ANSYS 1D Structural Beam Tutorial - Online Finite Element Analysis Consultancy Service

8/15/2019 ANSYS 1D Structural Beam Tutorial - Online Finite Element Analysis Consultancy Service

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ANSYS 1D Structural Beam Tutorial

Disclaimer:

This tutorial is an educational tool designed to assist those who wish to learn how to use the ANSYS finite element software package. It is not intended as a guide for determining suitable modelling methods or strategies for any

application. The authors of this tutorial have used their best efforts in preparing the tutorial. These efforts include thedevelopment, research and testing of the theories and computational models shown in the tutorial. The authors makeno warranty of any kind, express ed or implied, with regard to any text or models contained in this tutorial. The authorsshall not be liable in any event for incidental or consequential damages in connection with, or arising out of, thefurnishing, performance, or use of the text and models provided in this tutorial. There is no gaurantee that there areno mistakes or errors in the information provided and the authors assume no responsibility for the use of any of theinformation contained in this tutorial.

Overview

In this tutorial you will ex amine the deformation of a simple beam using ANSYS. We will examine three different loadcases: a vertical shear l oad, a distributed load and a bending moment. This example is loosely adapted from anexample in the book Prac tical Stress Analysis with Finite Elements (2nd Edition) by Bryan J. Mac Donald [4] and canbe found on pages 112 to 114 of that book. You will determine the deflection and slope of the beam due to the appliedloading and boundary co nditions. A one-dimensional structural beam element (often also known as a "simple beam"or "pure bending" elemen t) will be used for this analysis.

Case 1: Point Load on Centre of a Cantilever Beam

Figure 01 shows an overview of the beam problem for load case 1 (point load) and figure 02 shows a representativefinite element model for this load case.

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Figure 01: Overview of Simple Beam Problem with Vertical Point Load (Case 1)

Figure 02: Representative Finite Element Model of the Simple Beam Problem (Case 1)

The beam is 2 metres long with the left hand edge built into a thick wall and the centre of the beam is simplysupported. The free end of the beam supports a shear load of 40 kN and a bending moment of 20 kNm. The beam ismade from steel with E = 200 GPa and I = 4 x 10 -6 m 4 .

The relevant node and element data are given in the tables below. We will use SI system units for this tutorial: length= m, mass = kg, time = sec, force = N, stress/pressure = Pa.


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We can use the information in the tables above to define our nodes, elements and boundary conditions.

Step 1: Launch ANSYS

We have already covered how to launch ANSYS properly in tutorials 1 and 2. Please go back and re-read thesetutorials if you cannot remember how to do it.

Step 2: Define Element Type

1. In the Main Menu select Preprocessor > Element Type > Add/Edit/Delete

2. Click on Add in the dialog box that appears.

3.

4. Select Beam in the left hand menu and 2 node 188 in the right hand menu and then click on OK.5. This will define element type 1 as a BEAM 188 element. BEAM 188 is ac tually a 3D beam element but we are

going to use it as a 1D truss by later suppressing some of it's degrees of freedom6. Click Close to close the Element Type dialog box.


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Step 3: Define the Beam Cross Section

Unfortunately the problem definition doesn't actually specify which type of cross section the beam has. That isn't aproblem and we can work around it. We know that the beam cross section has a second moment of area of I = 4 x10 -6 m 4 so let's choose the simplest type of cross section to fit this second moment of area value. We will assumethat the beam has a rectangular cross section:

Figure 03: Calculating t he beam height from the given second moment of area

1. In the Main Menu select Preprocessor > Sections > Beam > Common Sections

2. The beam tool should appear as shown below. Enter a value of 0.0832358 for B and for H.


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3.

4. Click on OK to close the Beam Tool.

Step 4: Define the Material Behaviour

1. In the Main Menu click on Preprocessor > Material Props > Materia l Model s, the Define Material Model Behaviour dialog box will now appear.

