Spring 2017 MAE 4160 / MAE 5160 Homework # 2
Please show all the steps of your work!Due: Tuesday 1/31/2017 at 3:15pm
Please keep track of the number of hours you spend working on this assignment and report thenumber of hours as your answer to the last question in this homework. You will get 5 points fordoing this!
1. (30 points) Apply 1-D Euler-Bernoulli beam theory to the following beam shown in Figure 1under uniformly distributed loads as shown in Figure 2 and Figure 3. Answer the followingquestions for each load.
Figure 1: Dimensions of the beam
Figure 2: Loading 1
(a) List the assumptions that goes into the Euler-Bernoulli beam model (note this questionyou only need to answer once for both loads!)
(b) Plot the deformation of the top surface of beam in the loading direction as a function ofthe length of the beam.
Suppose we denote the displacement field of the beam by
u(x1, x2, x3) =
u1(x1, x2, x3)u2(x1, x2, x3)u3(x1, x2, x3)
1
Figure 3: Loading 2
with +x1 direction as the longtudinal direction, the Euler-Bernoulli assumptions are:
i. The cross-section is rigid in its own plane, this means that there is only rigid trans-lation in the plane:
u2(x1, x2, x3) = u2(x1),
andu3(x1, x2, x3) = u3(x1).
ii. The cross-section plane stays planer under deformation, this means that the dis-placement in the x1 direction is:
u1(x1, x2, x3) = u1(x1) + x2Φ3(x1) + x3Φ2(x1)
Where Φ1 and Φ2 represent the rotation as indicated in Figure 4.
Figure 4: Possible displacements in the longitudinal direction under the second assumption
iii. The cross-section remains normal to the deformed axis of the beam, this assumptionmeans that:
Φ3(x1) =du2(x1)
dx1
and
Φ2(x1) =du3(x1)
dx1
(c) Calculate the location and the value of the maximum deformation
By symmetry of the problem, the location of maximum deformation is going to be atthe center. The deflection formula for distributed load of a simply supported beam iswith the coordinates as shown in Figure 7.
y = − wx
24EI(L3 − 2Lx2 + x3)
2
Figure 5: Deflection for 5N/mm distributed load
Figure 6: Deflection for 100N/mm distributed load
The maximum deflection is y(L/2) = −9.523809523810mm for the 5N/mm load. The
maximum deflection is y(L/2) = −190.47619047619mm for the 100N/mm load. The
deflection for the beam as a function of x-axis is shown in Figures 5 and 6
(d) Calculate the location and the value of the maximum stress The stress that’s normal tothe loading direction for a simply supported beam under distributed load is:
σx =−zEρ
With z the distance away from the neutral axis in the y-direction, E = 2.1e5MPa asthe Young’s modulus. The curvature of the beam is:
1
ρ=d2y
dx2= − w
24EI(−12Lx+ 12x2)
The stress is maximum at x = L/2. The maximum stress is σ(L2 ) ≈ 300MPam for adistributed load of 5N/mm and the maximum stress is σ(L2 ) ≈ 600MPa for a distributed
3
Figure 7:
Figure 8: stress at the surface of the beam as a function of the x-axis
load of 100N/mm. The stress at the surface of the beam as function of the x-axis isshown in 8.
2. (65 points) Use the Ansys workbench 17.2 to perform a 3D FEA calculation of the beam underthe two loads. Follow this youtube video for instructions on how to use Ansys workbench forthis problem: https://www.youtube.com/watch?v=CTi1ru-pfi0.
Answer the following questions after you performed the FEA calculations for both loads.
(a) Find the maximum displacement in the direction of the loading for both loads. How doesit compare to your analytic calculation using Euler-Bernoulli beam?
For the first beam, the maximum displacement in the direction of the loading is: 9.5414mm.For the second beam, the maximum displacement in the direction of the loading is:190.83mm.
(b) Find the maximum normal stress to the cross-section for both loads. How does it com-pare to your analytic calculation using Euler-Bernoulli beam? For the first beam, themaximum normal stress normal to the cross-section is 300.06MPa. For the second beam,the maximum normal stress normal to the cross-section is 6000.09MPa.
(c) Make a plot of the deformation as a function the length at the top surface of the beam.How does it compared to your calculation from problem 1?
See Ansys Report document
4
(d) Make a plot of the deformation as a function the length at the neutral axis of the beam.Does this meet your expectation in the deformation of the neutral axis?
See Ansys Report document.
(e) Should we use 1D beam theory to approximate the load in Figure 2 and Figure 3? Whyor why not?
The maximum deflections are within 1% error from the Ansys 3D model, this shows theEuler-Bernoulli beam theory is a very good approximation.
3. (5 points) How many hours did you spend on this homework assignment?
5
Project
First Saved Monday, January 23, 2017
Last Saved Monday, January 23, 2017
Product Version 17.2 Release
Save Project Before Solution No
Save Project After Solution No
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Contents
� Units
� Model (A4)
� Geometry
� SYS\Solid
� Construction Geometry
� Paths
� Coordinate Systems
� Mesh
� Static Structural (A5)
� Analysis Settings
� Loads
� Solution (A6)
� Solution Information
� Results
� Directional_surface
� Directional_neutral_axis
� stress_surface
� stress_neutral_axis
� Material Data
� Structural Steel
Units
TABLE 1
Model (A4)
Unit System Metric (mm, kg, N, s, mV, mA) Degrees rad/s Celsius
Angle Degrees
Rotational Velocity rad/s
Temperature Celsius
Geometry
TABLE 2Model (A4) > Geometry
Object Name Geometry
State Fully Defined
Definition
Source C:\Users\xwang3\Documents\distributed_load_beam_files\dp0\SYS\DM\SYS.scdoc
Type SpaceClaim
Length Unit Meters
Element Control Program Controlled
Display Style Body Color
Bounding Box
Length X 20. mm
Length Y 800. mm
Length Z 20. mm
Properties
Volume 3.2e+005 mm³
Mass 2.512 kg
Scale Factor Value 1.
