Stressed Bar Problem: This problem illustrates that the factor of safety for a machine element depends on the particular point selected for analysis. Here you are to compare factors of safety, based upon the distortion-energy theory, for stress elements at A and B of the member shown in the figure. This bar is made of AISI 1006 cold-drawn steel and is loaded by the forces F = 0.55 kN, P = 8.0 kN, and T = 30 N· m. Joseph Shigley and Charles Mischke. Mechanical Engineering Design 5th ed. New York: McGraw Hill, May 2002.
Transcript
Stressed Bar
Problem:
This problem illustrates that the factor of safety for a machine element depends on theparticular point selected for analysis. Here you are to compare factors of safety, basedupon the distortion-energy theory, for stress elements at A and B of the member shownin the figure. This bar is made of AISI 1006 cold-drawn steel and is loaded by the forcesF = 0.55 kN, P = 8.0 kN, and T = 30 N· m.
Joseph Shigley and Charles Mischke. Mechanical Engineering Design5th ed. New York: McGraw Hill, May 2002.
Stressed BarOverview
Outcomes1) Learn how to start Ansys 8.0 2) Gain familiarity with the graphical user interface (GUI)3) Learn how to create and mesh a simple geometry4) Learn how to apply boundary constraints and solve problems
Tutorial OverviewThis tutorial is divided into six parts:
1) Tutorial Basics2) Starting Ansys3) Preprocessing4) Solution5) Post-Processing6) Hand Calculations
Anticipated time to complete this tutorial: 1 hour
AudienceThis tutorial assumes minimal knowledge of ANSYS 8.0; therefore, it goes into moderatedetail to explain each step. More advanced ANSYS 8.0 users should be able to completethis tutorial fairly quickly.
Prerequisites1) ANSYS 8.0 in house “Structural Tutorial”
Objectives1) Model the bar in ANSYS 8.02) Analyze the bar for appropriate stresses
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Stressed BarTutorial Basics
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In this tutorial:Instructions appear on the left.
Visual aids corresponding to the textappear on the right.
All commands on the toolbars arelabeled. However, only operationsapplicable to the tutorial are explained.
The instructions should be used as follows:
Bold > Text in bold are buttons, options, or selections that the user needs to click on
Example: > Preprocessor > Element Type > Add/Edit/DeleteFile would mean to follow the options as shown to the right to get you to the Element Types window
Italics Text in italics are hints and notes
MB1 Click on the left mouse buttonMB2 Click on the middle mouse
buttonMB3 Click on the right mouse
button
Some basic ANSYS functions are:
To rotate the models use Ctrl and MB3.
To zoom use Ctrl and MB2 and move themouse up and down.
To translate the models use Ctrl and MB1.
Stressed BarStarting Ansys
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For this tutorial the windows version ofANSYS 8.0 will be demonstrated. The pathbelow is one example of how to accessANSYS; however, this path will not be thesame on all computers.
For Windows XP start ANSYS by eitherusing:
> Start > All Programs > ANSYS 8.0> ANSYSor the desktop icon (right) if present.
Note: The path to start ANSYS 8.0 may be different foreach computer. Check with your local network manager tofind out how to start ANSYS 8.0.
Stressed BarStarting Ansys
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Once ANSYS 8.0 is loaded, two separatewindows appear: the main ANSYSAdvanced Utility Window and the ANSYSOutput Window.
The ANSYS Advanced Utility Window,also known as the Graphical User Interface(GUI), is the location where all the userinterface takes place.
The Output Window documents all actionstaken, displays errors, and solver status.
Graphical User Interface
Output Window
Stressed BarStarting Ansys
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The main utility window can be broken upinto three areas. A short explanation of eachwill be given.
First is the Utility Toolbar:
From this toolbar you can use the commandline approach to ANSYS and access multiplemenus that you can’t get to from the mainmenu.
Note: It would be beneficial to take some time and explorethese pull down menus and familiarize yourself with them.
Second is the ANSYS Main Menu as shownto the right. This menu is designed to use atop down approach and contains all thesteps and options necessary to properly pre-process, solve, and postprocess a model.
Third is the Graphical Interface windowwhere all geometry, boundary conditions,and results are displayed.
The tool bar located on the right hand sidehas all the visual orientation tools that areneeded to manipulate your model.
Stressed BarStarting Ansys
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With ANSYS 8.0 open select> File > Change Jobname
and enter a new job name in the blank fieldof the change jobname window.
