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Shear and Bending Moment

Problem:

For the loaded beam shown below, develop the corresponding shear force and bendingmoment diagrams. The beam is in equilibrium. For this problem L= 10 in.

Shear and Bending MomentOverview

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: 45 minutes

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) Learn how to define keypoints, lines, and elements 2) Learn how to apply structural constraints and loads 3) Learn how to find shear and bending moment diagrams

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Shear and Bending MomentTutorial 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.

Shear and Bending MomentStarting 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.


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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


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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, asshown to the right. This menu is designedto use a top down approach and contains allthe steps and options necessary to properlypreprocess, 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.


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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 avoidusing the 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.

Shear and Bending MomentPreprocessing

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To begin the analysis, a preference needs tobe set. Preferences allow you to apply filter-ing to the menu choices; ANSYS willremove or gray out functions that are notneeded. A structural analysis, for example,will not need all the options available for athermal, electromagnetic, or fluid dynamicanalysis.

> Main Menu > Preferences

Place a check marknext to theStructural box.

> OK

Look at the ANSYS Main Menu. Click onceon the “+” sign next to Preprocessor.

> Main Menu > Preprocessor

The Preprocessor options currently avail-able are displayed in the expansion of theMain Menu tree as shown to the right. Themost important preprocessing functions aredefining the element type, defining real con-straints and material properties, and model-ing and meshing the geometry.


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The ANSYS Main Menu is designed in sucha way that you should start at the beginningand work towards the bottom of the menuin preparing, solving, and analyzing yourmodel.

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 the problem. Fora pictorial description of what each elementcan be used for, click on the Help button.

For this model 2D Elastic Beam elementswill be used. The degrees of freedom forthis type of element are UX, UY, andROTZ, which will suit the needs of thisproblem.

> Beam > 2D Elastic 3> OK

In the Element Types window Type 1Beam3 should be visible signaling thatthe element type has been chosen.


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Before closing the Element Type window,and with Beam3 still highlighted select theOptions button.

> Options...

In the Beam3 Element Type Optionswindow change the the Member force+ moment output from Exclude out-put to Include output. This tellsANSYS to include the moment andforce information needed to create thediagrams.

> OK

Close the Element Types window.> Close

The properties for the Beam3 element needto be chosen. This is done by adding a RealConstant.

> 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 Beam 3 as the element type.

> Type 1 Beam3 > OK

The Real Constant window for Beam3 willappear. From this window you can interac-tively customize the element type.


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Enter the values into the table asshown at the right.

> OK

Close the Real Constants window.> Close

The material properties for the Beam3element need to be defined.

> Preprocessor > Material Props > Material Models

The Define Material Models Behavior win-dow should now be open.

We will use isotropic, linearly, elastic, struc-tural properties.

Select the following from the MaterialModels Available window:

> Structural > Linear > Elastic > Isotropic

The window titled Linear IsotropicProperties for Material Number 1 nowappears.

Enter 30e6 for EX (Young's Modulus) and0.3 for PRXY (Poission’s Ratio).

> OK

Close the Define Material Model Behaviorwindow.

> Material > Exit


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The next step is to define the keypoints(KP’s) that will help you build the rest ofyour model:

> Preprocessing > Modeling > Create > Keypoints > In Active CS

The Create Keypoints in Active CS win-dow will now appear. Here the KP’s will begiven numbers and their respective (XYZ)coordinates.

Enter the KP numbers and coordinatesthat will correctly define the beam.Select Apply after each KP has beendefined.

Note: Be sure to change the keypoint number everytime you click apply to finish adding a keypoint. Ifyou don’t it will replace the last keypoint you entered withthe new coordinates you just entered.

KP # 1: X=0, Y=0, Z=0KP # 2: X=2, Y=0, Z=0KP # 3: X=4, Y=0, Z=0KP # 4: X=6, Y=0, Z=0KP # 5: X=10, Y=0, Z=0

Select OK when complete.