Statistics
Bodies 1
Active Bodies 1
Nodes 14465
Elements 2560
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TABLE 3Model (A4) > Geometry > Parts
Mesh Metric None
Basic Geometry Options
Solid Bodies Yes
Surface Bodies Yes
Line Bodies Yes
Parameters Independent
Parameter Key
Attributes Yes
Attribute Key
Named Selections Yes
Named Selection Key
Material Properties Yes
Advanced Geometry Options
Use Associativity Yes
Coordinate Systems Yes
Coordinate System Key
Reader Mode Saves Updated File No
Use Instances Yes
Smart CAD Update Yes
Compare Parts On Update No
Attach File Via Temp File Yes
Temporary Directory C:\Users\xwang3\AppData\Local\Temp
Analysis Type 3-D
Mixed Import Resolution None
Decompose Disjoint Geometry Yes
Enclosure and Symmetry Processing Yes
Object Name SYS\Solid
State Meshed
Graphics Properties
Visible Yes
Transparency 1
Definition
Suppressed No
Stiffness Behavior Flexible
Coordinate System Default Coordinate System
Reference Temperature By Environment
Behavior None
Material
Assignment Structural Steel
Nonlinear Effects Yes
Thermal Strain Effects Yes
Bounding Box
Length X 20. mm
Length Y 800. mm
Length Z 20. mm
Properties
Volume 3.2e+005 mm³
Mass 2.512 kg
Centroid X 1. mm
Centroid Y -7.0586e-015 mm
Centroid Z 5.5145e-017 mm
Moment of Inertia Ip1 1.3406e+005 kg·mm²
Moment of Inertia Ip2 167.47 kg·mm²
Moment of Inertia Ip3 1.3406e+005 kg·mm²
Statistics
Nodes 14465
Elements 2560
Mesh Metric None
CAD Attributes
PartTolerance: 0.00000001
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TABLE 4Model (A4) > Construction Geometry
TABLE 5Model (A4) > Construction Geometry > Paths
Color:143.175.143
Object Name Construction Geometry
State Fully Defined
Display
Show Mesh No
Object Name Path Path 2
State Fully Defined
Definition
Path Type Two Points
Path Coordinate System Global Coordinate System
Number of Sampling Points 47.
Suppressed No
Start
Coordinate System Global Coordinate System
Start X Coordinate 1. mm
Start Y Coordinate -400. mm
Start Z Coordinate 10. mm 0. mm
Location Defined
End
Coordinate System Global Coordinate System
End X Coordinate 1. mm
End Y Coordinate 400. mm
End Z Coordinate 10. mm 0. mm
Location Defined
Coordinate Systems
TABLE 6Model (A4) > 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
Origin Z 0. mm
Directional Vectors
X Axis Data [ 1. 0. 0. ]
Y Axis Data [ 0. 1. 0. ]
Z Axis Data [ 0. 0. 1. ]
Mesh
TABLE 7Model (A4) > Mesh
Object Name Mesh
State Solved
Display
Display Style Body Color
Defaults
Physics Preference Mechanical
Relevance 0
Shape Checking Standard Mechanical
Element Midside Nodes Program Controlled
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Static Structural (A5)
TABLE 8Model (A4) > Analysis
TABLE 9Model (A4) > Static Structural (A5) > Analysis Settings
Sizing
Size Function Adaptive
Relevance Center Coarse
Element Size 5.0 mm
Initial Size Seed Active Assembly
Smoothing Medium
Transition Fast
Span Angle Center Coarse
Automatic Mesh Based Defeaturing On
Defeature Size Default
Minimum Edge Length 20.0 mm
Inflation
Use Automatic Inflation None
Inflation Option Smooth Transition
Transition Ratio 0.272
Maximum Layers 5
Growth Rate 1.2
Inflation Algorithm Pre
View Advanced Options No
Advanced
Number of CPUs for Parallel Part Meshing Program Controlled
Straight Sided Elements No
Number of Retries Default (4)
Rigid Body Behavior Dimensionally Reduced
Mesh Morphing Disabled
Triangle Surface Mesher Program Controlled
Topology Checking No
Pinch Tolerance Please Define
Generate Pinch on Refresh No
Statistics
Nodes 14465
Elements 2560
Mesh Metric None
Object Name Static Structural (A5)
State Solved
Definition
Physics Type Structural
Analysis Type Static Structural
Solver Target Mechanical APDL
Options
Environment Temperature 22. °C
Generate Input Only No
Object Name Analysis Settings
State Fully Defined
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 Off
Solver Pivot Checking Program Controlled
Large Deflection Off
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TABLE 10Model (A4) > Static Structural (A5) > Loads
FIGURE 1Model (A4) > Static Structural (A5) > Force
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:\Users\xwang3\Documents\distributed_load_beam_files\dp0\SYS\MECH\
Future Analysis None
Scratch Solver Files Directory
Save MAPDL db No
Delete Unneeded Files Yes
Nonlinear Solution No
Solver Units Active System
Solver Unit System nmm
Object Name Force Fixed Support Displacement
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 1 Face 1 Edge
Definition
Type Force Fixed Support Displacement
Define By Vector Components
Magnitude -4000. N (ramped)
Direction Defined
Suppressed No
Coordinate System Global Coordinate System
X Component 0. mm (ramped)
Y Component Free
Z Component 0. mm (ramped)
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FIGURE 2Model (A4) > Static Structural (A5) > Displacement
Solution (A6)
TABLE 11Model (A4) > Static Structural (A5) > Solution
Object Name Solution (A6)
State Solved
Adaptive Mesh Refinement
Max Refinement Loops 3.
Refinement Depth 2.
Information
Status Done
MAPDL Elapsed Time 6. s
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TABLE 12Model (A4) > Static Structural (A5) > Solution (A6) > Solution Information
TABLE 13Model (A4) > Static Structural (A5) > Solution (A6) > Results
MAPDL Memory Used 117. MB
MAPDL Result File Size 4.1875 MB
Post Processing
Beam Section Results No
Object Name Solution Information
State Solved
Solution Information
Solution Output Solver Output
Newton-Raphson Residuals 0
Identify Element Violations 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
Object Name
Directional Deformation
Equivalent Stress
Total Deformation
NormalStress
DirectionalDeformation_surface
DirectionalDeformation_neutral_axis
normalstress
surface
normal stressneutral
axis
State Solved
Scope
Scoping Method
Geometry Selection Path
Geometry All Bodies
Path Path Path 2 Path Path 2
Definition
TypeDirectional
Deformation
Equivalent(von-
Mises) Stress
Total Deformation
Normal Stress
Directional Deformation Normal Stress
Orientation Z Axis Y Axis X Axis
By Time
Display Time
Last
Coordinate System
Global Coordinate
SystemGlobal Coordinate System
Calculate Time
HistoryYes
Identifier
Suppressed No
Results
Minimum -9.5414 mm 0.125 MPa 0. mm-300.06
MPa-7.6421e-010 mm -1.5411e-009 mm
-0.13087
MPa
-5.3634e-
002 MPa
Maximum 0. mm300.04 MPa
9.549 mm300.06 MPa
9.3522e-010 mm 2.2685e-010 mm1.8789 MPa
0.76191 MPa
Minimum Occurs On
SYS\Solid
Maximum Occurs On
SYS\Solid
Information
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FIGURE 3Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation
TABLE 14Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation
FIGURE 4Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation > Figure
Time 1. s
Load Step 1
Substep 1
Iteration Number
1
Integration Point Results
DisplayOption
Averaged Averaged Averaged
Average AcrossBodies
No No No
Graph Controls
X-Axis S
Time [s] Minimum [mm] Maximum [mm]
1. -9.5414 0.