Enter the problem title for this tutorial.> OK
In order to know where all the output filesfrom ANSYS will be placed, the workingdirectory must be set in order to avoid usingthe default folder: C:\Documents andSettings.
> File > Change Directory > then select the location that you wantall of the ANSYS files to be saved.
Be sure to change the working directory atthe beginning of every problem.
With the jobname and directory, set theANSYS database (.db) file can be given atitle. Following the same steps as you didto change the jobname and the directory,give the model a title.
Stressed BarPreprocessing
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To begin the analysis, a preference needs tobe set.
> Main Menu > Preferences
Place a check mark next to the Structuralbox. This determines the type of analysisthat will be performed in ANSYS.
> Ok
The ANSYS Main Menu should now beopened. Click once on the “+” sign next toPreprocessor.
> Main Menu > Preprocessor
The Preprocessor options currently avail-able are displayed in the expansion of theMain Menu tree as shown to the right.
Stressed BarPreprocessing
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As mentioned previously, the ANSYS MainMenu is designed in such a way that oneshould start at the top and work towards thebottom of the menu in preparing, solving,and analyzing your model.
Note: This procedure will be shown throughout the tuto-rial.
Select the “+” next to Element Type or clickon Element Type. The extension of themenu is shown to the right.
> Element Type
Select Add/Edit/Delete and the Elementtype window appears. Select add and theLibrary of Element Types window appears.
> ADD/EDIT/DELETE > Add
In this window, select the types of elementsto be defined and used for this problem.
For this model Pipe16 elements will be used. > Pipe > Elast straight16> Ok
In the Element Types window Type 1Pipe16 should be visible signaling that theelement type has been chosen.
Close the Element Types window.> Close
Stressed BarPreprocessing
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The properties for the pipe 16 elements needto be chosen. This is done by adding RealConstants.
> Preprocessor > Real Constants > Add/Edit/Delete
The Real Constants window should appear.Select add to create a new set.
> Add
The Element Type for Real Constants win-dow should appear. From this window,select Pipe16 as the element type.
> Type 1 Pipe16 > OK
The Real Constant Set Number 1, forPIPE16 window will appear. From this win-dow you can interactively customize the ele-ment type.
The problem states that the outside diame-ter of the first shaft should be 0.02 meter.Since the pin is a solid, the thickness of theelements should be equal to the radius ofthe outside diameter (.01 meter).
Enter the values into the table, as shown tothe right.
> OK
Close the Real Constant window.> Close
Stressed BarPreprocessing
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The material properties for the Pipe16 ele-ments now need to be defined.
> Preprocessor > Material Props > Material Models
The Define Material Models Behavior win-dow should now be open.
This window has many different possibili-ties for defining the materials for yourmodel. We will use isotopic linearly elasticstructural properties.
Select the following from the MaterialModels Available window:
> Structural > Linear > Elastic > Isotropic
The window titled Linear isotropicProperties for Material Number 1 nowappears.
Enter 209e9 (209 Gpa) in for EX (Young'sModulus) and 0.3 for PRXY (Poisson’sRatio).
> OK
Close the Define Material Model Behaviorwindow.
> Material > Exit
Stressed BarPreprocessing
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The next step is to define the keypoints(KP’s) where loads and constraints will beapplied:
> Preprocessor > Modeling > Create > Keypoints > In Active CS
The Create Keypoints in Active CS win-dow will now appear. Here the KP’s will beassigned numbers and their respective(XYZ) coordinates.
Enter the KP numbers and coordinates forthe pin definition. Select Apply after eachKP has been defined.
Note: Be sure to change the keypoint number every timeyou click apply. If you don’t it will overwrite the last key-point you entered with the new coordinates.
This tutorial will use a different coordinatenotation than the one shown in the problemstatement.
KP # 1: X = 0, Y = 0, Z = 0> Apply
KP # 2: X = 0, Y = 0, Z = .1
Select Ok when completed.
If a mistake was made in creating the key-points, select:
> Preprocessor > Modeling > Delete > Keypoints
Select the inappropriate KP’s and select Ok.
The created KP’s should look similar to theexample to the right except the KP’s couldbe labeled with the KP numbers.
Stressed BarPreprocessing
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At times it will be helpful to turn on the key-point numbers.
> PlotCtrls > Numbering > put a checkmark next to keypointnumbers > OK
Other numbers (for lines, areas, etc..) can beturned on in a similar manner.
