spring 2017 mae 4160 / mae 5160 homework # 2

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

https://www.youtube.com/watch?v=CTi1ru-pfi0

(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

Page 1 of 24Project

1/23/2017file:///C:/Users/xwang3/AppData/Roaming/Ansys/v172/Mechanical_Report/Mechanical_R...

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

Page 2 of 24Project


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


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


Statistics

Nodes 14465

Elements 2560

Mesh Metric None

CAD Attributes

PartTolerance: 0.00000001

Page 3 of 24Project


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


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


Defaults

Physics Preference Mechanical

Relevance 0

Shape Checking Standard Mechanical

Element Midside Nodes Program Controlled

Page 4 of 24Project


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

Page 5 of 24Project


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


X Component 0. mm (ramped)

Y Component Free

Z Component 0. mm (ramped)

Page 6 of 24Project


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

Page 7 of 24Project


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

Page 8 of 24Project


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.

Page 9 of 24Project


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

Page 10 of 24Project


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


1. 0. 9.549


1. -300.06 300.06



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



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



TABLE 19Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_neutral_axis


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



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



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


0. 0.76191



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



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



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



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



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



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



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



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



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


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


Bounding Box

Length X 20. mm

Length Y 800. mm

Length Z 20. mm

Properties


Mass 2.512 kg

Scale Factor Value 1.

Statistics

Bodies 1

Active Bodies 1

Nodes 14465

Page 2 of 24Project


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


Mass 2.512 kg

Centroid X 1. mm

Centroid Y -7.0586e-015 mm

Centroid Z 5.5145e-017 mm


Moment of Inertia Ip2 167.47 kg·mm²


Statistics

Nodes 14465

Elements 2560

Mesh Metric None

Page 3 of 24Project


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


Start X Coordinate 1. mm

Start Y Coordinate -400. mm

Start Z Coordinate 10. mm 0. mm

Location Defined

End


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


Defaults

Physics Preference Mechanical

Relevance 0

Page 4 of 24Project


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

Page 5 of 24Project


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


X Component 0. mm (ramped)

Y Component Free

Z Component 0. mm (ramped)

Page 6 of 24Project


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

Page 7 of 24Project


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

Page 8 of 24Project


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


1. -190.83 0.

Page 9 of 24Project


FIGURE 5Model (A4) > Static Structural (A5) > Solution (A6) > Equivalent Stress

TABLE 15Model (A4) > Static Structural (A5) > Solution (A6) > Equivalent Stress

FIGURE 6


1. 2.5 6000.9



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


1. 0. 190.98


1. -6001.2 6001.2



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


0. -1.5284e-008

0.83333 -1.409e-008



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



TABLE 19Model (A4) > Static Structural (A5) > Solution (A6) > Directional Deformation_neutral_axis


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



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


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



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


0. 15.238



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



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



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



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



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



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



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



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