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FIGURE 5Model (A4) > Static Structural (A5) > Solution (A6) > Equivalent Stress
TABLE 15Model (A4) > Static Structural (A5) > Solution (A6) > Equivalent Stress
FIGURE 6
Time [s] Minimum [MPa] Maximum [MPa]
1. 0.125 300.04
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Model (A4) > Static Structural (A5) > Solution (A6) > Total Deformation
TABLE 16Model (A4) > Static Structural (A5) > Solution (A6) > Total Deformation
FIGURE 7Model (A4) > Static Structural (A5) > Solution (A6) > Normal Stress
TABLE 17Model (A4) > Static Structural (A5) > Solution (A6) > Normal Stress
FIGURE 8Model (A4) > Static Structural (A5) > Solution (A6) > Normal Stress > Figure
Time [s] Minimum [mm] Maximum [mm]
1. 0. 9.549
Time [s] Minimum [MPa] Maximum [MPa]
1. -300.06 300.06
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FIGURE 9Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_surface
TABLE 18Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_surface
Length [mm] Value [mm]
0. -7.6421e-010
16.667 4.8262e-010
33.333 5.4577e-010
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FIGURE 10Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_neutral_axis
50. 5.2049e-010
66.667 5.3853e-010
83.333 5.6574e-010
100. 5.4297e-010
116.67 2.8065e-010
133.33 -2.1359e-010
150. -3.087e-010
166.67 -5.2962e-010
183.33 -4.9274e-010
200. -5.395e-010
216.67 -5.6337e-010
233.33 -5.9518e-010
250. -4.2458e-010
266.67 -4.4645e-010
283.33 -2.9048e-010
300. -5.9452e-011
316.67 2.1121e-010
333.33 4.7881e-010
350. 8.4609e-010
366.67 9.3522e-010
383.33 2.9953e-010
400. 2.6716e-010
416.67 -1.3239e-010
433.33 -3.8928e-010
450. -4.9093e-010
466.67 -4.1621e-010
483.33 -4.7927e-010
500. -4.3569e-010
516.67 -2.681e-010
533.33 -1.2371e-010
550. 5.7361e-011
566.67 2.3816e-010
583.33 -3.9544e-011
600. -5.7555e-010
616.67 -5.8052e-010
633.33 -7.274e-010
650. -6.1076e-010
666.67 -6.2657e-010
683.33 -6.1923e-010
700. -5.8061e-010
716.67 -4.3326e-010
733.33 -3.9528e-010
750. -2.6117e-010
766.67 -7.2575e-011
783.33 1.4218e-010
800. 3.6791e-010
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TABLE 19Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_neutral_axis
Length [mm] Value [mm]
0. -1.6994e-010
16.667 -2.4444e-010
33.333 -3.6065e-010
50. -3.9904e-010
66.667 -4.438e-010
83.333 -5.7914e-010
100. -7.0832e-010
116.67 -9.2053e-010
133.33 -1.1752e-009
150. -1.307e-009
166.67 -1.4482e-009
183.33 -1.4761e-009
200. -1.5183e-009
216.67 -1.5128e-009
233.33 -1.5411e-009
250. -1.2977e-009
266.67 -1.1742e-009
283.33 -9.7646e-010
300. -7.3045e-010
316.67 -3.7863e-010
333.33 -1.9498e-010
350. -4.9713e-011
366.67 -1.8829e-010
383.33 -4.1476e-010
400. -4.8356e-010
416.67 -7.4825e-010
433.33 -1.0533e-009
450. -1.0748e-009
466.67 -9.2145e-010
483.33 -9.1506e-010
500. -7.9111e-010
516.67 -5.557e-010
533.33 -3.872e-010
550. -3.3882e-010
566.67 -3.5448e-010
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FIGURE 11Model (A4) > Static Structural (A5) > Solution (A6) > normal stress surface
TABLE 20Model (A4) > Static Structural (A5) > Solution (A6) > normal stress surface
583.33 -5.6036e-010
600. -8.0188e-010
616.67 -8.5531e-010
633.33 -9.2289e-010
650. -8.895e-010
666.67 -8.7675e-010
683.33 -8.4752e-010
700. -8.0896e-010
716.67 -6.3208e-010
733.33 -4.971e-010
750. -3.2743e-010
766.67 -1.2552e-010
783.33 7.097e-011
800. 2.2685e-010
Length [mm] Value [MPa]
0. 1.8789
16.667 -0.13083
33.333 -3.3255e-002
50. -2.1785e-002
66.667 -2.2684e-002
83.333
-2.2672e-002100.
116.67
133.33 -2.2671e-002
150. -2.2673e-002
166.67 -2.2672e-002
183.33 -2.2673e-002
200. -2.2669e-002
216.67 -2.267e-002
233.33 -2.2672e-002
250. -2.2671e-002
266.67 -2.2673e-002
283.33 -2.2672e-002
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FIGURE 12Model (A4) > Static Structural (A5) > Solution (A6) > normal stress neutral axis
TABLE 21Model (A4) > Static Structural (A5) > Solution (A6) > normal stress neutral axis
300. -2.267e-002
316.67 -2.2669e-002
333.33 -2.2671e-002
350. -2.2672e-002
366.67 -2.2671e-002
383.33 -2.2674e-002
400. -2.2673e-002
416.67 -2.2674e-002
433.33 -2.2672e-002
450. -2.2673e-002
466.67 -2.2672e-002
483.33 -2.2675e-002
500. -2.267e-002
516.67 -2.2674e-002
533.33 -2.267e-002
550. -2.2671e-002
566.67 -2.2673e-002
583.33 -2.2672e-002
600. -2.267e-002
616.67 -2.2673e-002
633.33-2.2672e-002
650.