The Create Straight Lines window shouldappear. You will create 1 line. Create line 1between the two keypoints.
For line 1: MB1 KP1 then MB1 KP 2.
Verify that the line only goes between thespecified keypoints. When you are donecreating the line click OK in the CreateStraight Lines window.
> Ok
If you make a mistake, use the following todelete the lines:
> Preprocessor > Modeling > Delete > Lines Only
Select the inappropriate line and select Ok.
Stressed BarPreprocessing
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Now that the model has been created, itneeds to be meshed. Only meshed modelscan be run to find a solution.
First, the element size will be specified.> Preprocessor > Meshing> Size Cntrls > Manual Size > Lines > All Lines
The Element Sizes on All Selected Lineswindow should appear. From this window,the number of elements per line segmentcan be defined along with the Element edgelength.
Approximately 20 elements along thelength of the line will produce reasonableresults.
Enter 20 into the No. of element divisionsfield
> Ok
Note: you could change the No. of element divisions aftercompleting the tutorial to a different value and rerun thesolution to see how it affects the results.
With the mesh parameters complete thelines representing the pin can now bemeshed. Select:
> Preprocessor > Meshing > Mesh > Lines
From the Mesh Lines window select PickAll.
> Pick all
This will select all the line segments andmesh them all at the same time.
The meshed line should appear similar tothe one shown to the right.
Stressed BarSolution
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We will now move into the solution phase.
Before applying the loads and constraints tothe bar, you will select a new static analysis
> Solution > Analysis Type > New Analysis
For type of analysis select static and selectOk.
The constraints will now be added.
For this problem, KP 1 needs to be con-strained in all six degrees of freedom.
To apply constraints select:> Solution > Define Loads > Apply > Structural > Displacement > On Keypoints
Select the Key point in need of constraints.Select KP 1 in the graphics window.
> Ok
The Apply U, ROT on KP’s large windowshould appear. From this window thedegrees of freedom can be specified.
To the right of DOFs to be constrainedselect ALL DOF.
> Apply.
Stressed BarSolution
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The constraints now appear at keypoint 1.
The loads will now be applied to the bar.> Solutions > Define Loads > Apply> Structural > Force/Moment > On Keypoints
The Apply F/M on KP’s window shouldappear.
Select KP 2 in the graphics window.> Apply
The expanded Apply F/M on KP’s windowshould appear. From this window the direc-tion of the force and magnitude can be spec-ified.
Stressed BarSolution
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Select FY for the Direction of force/moment.Select Constant value for Apply as.
Enter -550 in the Force/moment value fieldwhich will apply a 550 N force downward.
Verify that all the fields match those of thefigure shown to the right.
> Apply
Select FZ and enter 8000.> Apply
Select MZ and enter 30.> Ok
The fully loaded and constrained modelshould appear similar to the picture shownon the right.
Stressed BarSolution
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Before solving the problem, display the ele-ment in three dimensions.
> Plot Controls > Style > Size and Shape
The Size and Shape window opens. Clickthe check box next to Display of element toturn on the 3D image.
The next step in completion of the tutorial isto solve the current load step that has beencreated. Select:
> Solution > Solve > Current LS
The Solve Current Load Step window willappear. To begin the analysis select Ok.
The analysis should begin and when com-plete a Note window should appear thatstates the analysis is complete.
Close both the Note window and /STATUSCommand window.
Stressed BarPost Processing
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From the problem statement, we will esti-mate the maximum stress at point A (ontop of the bar) point B (on the side of thebar). To obtain the stress, select Nodalsolution from the drop down menu, Stressand Von Mises stress.
Select the contour icon and look at thestress value at point A
Notice that (as expected) there is a max atpoint A labeled MX. The numerical valueis shown at the value on the far right of thescale and also is labeled SMX in the upperleft corner of the screen. The value is 101MPa.
Stressed BarPost Processing
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To find the stress at Point B, we will look atthe stress in the x direction. Change theitem in results viewer from Von Mises to X-component of stress at replot the contours.Noticed that near point B is a minimumstress value labeled MN. This value is alsoshown in the upper left as SMN. The valueis 44.6MPa.
For AISI 1006 cold-drawn steel Sy = 330MPa.
The safety factor n = Sy/Smax.
For A, n = 330/101.56 = 3.25.For B, n = 330/44.6 = 7.19.
Stressed BarHand Calculations
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To find the factor of safety of the element A and B: At A:
