces applied to the bolt and nut, and the static structural analysis solved over time with results such as total deformation, equivalent stress, and stress components displayed.

1. Project
First Saved Tuesday, October 25, 2016
Last Saved Tuesday, October 25, 2016
Product Version 16.0 Release
Save Project Before Solution No
Save Project After Solution No

2. Contents
 Units
 Model (C4)
o Geometry
 Parts
o Coordinate Systems
o Connections
 Contacts
 Frictional - Bolt To Nut
o Mesh
 Mesh Controls
o Static Structural (C5)
 Analysis Settings
 Loads
 Solution (C6)
 Solution Information
 Results
 Material Data
o Structural Steel
Units
TABLE 1
Unit System Metric (mm, kg, N, s, mV, mA) Degrees RPM Celsius
Angle Degrees
Rotational Velocity RPM
Temperature Celsius
Model (C4)
Geometry
TABLE 2
Model (C4) > Geometry
Object Name Geometry
State Fully Defined
Definition
Source
C:UsersVishnu
RajaranganAppDataLocalTempThreads.tmpThreads_filesdp0Geom-
1DMGeom-1.agdb
Type DesignModeler
Length Unit Millimeters
Element Control Program Controlled
2D Behavior Axisymmetric
Display Style Body Color
Bounding Box

3. Length X 17. mm
Length Y 32. mm
Properties
Volume N/A
Mass N/A
Surface
Area(approx.)
450.55 mm²
Scale Factor Value 1.
Statistics
Bodies 2
Active Bodies 2
Nodes 6926
Elements 2098
Mesh Metric None
Basic Geometry Options
Parameters Yes
Parameter Key DS
Attributes No
Named Selections No
Material Properties No
Advanced Geometry Options
Use Associativity Yes
Coordinate
Systems
No
Reader Mode
Saves Updated File
No
Use Instances Yes
Smart CAD Update No
Compare Parts On
Update
No
Attach File Via
Temp File
Yes
Temporary
Directory
C:UsersVishnu RajaranganAppDataLocalTemp
Analysis Type 2-D
Decompose Disjoint
Geometry
Yes
Enclosure and
Symmetry
Processing
Yes
TABLE 3
Model (C4) > Geometry > Parts
Object Name Bolt Nut
State Meshed
Graphics Properties
Visible Yes
Transparency 1
Definition
Suppressed No

4. Stiffness Behavior Flexible
Coordinate System Default Coordinate System
Reference Temperature By Environment
Material
Assignment Structural Steel
Nonlinear Effects Yes
Thermal Strain Effects Yes
Bounding Box
Length X 10. mm 8.353 mm
Length Y 32. mm 19.686 mm
Properties
Volume N/A
Mass N/A
Centroid X N/A
Centroid Y N/A
Centroid Z N/A
Moment of Inertia Ip1 N/A
Moment of Inertia Ip2 N/A
Moment of Inertia Ip3 N/A
Surface Area(approx.) 297.67 mm² 152.88 mm²
Statistics
Nodes 3795 3131
Elements 1148 950
Mesh Metric None
Coordinate Systems
TABLE 4
Model (C4) > Coordinate Systems > Coordinate System
Object Name Global Coordinate System
State Fully Defined
Definition
Type Cartesian
Coordinate System ID 0.
Origin
Origin X 0. mm
Origin Y 0. mm
Directional Vectors
X Axis Data [ 1. 0. ]
Y Axis Data [ 0. 1. ]
Connections
TABLE 5
Model (C4) > Connections
Object Name Connections
State Fully Defined
Auto Detection

5. Generate Automatic Connection On Refresh Yes
Transparency
Enabled Yes
TABLE 6
Model (C4) > Connections > Contacts
Object Name Contacts
State Fully Defined
Definition
Connection Type Contact
Scope
Scoping Method Geometry Selection
Geometry All Bodies
Auto Detection
Tolerance Type Slider
Tolerance Slider 0.
Tolerance Value 9.0588e-002 mm
Use Range No
Edge/Edge Yes
Priority Include All
Group By Bodies
Search Across Bodies
Statistics
Connections 1
Active Connections 1
TABLE 7
Model (C4) > Connections > Contacts > Contact Regions
Object Name Frictional - Bolt To Nut
State Fully Defined
Scope
Scoping Method Geometry Selection
Contact 8 Edges
Target 8 Edges
Contact Bodies Bolt
Target Bodies Nut
Shell Thickness Effect No
Definition
Type Frictional
Friction Coefficient 0.3
Scope Mode Manual
Behavior Symmetric
Trim Contact Program Controlled
Suppressed No
Advanced
Formulation Augmented Lagrange
Detection Method Program Controlled
Penetration Tolerance Program Controlled
Elastic Slip Tolerance Program Controlled

6. Normal Stiffness Program Controlled
Update Stiffness Program Controlled
Stabilization Damping Factor 0.
Pinball Region Program Controlled
Time Step Controls None
Geometric Modification
Interface Treatment Add Offset, No Ramping
Offset 0. mm
Contact Geometry Correction None
Target Geometry Correction None
Mesh
TABLE 8
Model (C4) > Mesh
Object Name Mesh
State Solved
Display
Display Style Body Color
Defaults
Physics Preference Mechanical
Relevance 0
Sizing
Use Advanced Size Function Off
Relevance Center Coarse
Element Size Default
Initial Size Seed Active Assembly
Smoothing Medium
Transition Fast
Span Angle Center Coarse
Minimum Edge Length 0.312920 mm
Inflation
Use Automatic Inflation None
Inflation Option Smooth Transition
Transition Ratio 0.272
Maximum Layers 2
Growth Rate 1.2
Inflation Algorithm Pre
View Advanced Options No
Patch Conforming Options
Triangle Surface Mesher Program Controlled
Patch Independent Options
Topology Checking No
Advanced
Number of CPUs for Parallel Part Meshing Program Controlled
Shape Checking Standard Mechanical
Element Midside Nodes Program Controlled
Straight Sided Elements No

7. Number of Retries Default (4)
Extra Retries For Assembly Yes
Rigid Body Behavior Dimensionally Reduced
Mesh Morphing Disabled
Defeaturing
Use Sheet Thickness for Pinch No
Pinch Tolerance Please Define
Generate Pinch on Refresh No
Sheet Loop Removal No
Automatic Mesh Based Defeaturing On
Defeaturing Tolerance Default
Statistics
Nodes 6926
Elements 2098
Mesh Metric None
TABLE 9
Model (C4) > Mesh > Mesh Controls
Object Name Edge Sizing Edge Sizing 2
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 16 Edges 15 Edges
Definition
Suppressed No
Type Element Size
Element Size 0.1 mm
Behavior Soft
Bias Type No Bias
Static Structural (C5)
TABLE 10
Model (C4) > Analysis
Object Name Static Structural (C5)
State Solved
Definition
Physics Type Structural
Analysis Type Static Structural
Solver Target Mechanical APDL
Options
Environment Temperature 22. °C
Generate Input Only No
TABLE 11
Model (C4) > Static Structural (C5) > Analysis Settings
Object Name Analysis Settings
State Fully Defined

8. Step Controls
Number Of Steps 1.
Current Step
Number
1.
Step End Time 1. s
Auto Time
Stepping
Program Controlled
Solver Controls
Solver Type Program Controlled
Weak Springs Program Controlled
Solver Pivot
Checking
Program Controlled
Large Deflection Off
Inertia Relief Off
Restart Controls
Generate Restart
Points
Program Controlled
Retain Files After
Full Solve
No
Nonlinear Controls
Newton-Raphson
Option
Program Controlled
Force
Convergence
Program Controlled
Moment
Convergence
Program Controlled
Displacement
Convergence
Program Controlled
Rotation
Convergence
Program Controlled
Line Search Program Controlled
Stabilization Off
Output Controls
Stress Yes
Strain Yes
Nodal Forces No
Contact
Miscellaneous
No
General
Miscellaneous
No
Store Results At All Time Points
Analysis Data Management
Solver Files
Directory
C:UsersVishnu
RajaranganAppDataLocalTempThreads.tmpThreads_filesdp0SYSMECH
Future Analysis None
Scratch Solver
Files Directory
Save MAPDL db No
Delete Unneeded
Files
Yes