666.67 -2.267e-002
683.33 -2.2671e-002
700.-2.2672e-002
716.67
733.33 -2.2684e-002
750. -2.1786e-002
766.67 -3.3446e-002
783.33 -0.13087
800. 1.8727
Length [mm] Value [MPa]
0. 0.76191
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Directional_surface
FIGURE 13Model (A4) > Directional_surface
16.667 -5.3634e-002
33.333 6.7448e-004
50. 4.1796e-004
66.667 -1.2022e-005
83.333 -3.0787e-007
100. 1.6799e-007
116.67 -6.9296e-007
133.33 8.2043e-007
150. -4.3923e-007
166.67 -3.3858e-007
183.33 4.2674e-007
200. -2.5318e-007
216.67 -6.765e-007
233.33 -4.5586e-007
250. 2.6538e-007
266.67 5.249e-007
283.33 -1.6241e-007
300. -1.4212e-006
316.67 2.2965e-007
333.33 1.1439e-007
350. 1.0113e-007
366.67 -8.3339e-007
383.33 2.5294e-006
400. -1.8354e-007
416.67 1.8069e-006
433.33 -4.7399e-007
450. 1.8341e-007
466.67 -1.8274e-007
483.33 8.1933e-007
500. 1.1121e-007
516.67 -7.2178e-007
533.33 5.1367e-007
550. 1.3021e-007
566.67 1.4067e-007
583.33 -6.741e-007
600. 7.1839e-007
616.67 4.5611e-008
633.33 -6.2942e-007
650. 1.4676e-008
666.67 2.5293e-007
683.33 -5.9362e-007
700. -1.0444e-006
716.67 -4.5694e-007
733.33 -1.1415e-005
750. 4.1518e-004
766.67 5.9604e-004
783.33 -4.7803e-002
800. 0.73768
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TABLE 22Model (A4) > Directional_surface
Length [mm] [A] Directional Deformation_surface [mm]
0. -7.6421e-010
16.667 4.8262e-010
33.333 5.4577e-010
50. 5.2049e-010
66.667 5.3853e-010
83.333 5.6574e-010
100. 5.4297e-010
116.67 2.8065e-010
133.33 -2.1359e-010
150. -3.087e-010
166.67 -5.2962e-010
183.33 -4.9274e-010
200. -5.395e-010
216.67 -5.6337e-010
233.33 -5.9518e-010
250. -4.2458e-010
266.67 -4.4645e-010
283.33 -2.9048e-010
300. -5.9452e-011
316.67 2.1121e-010
333.33 4.7881e-010
350. 8.4609e-010
366.67 9.3522e-010
383.33 2.9953e-010
400. 2.6716e-010
416.67 -1.3239e-010
433.33 -3.8928e-010
450. -4.9093e-010
466.67 -4.1621e-010
483.33 -4.7927e-010
500. -4.3569e-010
516.67 -2.681e-010
533.33 -1.2371e-010
550. 5.7361e-011
566.67 2.3816e-010
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Directional_neutral_axis
FIGURE 14Model (A4) > Directional_neutral_axis
TABLE 23Model (A4) > Directional_neutral_axis
583.33 -3.9544e-011
600. -5.7555e-010
616.67 -5.8052e-010
633.33 -7.274e-010
650. -6.1076e-010
666.67 -6.2657e-010
683.33 -6.1923e-010
700. -5.8061e-010
716.67 -4.3326e-010
733.33 -3.9528e-010
750. -2.6117e-010
766.67 -7.2575e-011
783.33 1.4218e-010
800. 3.6791e-010
Length [mm] [A] Directional Deformation_neutral_axis [mm]
0. -1.6994e-010
16.667 -2.4444e-010
33.333 -3.6065e-010
50. -3.9904e-010
66.667 -4.438e-010
83.333 -5.7914e-010
100. -7.0832e-010
116.67 -9.2053e-010
133.33 -1.1752e-009
150. -1.307e-009
166.67 -1.4482e-009
183.33 -1.4761e-009
200. -1.5183e-009
216.67 -1.5128e-009
233.33 -1.5411e-009
250. -1.2977e-009
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stress_surface
FIGURE 15Model (A4) > stress_surface
266.67 -1.1742e-009
283.33 -9.7646e-010
300. -7.3045e-010
316.67 -3.7863e-010
333.33 -1.9498e-010
350. -4.9713e-011
366.67 -1.8829e-010
383.33 -4.1476e-010
400. -4.8356e-010
416.67 -7.4825e-010
433.33 -1.0533e-009
450. -1.0748e-009
466.67 -9.2145e-010
483.33 -9.1506e-010
500. -7.9111e-010
516.67 -5.557e-010
533.33 -3.872e-010
550. -3.3882e-010
566.67 -3.5448e-010
583.33 -5.6036e-010
600. -8.0188e-010
616.67 -8.5531e-010
633.33 -9.2289e-010
650. -8.895e-010
666.67 -8.7675e-010
683.33 -8.4752e-010
700. -8.0896e-010
716.67 -6.3208e-010
733.33 -4.971e-010
750. -3.2743e-010
766.67 -1.2552e-010
783.33 7.097e-011
800. 2.2685e-010
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TABLE 24Model (A4) > stress_surface
stress_neutral_axis
FIGURE 16Model (A4) > stress_neutral_axis
Length [mm] [A] normal stress surface [MPa]
0. 1.8789
16.667 -0.13083
33.333 -3.3255e-002
50. -2.1785e-002
66.667 -2.2684e-002
83.333
-2.2672e-002100.
116.67
133.33 -2.2671e-002
150. -2.2673e-002
166.67 -2.2672e-002
183.33 -2.2673e-002
200. -2.2669e-002
216.67 -2.267e-002
233.33 -2.2672e-002
250. -2.2671e-002
266.67 -2.2673e-002
283.33 -2.2672e-002
300. -2.267e-002
316.67 -2.2669e-002
333.33 -2.2671e-002
350. -2.2672e-002
366.67 -2.2671e-002
383.33 -2.2674e-002
400. -2.2673e-002
416.67 -2.2674e-002
433.33 -2.2672e-002
450. -2.2673e-002
466.67 -2.2672e-002
483.33 -2.2675e-002
500. -2.267e-002
516.67 -2.2674e-002
533.33 -2.267e-002
550. -2.2671e-002
566.67 -2.2673e-002
583.33 -2.2672e-002
600. -2.267e-002
616.67 -2.2673e-002
633.33-2.2672e-002
650.