In case you make a mistake in creating thekeypoints, select:

> Preprocessing > Modeling > Delete > Keypoints

Select the incorrect KP’s and select OK.

Your screen should look similar to the exam-ple below.


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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.

At times it will also be helpful to have a listof keypoints (or nodes, lines, elements,loads, etc.). To generate a list of keypoints:

> List > Keypoint > Coordinates Only

A list similar to the one to theright should appear.

The next step is to create lines between theKP’s.

> Preprocessing > Modeling > Create > Lines > Lines > Straight Lines

The Create Straight Lines window shouldappear. You will create 4 lines. Create line 1between the first two keypoints.

For line 1: MB1 KP1 then MB1 KP 2.

The other lines will be created in a similarmanner.

For line 2: MB1 KP2 then MB1 KP 3.For line 3: MB1 KP3 then MB1 KP 4.For line 4: MB1 KP4 then MB1 KP 5.

Verify that each line only goes between thespecified keypoints. When you are donecreating the lines click ok in the CreateStraight Lines window.

> OK

If you make a mistake, use the followingsteps to delete the lines:

> Preprocessing > Modeling > Delete > Lines Only

You should now have something similar tothe image shown below.


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Now that the model has been created, itneeds to be meshed. Models must bemeshed before they can be solved. Modelsare meshed with elements.

First, the element size needs to be specified.> Preprocessing > Meshing > Size Cntrls > Manual Size > Lines > All Lines

The Element Sizes on All Selected Lineswindow should appear. From this window,the number of divisions per element can bedefined and also the element edge length.

Enter 0.1 into the Element edge length field.> OK

Note: you could change the element edge length after com-pleting the tutorial to a different value and rerun the solu-tion to see how it affects the results.

With the mesh parameters complete, thelines representing the beam can now bemeshed. Select:

> Preprocessing > Meshing > Mesh > Lines

From the Mesh Lines window select PickAll.

> Pick all

Selecting Pick all will mesh all of the linesegments that have been created.

The meshed line should appear similar tothe one shown below. This completes thepreprocessing phase.

Shear and Bending MomentSolution

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We will now move into the solution phase.

Before applying the loads and constraints tothe beam, we will select to start a new analy-sis:

> Solution > Analysis Type > New Analysis

For Type of Analysis select Static and selectOK.

The way this problem is setup, no con-straints need to be added. Other problemswhich ask you to find shear and bendingmoment diagrams may require the use ofconstraints.

The forces and moments will now be added.It will be easier to select the keypoints (thelocations of the forces and moments) if thekeypoint numbers are turned on as previ-ously explained. However, the current viewprobably shows just the elements and notthe keypoints. You can see both the elementsand the keypoints on the screen by selecting:

> Plot > Multiplots

To see just the keypoints;> Plot > Keypoints > Keypoints

Use the plot menu to view your model in theway that will make it easier to completeeach step in tutorial.


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The loads will now be applied to the beam.> Solutions > Define Loads > Apply> Structural > Force/Moment > On Keypoints

The Apply F/M on KPs window shouldnow appear.

Select KP1 (hint it might be hidden behindthe symbol for the coordinate system) andselect OK.

In the Apply F/M on KPs window that nowappears change the direction to of the forceto FY and give it a value of 400.

> Apply

Repeat these same steps to apply the restof the forces and moments. Moments areapplied in the same way except that in theApply F/M on KPs window MZ is chosenas the direction. Select Apply after eachone you create and close the window whenyou are done creating all of the them.

Location Direction ValueKP1 MZ 400KP2 FY -400KP2 MZ -400KP3 FY 200KP4 FY -200KP5 FY 400

When you are done, your screen shouldlook similar to the picture below.


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The distributed loads will now be applied tothe beam.

> Solutions > Define Loads > Apply> Structural > Pressure > On Beams

The Apply PRES on Beams window shouldappear.

Select all the elements between keypoints 2and 3 (there should be 20 in all).

> Apply

The expanded Apply Pressure on Beamswindow should appear. From this win-dow the direction of the pressure and itsmagnitude can be specified.