9. Nonlinear Solution Yes
Solver Units Active System
Solver Unit System nmm
TABLE 12
Model (C4) > Static Structural (C5) > Loads
Object Name Force Frictionless Support
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 1 Edge 2 Edges
Definition
Type Force Frictionless Support
Define By Components
Coordinate System Global Coordinate System
X Component 0. N (ramped)
Y Component -10000 N (ramped)
Suppressed No
FIGURE 1
Model (C4) > Static Structural (C5) > Force
Solution (C6)
TABLE 13
Model (C4) > Static Structural (C5) > Solution

10. Object Name Solution (C6)
State Solved
Adaptive Mesh Refinement
Max Refinement Loops 1.
Refinement Depth 2.
Information
Status Done
Post Processing
Calculate Beam Section Results No
TABLE 14
Model (C4) > Static Structural (C5) > Solution (C6) > Solution Information
Object Name Solution Information
State Solved
Solution Information
Solution Output Force Convergence
Newton-Raphson Residuals 0
Update Interval 2.5 s
Display Points All
FE Connection Visibility
Activate Visibility Yes
Display All FE Connectors
Draw Connections Attached To All Nodes
Line Color Connection Type
Visible on Results No
Line Thickness Single
Display Type Lines
FIGURE 2
Model (C4) > Static Structural (C5) > Solution (C6) > Solution Information

11. FIGURE 3
Model (C4) > Static Structural (C5) > Solution (C6) > Solution Information

12. TABLE 15
Model (C4) > Static Structural (C5) > Solution (C6) > Results
Object Name
Total
Deformation
Equivalent Stress Radial Axial
hoop
stress
State Solved
Scope
Scoping Method Geometry Selection
Geometry All Bodies
Definition
Type
Total
Deformation
Equivalent (von-Mises)
Stress
Normal Stress
By Time
Display Time Last
Calculate Time
History
Yes
Identifier
Suppressed No
Orientation X Axis Y Axis Z Axis
Coordinate System Global Coordinate System
Results
Minimum
3.4001e-004
mm
0.78379 MPa
-84.653
MPa
-175.27
MPa
-51.136
MPa
Maximum
5.7106e-003
mm
171.87 MPa
87.029
MPa
193.43
MPa
62.511
MPa
Minimum Occurs On Nut
Maximum Occurs
On
Bolt
Minimum Value Over Time
Minimum
6.7975e-005
mm
0.15677 MPa
-84.653
MPa
-175.27
MPa
-51.136
MPa
Maximum
3.4001e-004
mm
0.78379 MPa
-16.934
MPa
-35.06
MPa
-10.239
MPa
Maximum Value Over Time
Minimum
1.1416e-003
mm
34.4 MPa 17.46 MPa
38.715
MPa
12.518
MPa
Maximum
5.7106e-003
mm
171.87 MPa
87.029
MPa
193.43
MPa
62.511
MPa
Information
Time 1. s
Load Step 1
Substep 4
Iteration Number 7
Integration Point Results
Display Option Averaged
Average Across
Bodies
No
FIGURE 4
Model (C4) > Static Structural (C5) > Solution (C6) > Total Deformation

13. TABLE 16
Model (C4) > Static Structural (C5) > Solution (C6) > Total Deformation
Time [s] Minimum [mm] Maximum [mm]
0.2 6.7975e-005 1.1416e-003
0.4 1.3597e-004 2.2838e-003
0.7 2.3799e-004 3.9973e-003
1. 3.4001e-004 5.7106e-003
FIGURE 5
Model (C4) > Static Structural (C5) > Solution (C6) > Total Deformation > Figure