666.67 -2.267e-002
683.33 -2.2671e-002
700.-2.2672e-002
716.67
733.33 -2.2684e-002
750. -2.1786e-002
766.67 -3.3446e-002
783.33 -0.13087
800. 1.8727
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TABLE 25Model (A4) > stress_neutral_axis
Length [mm] [A] normal stress neutral axis [MPa]
0. 0.76191
16.667 -5.3634e-002
33.333 6.7448e-004
50. 4.1796e-004
66.667 -1.2022e-005
83.333 -3.0787e-007
100. 1.6799e-007
116.67 -6.9296e-007
133.33 8.2043e-007
150. -4.3923e-007
166.67 -3.3858e-007
183.33 4.2674e-007
200. -2.5318e-007
216.67 -6.765e-007
233.33 -4.5586e-007
250. 2.6538e-007
266.67 5.249e-007
283.33 -1.6241e-007
300. -1.4212e-006
316.67 2.2965e-007
333.33 1.1439e-007
350. 1.0113e-007
366.67 -8.3339e-007
383.33 2.5294e-006
400. -1.8354e-007
416.67 1.8069e-006
433.33 -4.7399e-007
450. 1.8341e-007
466.67 -1.8274e-007
483.33 8.1933e-007
500. 1.1121e-007
516.67 -7.2178e-007
533.33 5.1367e-007
550. 1.3021e-007
566.67 1.4067e-007
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Material Data
583.33 -6.741e-007
600. 7.1839e-007
616.67 4.5611e-008
633.33 -6.2942e-007
650. 1.4676e-008
666.67 2.5293e-007
683.33 -5.9362e-007
700. -1.0444e-006
716.67 -4.5694e-007
733.33 -1.1415e-005
750. 4.1518e-004
766.67 5.9604e-004
783.33 -4.7803e-002
800. 0.73768
Structural Steel
TABLE 26Structural Steel > Constants
TABLE 27Structural Steel > Color
TABLE 28Structural Steel > Compressive Ultimate Strength
TABLE 29Structural Steel > Compressive Yield Strength
TABLE 30Structural Steel > Tensile Yield Strength
TABLE 31Structural Steel > Tensile Ultimate Strength
TABLE 32Structural Steel > Isotropic Secant Coefficient of Thermal Expansion
TABLE 33Structural Steel > Alternating Stress Mean Stress
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
Red Green Blue
132 139 179
Compressive Ultimate Strength MPa
0
Compressive Yield Strength MPa
250
Tensile Yield Strength MPa
250
Tensile Ultimate Strength MPa
460
Zero-Thermal-Strain Reference Temperature C
22
Alternating Stress MPa Cycles Mean Stress MPa
3999 10 0
2827 20 0
1896 50 0
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TABLE 34Structural Steel > Strain-Life Parameters
TABLE 35Structural Steel > Isotropic Elasticity
TABLE 36Structural Steel > Isotropic Relative Permeability
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
Strength Coefficient MPa
Strength Exponent
DuctilityCoefficient
Ductility Exponent
Cyclic Strength Coefficient MPa
Cyclic Strain Hardening Exponent
920 -0.106 0.213 -0.47 1000 0.2
Temperature C Young's Modulus MPa Poisson's Ratio Bulk Modulus MPa Shear Modulus MPa
2.1e+005 0.3 1.75e+005 80769
Relative Permeability
10000
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Project
First Saved Monday, January 23, 2017
Last Saved Monday, January 23, 2017
Product Version 17.2 Release
Save Project Before Solution No
Save Project After Solution No
Page 1 of 24Project
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Contents
� Units
� Model (A4)
� Geometry
� SYS\Solid
� Construction Geometry
� Paths
� Coordinate Systems
� Mesh
� Static Structural (A5)
� Analysis Settings
� Loads
� Solution (A6)
� Solution Information
� Results
� Directional_surface
� Directional_neutral_axis
� stress_surface
� stress_neutral_axis
� Material Data
� Structural Steel
Units
TABLE 1
Model (A4)
Unit System Metric (mm, kg, N, s, mV, mA) Degrees rad/s Celsius
Angle Degrees
Rotational Velocity rad/s
Temperature Celsius
Geometry
TABLE 2Model (A4) > Geometry
Object Name Geometry
State Fully Defined
Definition
Source C:\Users\xwang3\Documents\distributed_load_beam_files\dp0\SYS\DM\SYS.scdoc
Type SpaceClaim
Length Unit Meters
Element Control Program Controlled
Display Style Body Color
Bounding Box
Length X 20. mm
Length Y 800. mm
Length Z 20. mm
Properties
Volume 3.2e+005 mm³
Mass 2.512 kg
Scale Factor Value 1.
Statistics
Bodies 1
Active Bodies 1
Nodes 14465
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TABLE 3Model (A4) > Geometry > Parts
Elements 2560
Mesh Metric None
Basic Geometry Options
Solid Bodies Yes
Surface Bodies Yes
Line Bodies Yes
Parameters Independent
Parameter Key
Attributes Yes
Attribute Key
Named Selections Yes
Named Selection Key
Material Properties Yes
Advanced Geometry Options
Use Associativity Yes
Coordinate Systems Yes
Coordinate System Key
Reader Mode Saves Updated File No
Use Instances Yes
Smart CAD Update Yes
Compare Parts On Update No
Attach File Via Temp File Yes
Temporary Directory C:\Users\xwang3\AppData\Local\Temp
Analysis Type 3-D
Mixed Import Resolution None
Decompose Disjoint Geometry Yes
Enclosure and Symmetry Processing Yes
Object Name SYS\Solid
State Meshed
Graphics Properties
Visible Yes
Transparency 1
Definition
Suppressed No
Stiffness Behavior Flexible
Coordinate System Default Coordinate System
Reference Temperature By Environment
Behavior None
Material
Assignment Structural Steel
Nonlinear Effects Yes
Thermal Strain Effects Yes
Bounding Box
Length X 20. mm
Length Y 800. mm
Length Z 20. mm
Properties
Volume 3.2e+005 mm³
Mass 2.512 kg
Centroid X 1. mm
Centroid Y -7.0586e-015 mm
Centroid Z 5.5145e-017 mm
Moment of Inertia Ip1 1.3406e+005 kg·mm²
Moment of Inertia Ip2 167.47 kg·mm²
Moment of Inertia Ip3 1.3406e+005 kg·mm²
Statistics
Nodes 14465
Elements 2560
Mesh Metric None
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TABLE 4Model (A4) > Construction Geometry
TABLE 5Model (A4) > Construction Geometry > Paths
CAD Attributes
PartTolerance: 0.00000001
Color:143.175.143
Object Name Construction Geometry
State Fully Defined
Display
Show Mesh No
Object Name Path Path 2
State Fully Defined
Definition
Path Type Two Points
Path Coordinate System Global Coordinate System
Number of Sampling Points 47.