2. Expand the options in the right hand pane of the dialog box: Structural > Linear > Isotropic

3. In the dialog box that pops up, enter suitable material parameters for steel ( E = 200 x 10 9 Pa, Poissons ratio= 0.3)

4. Click on Ok to close the dialog box in which you entered the material parameters.

5. Close the Define Material Model Behaviour dialog box by clicking on the X in the upper right corner.

Step 5: Define Nodes and Elements


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1. In the Main Menu click on Preprocessor > Modeling > Create > Nodes > In Active CS

2. In the dialog box that appears: enter the x and y coordinates for node 1 (i.e. 0,0) and click on Apply (note that Apply issues the command to create the node but keeps the dialog box open, clicking OK would also issuethe command to create the node but would close the dialog box).

3. Now enter the x and y coordinates for node 2 (i.e. 1,0) and click Apply

4. Finally, enter the x and y coordinate for node 3 (i.e. 2,0) and click OK.

5. We must now create the elements that join the nodes together: click on Preprocessor > Modeling > Create> Elements > Auto Numbered > Thru Nodes

6. In the main window click on node 1 and then node 2. Then click Apply in the dialog box. You should see aline element appear joining nodes 1 and 2. (Note: node 1 is probably hidden behind the x-y symbol ar theorigin - this is know as "the triad" - if you can't see node 1 then just click on the triad and it shouldautomatically be selected.)

7. Now click on node 2 and then node 3 and click OK. A line element should appear joining nodes 2 and 3.8. Your screen should now look something like this:

Step 6: Define Boundary Conditions

1. In this case we are using a 3D beam to model a 1D beam problem so we must prevent the nodes from movingin the X and Z direction (i.e. only allow movement in the Y direction for bending). Since beam elements alsohave rotational degrees of freedom at each node we must also constrain rotations about the X and Y axis (i.e.only allow rotations about the Z axis - for bending moments in the X-Y plane). In order to do this we constrainall nodes in the finite element model in the UX, UZ, ROTX and ROTY directions.


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2. Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes

3. Select Pick All in the dialog box that appears.

4. Select UX, UZ, ROTX and ROTY in the next dialog box that appears and enter a value of 0 for displacement value - your screen should look like this:

5. Click Ok to close the dialog box. You should notice constraints appearing at each of the nodes. The bluetriangles represent a node constrained from displacing in a particular direction and the orange double arrows

show that the node is prevented from rotating about that axis.


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6. Now we can apply the problem boundary conditions.

7. Using the table above: we must constrain node 1 in all degrees of freedom:

8. Again, select: Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes

9. Click on Node 1 then click Ok.

10. Select All DOF and enter a value of 0 for displacement value

11. Click Ok to close the dialog box. Your should have noticed extra constraints appearing at node 1.

Step 7: Define Point Loads

1. Select Preprocessor > Loads > Define Loads > Apply > Structural > Force/ Moment > On Nodes

2. Pick node 2 and click on Ok

3. In the dialog box that appears make sure that the direction of force is set to FY and that the Force/ Moment value is -40000. The minus ensures that the load acts downwards.

4. You should notice a red arrow appearing at node 2 pointing downwards.

Step 8: Solve the Problem


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1. In the Main Menu select Solution > Analysis Type > New Analysis

2. Make sure that Static is selected in the dialog box that pops up and then click on OK to dismiss the dialog.

3. Select Solution > Solve > Current LS to solve the problem

4. A new window and a dialog box will pop up. Take a quick look at the infromation in the window ( /STATUSCommand) before closing it .

5. Click on OK in the dialog box to solve the problem.

6. Once the problem has been solved you will get a message to say that the solution is done, close this windowwhen you are ready.

Step 10: Examine the Results

1. In the Main Menu select General Postproc > Plot Results > Deformed Shape

2. You screen should look something like this:

3. Now we must examine the displacement of each node: General Postproc > List Results > Nodal Solution> DOF Solution > Displacement Vector Sum


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4. You should get a printout of the displacement of the beam at each node:


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5. Notice that Node 2 has moved downwards by 0.0133 m and Node 3 has moved 0.03839 m.6. Now, we must check the slope of the beam: General Postproc > List Results > Nodal Solution > DOF

Solution > Rotation Vector Sum

7. You should get a printout of the slope of the beam (i.e. rotation) at each node:


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8. Notice that the slope at nodes 2 and 3 is 0.025 radians.

Case 2: Bending Moment on Centre of a Cantilever Beam

We are now going to change the loading on the model we used for case 1 and replace the vertical point load with abending moment applied to node 2. In this case an overview of the beam probelm is shown in figure 3 and arepresentative finite element model is shown in figure 4.