Enter 100 in the Pressure at Node I valuefield which will apply the pressure overthe beam from keypoints 2 to 3. A positiveentry in this field is defined as a down-ward pressure.

> OK

The first distributed load now appears onthe model.


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Add the other two distributed load in a sim-ilar manner. Use the same commands asshown, but with the following changes:

For the second distributed load select all ofthe elements between KP3 and KP4 (shouldbe 20 of them). Set the value at node I to be-100 (this will make the load act upward).

> OK

For the third distributed load select all of theelements between KP4 and KP5 (should be40 of them). Set the value at node I to be 100.

> OK

The model is now completed.


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If you wish to view a 3D picture of yourmodel select

> 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.

> OK

Now when you rotate your model usingCTRL + MB3 , the model should appear tobe 3D. You should see something similar tothe image below.

You are now ready to solve the model.


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The next step in completing this tutorial is tosolve the current load step that has been cre-ated. Select:

Solution > Solve > Current LS

The Solve Current Load Step window willappear. To begin the analysis select OK.

If a Verify window appearstelling that the load data pro-duced 1 warning, just selectYes to proceed with the solu-tion.

The analysis should begin and whencomplete a Note window should appearthat states the analysis is done.

Close both the Note window and /STATUSCommand window.

If your model is still in the 3-D view use theview icons on the right of the screen to bringthe model to a front view again.

Shear and Bending MomentPost Processing

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There are several different ways to view theresults of a solution. To find the shear andbending moment diagrams we define whatis called an element table and then plot acontour plot.

Defining an element table is nothing morethan a way of telling ANSYS which solutionitems you want to see.

To define an element table, select the follow-ing:

> General Postproc > Element Table> Define Table

The Element Table Data window nowappears. Select Add..

> Add...

We will define the element table items byusing the “By sequence num” option. Forthe Beam3 element, the sequence numbersfor the I moment (at left end of beam) andthe J moment (at right end of beam) are 6and 12. The sequence numbers for theforces in the Y direction are 2 and 8. Thesequence numbers can be found for any ele-ment in the help documentation. Simply doa search in help for the element that you areusing, and then scroll down in the text tofind the table that lists the sequence num-bers.


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Give the first item a label name of Imoment, select By sequence num-ber, select SMISC, and type in thenumber 6 as shown to the right.

> Apply

Give the second item a label name ofJ moment, select By sequence num-ber, select SMISC, and type in thenumber 12

> Apply

Give the third item a label name of I force, select By sequence number, selectSMISC, and type in the number 2 as shownto the right.

> Apply

Give the fourth item a label name of J force, select By sequence number, selectSMISC, and type in the number 8 as shownto the right.

> OK

When you are done you should have fouritems in the Element Table Data window.

Close the Element Table Data window.> Close


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The shear force diagram will now be plot-ted.

> General Postproc > Plot Results > Contour Plot > Line Elem Res

The Plot Line-Element Results windownow appears.

Select IFORCE the table item at node I andJFORCE as the table item at node J.

> OK

The shear force diagram is plotted on thescreen and shown below. From the dia-gram, the max and min shear force can eas-ily be seen.


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The bending moment diagram will now beplotted.

> General Postproc > Plot Results > Contour Plot > Line Elem Res

The Plot Line-Element Results windownow appears.

Select IMOMENT as the table item at nodeI and JMOMENT as the table item at node J.

> OK

The bending moment diagram is plotted onthe screen and shown below. From the dia-gram, the max and min bending momentcan easily be seen.

Shear and Bending MomentHand Calculations

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Generally, shear and bending moment diagrams can easily be constructed by hand forproblems such as the one shown in this tutorial. The purpose of the tutorial was to showhow to find shear and bending moment diagrams in ANSYS, so that the process couldthen be applied to more complex geometry and load conditions. Please note the nota-tion used for the hand calculations (shown at the bottom of the diagrams) as it explainswhy the shear diagram given by ANSYS and the one shown in the hand calculations areopposites.