Suppressed No
Start
Coordinate System Global Coordinate System
Start X Coordinate 1. mm
Start Y Coordinate -400. mm
Start Z Coordinate 10. mm 0. mm
Location Defined
End
Coordinate System Global Coordinate System
End X Coordinate 1. mm
End Y Coordinate -360. mm
End Z Coordinate 10. mm 0. mm
Location Defined
Coordinate Systems
TABLE 6Model (A4) > 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
Origin Z 0. mm
Directional Vectors
X Axis Data [ 1. 0. 0. ]
Y Axis Data [ 0. 1. 0. ]
Z Axis Data [ 0. 0. 1. ]
Mesh
TABLE 7Model (A4) > Mesh
Object Name Mesh
State Solved
Display
Display Style Body Color
Defaults
Physics Preference Mechanical
Relevance 0
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Static Structural (A5)
TABLE 8Model (A4) > Analysis
TABLE 9Model (A4) > Static Structural (A5) > Analysis Settings
Shape Checking Standard Mechanical
Element Midside Nodes Program Controlled
Sizing
Size Function Adaptive
Relevance Center Coarse
Element Size 5.0 mm
Initial Size Seed Active Assembly
Smoothing Medium
Transition Fast
Span Angle Center Coarse
Automatic Mesh Based Defeaturing On
Defeature Size Default
Minimum Edge Length 20.0 mm
Inflation
Use Automatic Inflation None
Inflation Option Smooth Transition
Transition Ratio 0.272
Maximum Layers 5
Growth Rate 1.2
Inflation Algorithm Pre
View Advanced Options No
Advanced
Number of CPUs for Parallel Part Meshing Program Controlled
Straight Sided Elements No
Number of Retries Default (4)
Rigid Body Behavior Dimensionally Reduced
Mesh Morphing Disabled
Triangle Surface Mesher Program Controlled
Topology Checking No
Pinch Tolerance Please Define
Generate Pinch on Refresh No
Statistics
Nodes 14465
Elements 2560
Mesh Metric None
Object Name Static Structural (A5)
State Solved
Definition
Physics Type Structural
Analysis Type Static Structural
Solver Target Mechanical APDL
Options
Environment Temperature 22. °C
Generate Input Only No
Object Name Analysis Settings
State Fully Defined
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
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TABLE 10Model (A4) > Static Structural (A5) > Loads
FIGURE 1Model (A4) > Static Structural (A5) > Force
Weak Springs Off
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:\Users\xwang3\Documents\distributed_load_beam_files\dp0\SYS\MECH\
Future Analysis None
Scratch Solver Files Directory
Save MAPDL db No
Delete Unneeded Files Yes
Nonlinear Solution No
Solver Units Active System
Solver Unit System nmm
Object Name Force Fixed Support Displacement
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 1 Face 1 Edge
Definition
Type Force Fixed Support Displacement
Define By Vector Components
Magnitude -80000 N (ramped)
Direction Defined
Suppressed No
Coordinate System Global Coordinate System
X Component 0. mm (ramped)
Y Component Free
Z Component 0. mm (ramped)
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FIGURE 2Model (A4) > Static Structural (A5) > Displacement
Solution (A6)
TABLE 11Model (A4) > Static Structural (A5) > Solution
Object Name Solution (A6)
State Solved
Adaptive Mesh Refinement
Max Refinement Loops 3.
Refinement Depth 2.
Information
Status Done
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TABLE 12Model (A4) > Static Structural (A5) > Solution (A6) > Solution Information
TABLE 13Model (A4) > Static Structural (A5) > Solution (A6) > Results
MAPDL Elapsed Time 7. s
MAPDL Memory Used 117. MB
MAPDL Result File Size 4.1875 MB
Post Processing
Beam Section Results No
Object Name Solution Information
State Solved
Solution Information
Solution Output Solver Output
Newton-Raphson Residuals 0
Identify Element Violations 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
Object Name
Directional Deformation
Equivalent Stress
Total Deformation
NormalStress
DirectionalDeformation_surface
DirectionalDeformation_neutral_axis
normalstress
surface
normal stressneutral
axis
State Solved
Scope
Scoping Method
Geometry Selection Path
Geometry All Bodies
Path Path Path 2 Path Path 2
Definition
TypeDirectional
Deformation
Equivalent(von-
Mises) Stress
Total Deformation
Normal Stress
Directional Deformation Normal Stress
Orientation Z Axis Y Axis X Axis
By Time
Display Time
Last
Coordinate System
Global Coordinate
SystemGlobal Coordinate System
Calculate Time
HistoryYes
Identifier
Suppressed No
Results
Minimum -190.83 mm 2.5 MPa 0. mm-6001.2
MPa-1.5284e-008 mm -7.6344e-009 mm
-3.7886 MPa
-1.2847MPa
Maximum 0. mm6000.9MPa
190.98 mm6001.2 MPa
1.1392e-008 mm -2.1575e-009 mm37.577 MPa
15.238MPa
Minimum Occurs On
SYS\Solid
Maximum Occurs On
SYS\Solid
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FIGURE 3Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation
TABLE 14Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation
FIGURE 4Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation > Figure
Information
Time 1. s
Load Step 1
Substep 1
Iteration Number
1
Integration Point Results
DisplayOption
Averaged Averaged Averaged
Average AcrossBodies
No No No
Graph Controls
X-Axis S
Time [s] Minimum [mm] Maximum [mm]
1. -190.83 0.