14. FIGURE 6
Model (C4) > Static Structural (C5) > Solution (C6) > Equivalent Stress

15. TABLE 17
Model (C4) > Static Structural (C5) > Solution (C6) > Equivalent Stress
Time [s] Minimum [MPa] Maximum [MPa]
0.2 0.15677 34.4
0.4 0.31349 68.768
0.7 0.5486 120.32
1. 0.78379 171.87
FIGURE 7
Model (C4) > Static Structural (C5) > Solution (C6) > Equivalent Stress > Figure

16. FIGURE 8
Model (C4) > Static Structural (C5) > Solution (C6) > Radial

17. TABLE 18
Model (C4) > Static Structural (C5) > Solution (C6) > Radial
Time [s] Minimum [MPa] Maximum [MPa]
0.2 -16.934 17.46
0.4 -33.862 34.846
0.7 -59.255 60.923
1. -84.653 87.029
FIGURE 9
Model (C4) > Static Structural (C5) > Solution (C6) > Radial > Figure

18. FIGURE 10
Model (C4) > Static Structural (C5) > Solution (C6) > Axial

19. TABLE 19
Model (C4) > Static Structural (C5) > Solution (C6) > Axial
Time [s] Minimum [MPa] Maximum [MPa]
0.2 -35.06 38.715
0.4 -70.113 77.395
0.7 -122.69 135.41
1. -175.27 193.43
FIGURE 11
Model (C4) > Static Structural (C5) > Solution (C6) > Axial > Figure

20. FIGURE 12
Model (C4) > Static Structural (C5) > Solution (C6) > hoop stress

21. TABLE 20
Model (C4) > Static Structural (C5) > Solution (C6) > hoop stress
Time [s] Minimum [MPa] Maximum [MPa]
0.2 -10.239 12.518
0.4 -20.461 25.016
0.7 -35.793 43.76
1. -51.136 62.511
FIGURE 13
Model (C4) > Static Structural (C5) > Solution (C6) > hoop stress > Figure

22. Material Data
Structural Steel
TABLE 21
Structural Steel > Constants
Density 7.85e-006 kg mm^-3
Coefficient of Thermal Expansion 1.2e-005 C^-1
Specific Heat 4.34e+005 mJ kg^-1 C^-1
Thermal Conductivity 6.05e-002 W mm^-1 C^-1
Resistivity 1.7e-004 ohm mm
TABLE 22
Structural Steel > Compressive Ultimate Strength
Compressive Ultimate Strength MPa
0
TABLE 23
Structural Steel > Compressive Yield Strength

23. Compressive Yield Strength MPa
250
TABLE 24
Structural Steel > Tensile Yield Strength
Tensile Yield Strength MPa
250
TABLE 25
Structural Steel > Tensile Ultimate Strength
Tensile Ultimate Strength MPa
460
TABLE 26
Structural Steel > Isotropic Secant Coefficient of Thermal Expansion
Reference Temperature C
22
TABLE 27
Structural Steel > Alternating Stress Mean Stress
Alternating Stress MPa Cycles Mean Stress MPa
3999 10 0
2827 20 0
1896 50 0
1413 100 0
1069 200 0
441 2000 0
262 10000 0
214 20000 0
138 1.e+005 0
114 2.e+005 0
86.2 1.e+006 0
TABLE 28
Structural Steel > Strain-Life Parameters
Strength
Coefficient MPa
Strength
Exponent
Ductility
Coefficient
Ductility
Exponent
Cyclic Strength
Coefficient MPa
Cyclic Strain
Hardening Exponent
920 -0.106 0.213 -0.47 1000 0.2
TABLE 29
Structural Steel > Isotropic Elasticity
Temperature C Young's Modulus MPa Poisson's Ratio Bulk Modulus MPa Shear Modulus MPa
2.e+005 0.3 1.6667e+005 76923
TABLE 30
Structural Steel > Isotropic Relative Permeability
Relative Permeability
10000