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FIGURE 5Model (A4) > Static Structural (A5) > Solution (A6) > Equivalent Stress
TABLE 15Model (A4) > Static Structural (A5) > Solution (A6) > Equivalent Stress
FIGURE 6
Time [s] Minimum [MPa] Maximum [MPa]
1. 2.5 6000.9
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Model (A4) > Static Structural (A5) > Solution (A6) > Total Deformation
TABLE 16Model (A4) > Static Structural (A5) > Solution (A6) > Total Deformation
FIGURE 7Model (A4) > Static Structural (A5) > Solution (A6) > Normal Stress
TABLE 17Model (A4) > Static Structural (A5) > Solution (A6) > Normal Stress
FIGURE 8
Time [s] Minimum [mm] Maximum [mm]
1. 0. 190.98
Time [s] Minimum [MPa] Maximum [MPa]
1. -6001.2 6001.2
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Model (A4) > Static Structural (A5) > Solution (A6) > Normal Stress > Figure
FIGURE 9Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_surface
TABLE 18Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_surface
Length [mm] Value [mm]
0. -1.5284e-008
0.83333 -1.409e-008
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FIGURE 10Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_neutral_axis
1.6667 -1.2892e-008
2.5 -1.1689e-008
3.3333 -1.0481e-008
4.1667 -9.2691e-009
5. -8.0523e-009
5.8333 -6.0478e-009
6.6667 -4.1835e-009
7.5 -2.4596e-009
8.3333 -8.7589e-010
9.1667 5.6751e-010
10. 1.8706e-009
10.833 3.2688e-009
11.667 4.5705e-009
12.5 5.7759e-009
13.333 6.8848e-009
14.167 7.8973e-009
15. 8.8133e-009
15.833 9.2396e-009
16.667 9.6525e-009
17.5 1.0052e-008
18.333 1.0438e-008
19.167 1.0811e-008
20. 1.1171e-008
20.833 1.1154e-008
21.667 1.1158e-008
22.5 1.1184e-008
23.333 1.1232e-008
24.167 1.1301e-008
25. 1.1392e-008
25.833 1.1325e-008
26.667 1.1263e-008
27.5 1.1206e-008
28.333 1.1154e-008
29.167 1.1107e-008
30. 1.1064e-008
30.833 1.1026e-008
31.667 1.0989e-008
32.5 1.0952e-008
33.333 1.0916e-008
34.167 1.088e-008
35. 1.0844e-008
35.833 1.0823e-008
36.667 1.0776e-008
37.5 1.0703e-008
38.333 1.0605e-008
39.167 1.048e-008
40. 1.033e-008
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TABLE 19Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_neutral_axis
Length [mm] Value [mm]
0. -3.3988e-009
0.83333 -3.4195e-009
1.6667 -3.3491e-009
2.5 -3.1878e-009
3.3333 -2.9354e-009
4.1667 -2.5919e-009
5. -2.1575e-009
5.8333 -2.1803e-009
6.6667 -2.1947e-009
7.5 -2.2007e-009
8.3333 -2.1983e-009
9.1667 -2.1875e-009
10. -2.1682e-009
10.833 -2.5681e-009
11.667 -2.9575e-009
12.5 -3.3364e-009
13.333 -3.705e-009
14.167 -4.063e-009
15. -4.4107e-009
15.833 -4.6612e-009
16.667 -4.8887e-009
17.5 -5.093e-009
18.333 -5.2743e-009
19.167 -5.4324e-009
20. -5.5674e-009
20.833 -5.6989e-009
21.667 -5.8132e-009
22.5 -5.9104e-009
23.333 -5.9904e-009
24.167 -6.0533e-009
25. -6.0991e-009
25.833 -6.3017e-009
26.667 -6.469e-009
27.5 -6.601e-009
28.333 -6.6978e-009
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FIGURE 11Model (A4) > Static Structural (A5) > Solution (A6) > normal stress surface
TABLE 20Model (A4) > Static Structural (A5) > Solution (A6) > normal stress surface
29.167 -6.7592e-009
30. -6.7854e-009
30.833 -6.9047e-009
31.667 -7.0157e-009
32.5 -7.1184e-009
33.333 -7.2128e-009
34.167 -7.2989e-009
35. -7.3767e-009
35.833 -7.4176e-009
36.667 -7.4593e-009
37.5 -7.5019e-009
38.333 -7.5452e-009
39.167 -7.5894e-009
40. -7.6344e-009
Length [mm] Value [MPa]
0. 37.577
0.83333 36.274
1.6667 34.97
2.5 33.667
3.3333 32.364
4.1667 31.06
5. 29.757
5.8333 26.327
6.6667 22.896
7.5 19.466
8.3333 16.036
9.1667 12.606
10. 9.1753
10.833 7.3077
11.667 5.4401
12.5 3.5724
13.333 1.7048
14.167 -0.16284
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FIGURE 12Model (A4) > Static Structural (A5) > Solution (A6) > normal stress neutral axis
TABLE 21Model (A4) > Static Structural (A5) > Solution (A6) > normal stress neutral axis
15. -2.0305
15.833 -2.3235
16.667 -2.6165
17.5 -2.9096
18.333 -3.2026
19.167 -3.4956
20. -3.7886
20.833 -3.5143
21.667 -3.2399
22.5 -2.9655
23.333 -2.6911
24.167 -2.4168
25. -2.1424
25.833 -1.9495
26.667 -1.7567
27.5 -1.5639
28.333 -1.371
29.167 -1.1782
30. -0.98536
30.833 -0.90529
31.667 -0.82523
32.5 -0.74516
33.333 -0.66509
34.167 -0.58503
35. -0.50496
35.833 -0.48853
36.667 -0.4721
37.5 -0.45567
38.333 -0.43924
39.167 -0.42281
40. -0.40639
Length [mm] Value [MPa]
0. 15.238
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Directional_surface
FIGURE 13Model (A4) > Directional_surface
0.83333 12.484
1.6667 9.7306
2.5 6.9767
3.3333 4.2229
4.1667 1.4691
5. -1.2847
5.8333 -0.66235
6.6667 -4.0005e-002
7.5 0.58234
8.3333 1.2047
9.1667 1.827
10. 2.4494
10.833 1.839
11.667 1.2287
12.5 0.61835
13.333 8.0011e-003
14.167 -0.60234
15. -1.2127
15.833 -1.1427
16.667 -1.0727
17.5 -1.0027
18.333 -0.93267
19.167 -0.86266
20. -0.79266
20.833 -0.71657
21.667 -0.64049
22.5 -0.5644
23.333 -0.48831
24.167 -0.41223
25. -0.33614
25.833 -0.28834
26.667 -0.24053
27.5 -0.19273
28.333 -0.14492
29.167 -9.7115e-002
30. -4.931e-002
30.833 -3.361e-002
31.667 -1.791e-002
32.5 -2.2102e-003
33.333 1.349e-002
34.167 2.9189e-002
35. 4.4889e-002
35.833 4.4357e-002
36.667 4.3824e-002
37.5 4.3291e-002
38.333 4.2758e-002
39.167 4.2225e-002
40. 4.1692e-002
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TABLE 22Model (A4) > Directional_surface
Length [mm] [A] Directional Deformation_surface [mm]
0. -1.5284e-008
0.83333 -1.409e-008
1.6667 -1.2892e-008
2.5 -1.1689e-008
3.3333 -1.0481e-008
4.1667 -9.2691e-009
5. -8.0523e-009
5.8333 -6.0478e-009
6.6667 -4.1835e-009
7.5 -2.4596e-009
8.3333 -8.7589e-010
9.1667 5.6751e-010
10. 1.8706e-009
10.833 3.2688e-009
11.667 4.5705e-009
12.5 5.7759e-009
13.333 6.8848e-009
14.167 7.8973e-009
15. 8.8133e-009
15.833 9.2396e-009
16.667 9.6525e-009
17.5 1.0052e-008
18.333 1.0438e-008
19.167 1.0811e-008
20. 1.1171e-008
20.833 1.1154e-008
21.667 1.1158e-008
22.5 1.1184e-008
23.333 1.1232e-008
24.167 1.1301e-008
25. 1.1392e-008
25.833 1.1325e-008
26.667 1.1263e-008
27.5 1.1206e-008
28.333 1.1154e-008
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Directional_neutral_axis
FIGURE 14Model (A4) > Directional_neutral_axis
TABLE 23Model (A4) > Directional_neutral_axis
29.167 1.1107e-008
30. 1.1064e-008
30.833 1.1026e-008
31.667 1.0989e-008
32.5 1.0952e-008
33.333 1.0916e-008
34.167 1.088e-008
35. 1.0844e-008
35.833 1.0823e-008
36.667 1.0776e-008
37.5 1.0703e-008
38.333 1.0605e-008
39.167 1.048e-008
40. 1.033e-008
Length [mm] [A] Directional Deformation_neutral_axis [mm]
0. -3.3988e-009
0.83333 -3.4195e-009
1.6667 -3.3491e-009
2.5 -3.1878e-009
3.3333 -2.9354e-009
4.1667 -2.5919e-009
5. -2.1575e-009
5.8333 -2.1803e-009
6.6667 -2.1947e-009
7.5 -2.2007e-009
8.3333 -2.1983e-009
9.1667 -2.1875e-009
10. -2.1682e-009
10.833 -2.5681e-009
11.667 -2.9575e-009
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stress_surface
FIGURE 15Model (A4) > stress_surface
12.5 -3.3364e-009
13.333 -3.705e-009
14.167 -4.063e-009
15. -4.4107e-009
15.833 -4.6612e-009
16.667 -4.8887e-009
17.5 -5.093e-009
18.333 -5.2743e-009
19.167 -5.4324e-009
20. -5.5674e-009
20.833 -5.6989e-009
21.667 -5.8132e-009
22.5 -5.9104e-009
23.333 -5.9904e-009
24.167 -6.0533e-009
25. -6.0991e-009
25.833 -6.3017e-009
26.667 -6.469e-009
27.5 -6.601e-009
28.333 -6.6978e-009
29.167 -6.7592e-009
30. -6.7854e-009
30.833 -6.9047e-009
31.667 -7.0157e-009
32.5 -7.1184e-009
33.333 -7.2128e-009
34.167 -7.2989e-009
35. -7.3767e-009
35.833 -7.4176e-009
36.667 -7.4593e-009
37.5 -7.5019e-009
38.333 -7.5452e-009
39.167 -7.5894e-009
40. -7.6344e-009
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TABLE 24Model (A4) > stress_surface
Length [mm] [A] normal stress surface [MPa]
0. 37.577
0.83333 36.274
1.6667 34.97
2.5 33.667
3.3333 32.364
4.1667 31.06
5. 29.757
5.8333 26.327
6.6667 22.896
7.5 19.466
8.3333 16.036
9.1667 12.606
10. 9.1753
10.833 7.3077
11.667 5.4401
12.5 3.5724
13.333 1.7048
14.167 -0.16284
15. -2.0305
15.833 -2.3235
16.667 -2.6165
17.5 -2.9096
18.333 -3.2026
19.167 -3.4956
20. -3.7886
20.833 -3.5143
21.667 -3.2399
22.5 -2.9655
23.333 -2.6911
24.167 -2.4168
25. -2.1424
25.833 -1.9495
26.667 -1.7567
27.5 -1.5639
28.333 -1.371
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stress_neutral_axis
FIGURE 16Model (A4) > stress_neutral_axis
TABLE 25Model (A4) > stress_neutral_axis
29.167 -1.1782
30. -0.98536
30.833 -0.90529
31.667 -0.82523
32.5 -0.74516
33.333 -0.66509
34.167 -0.58503
35. -0.50496
35.833 -0.48853
36.667 -0.4721
37.5 -0.45567
38.333 -0.43924
39.167 -0.42281
40. -0.40639
Length [mm] [A] normal stress neutral axis [MPa]
0. 15.238
0.83333 12.484
1.6667 9.7306
2.5 6.9767
3.3333 4.2229
4.1667 1.4691
5. -1.2847
5.8333 -0.66235
6.6667 -4.0005e-002
7.5 0.58234
8.3333 1.2047
9.1667 1.827
10. 2.4494
10.833 1.839
11.667 1.2287
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Material Data
12.5 0.61835
13.333 8.0011e-003
14.167 -0.60234
15. -1.2127
15.833 -1.1427
16.667 -1.0727
17.5 -1.0027
18.333 -0.93267
19.167 -0.86266
20. -0.79266
20.833 -0.71657
21.667 -0.64049
22.5 -0.5644
23.333 -0.48831
24.167 -0.41223
25. -0.33614
25.833 -0.28834
26.667 -0.24053
27.5 -0.19273
28.333 -0.14492
29.167 -9.7115e-002
30. -4.931e-002
30.833 -3.361e-002
31.667 -1.791e-002
32.5 -2.2102e-003
33.333 1.349e-002
34.167 2.9189e-002
35. 4.4889e-002
35.833 4.4357e-002
36.667 4.3824e-002
37.5 4.3291e-002
38.333 4.2758e-002
39.167 4.2225e-002
40. 4.1692e-002
Structural Steel
TABLE 26Structural Steel > Constants
TABLE 27Structural Steel > Color
TABLE 28Structural Steel > Compressive Ultimate Strength
TABLE 29Structural Steel > Compressive Yield Strength
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
Red Green Blue
132 139 179
Compressive Ultimate Strength MPa
0
Compressive Yield Strength MPa
250
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TABLE 30Structural Steel > Tensile Yield Strength
TABLE 31Structural Steel > Tensile Ultimate Strength
TABLE 32Structural Steel > Isotropic Secant Coefficient of Thermal Expansion
TABLE 33Structural Steel > Alternating Stress Mean Stress
TABLE 34Structural Steel > Strain-Life Parameters
TABLE 35Structural Steel > Isotropic Elasticity
TABLE 36Structural Steel > Isotropic Relative Permeability
Tensile Yield Strength MPa
250
Tensile Ultimate Strength MPa
460
Zero-Thermal-Strain Reference Temperature C
22
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
Strength Coefficient MPa
Strength Exponent
DuctilityCoefficient
Ductility Exponent
Cyclic Strength Coefficient MPa
Cyclic Strain Hardening Exponent
920 -0.106 0.213 -0.47 1000 0.2
Temperature C Young's Modulus MPa Poisson's Ratio Bulk Modulus MPa Shear Modulus MPa
2.1e+005 0.3 1.75e+005 80769
Relative Permeability
10000
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