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Figure 03: Overview of Simple Beam Problem with Applied Bending Moment (Case 2)

Figure 04: Representative Finite Element Model of the Simple Beam Problem with Applied Bending Moment (Case 2)

Steps 1 to 6 : Create the Model and Define the Boundary Conditions

These steps are identical to case 1 (above). If you still have the previous model open then you can just delete thepoint load as follows:

Preprocessor > Loads > Define Loads > Delete > Structural > Force/Moment > On Nodes

Click on Pick All in the dialog box that appears and then click on OK in the next dialog box to delete all forces on allnodes.

Step 7: Apply a Moment to Node 2

1. Preprocessor > Loads > Define Loads > Apply > Structrual > Force/Moment > On Nodes2. Click on Node 2 (the centre one) and the click on OK in the dialog box.3. Change the Direction of Force/Mom to MZ and enter 20000 for the force/moment value :

l l l l l l


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4. Click on OK to close the dialog box.5. You should see a blue cross appear at node 2 to indicate that a moment has been applied.











06/06/2016 ANSYS 1D St t l B T t i l O li Fi it El t A l i C lt S i


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3. Notice that the beam has deflected upwards! This is due to the fact that positive moments are assumed to actin the anti-clockwise direction (look at figures 03 and 04 again).

4. Now we must examine the displacement and rotation (i.e. slope) at each node, as before. Follow theinstructions given above for case 1 to get printouts of the displacement and rotation of each node in the finiteelement model. You should obtain results similar to these:

06/06/2016 ANSYS 1D Structural Beam Tutorial Online Finite Element Analysis ConsultancyService


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5.6. Notice that the deflection of Node 2 is 0.0125 m and the deflection of Node 3 is 0.0375 m. The slope at both

nodes is 0.025 radians.

Case 3: Distributed Load on a Cantile ver Beam

We are now going to replace the loading used on the previous model with a distributed load acting on element 1. Inthis case an overview of the beam probelm is shown in figure 5 and a representative finite element model is shown infigure 6.

Figure 03: Overview of Simple Beam Problem with Applied Bending Moment (Case 2)

06/06/2016 ANSYS 1D Structural Beam Tutorial - Online Finite Element Analysis ConsultancyService


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06/06/2016 ANSYS 1D Structural Beam Tutorial Online Finite Element Analysis Consultancy Service


Figure 04: Representative Finite Element Model of the Simple Beam Problem with Applied Bending Moment (Case 2)

Steps 1 to 6 : Create the Model and Define the Boundary ConditionsThese steps are identical to case 1 (above). If you still have the previous model open then you can just delete thepoint load as follows:

Preprocessor > Loads > Define Loads > Delete > Structural > Force/Moment > On Nodes

Click on Pick All in the dialog box that appears and then click on OK in the next dialog box to delete all forces on allnodes.

Step 7: Apply a Distributed Load to Element 1

1. Preprocessor > Loads > Define Loads > Apply > Structrual > Pressure > On Beams

2. Click on element 1 and then click on OK to close the picker dialog box3. Make sure the Load Key is changed to 2 and enter 12000 for the Pressure Value at Node I



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y y


4. The default Load Key is 1 and this makes the distributed load act in the Y-Z plane, which is the default for beam elements. Putting a value of 2 here makes the load act in the X-Y plane, which is what we want. If wewanted a non-constant distributed load in the beam then we could enter another value for node J, but becausewe want a constant load, we simply leave this blank.

5. Now, click on OK to close the dialog box.6. Your screen should now look something like this:

7. Notice the red line indicating the distributed load.













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3. Now we must examine the displacement and rotation (i.e. slope) at each node, as before. Follow theinstructions given above for case 1 to get printouts of the displacement and rotation of each node in the finiteelement model. You should obtain results similar to these:



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4. Notice that the dispalcement of node 1 is 0.002 m and the displacement of node 2 is 0.0057 m. The slope atboth nodes is 0.00375 radians.

Results Validation

We have used the online beam calculator available at: http://www.engineeringcalculator.net/beam_calculator.html tovalidate the results from the beam finite element models:


http://www.engineeringcalculator.net/beam_calculator.html


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Note that the beam calculator gives slope results in degrees and you will need to convert them to radians in order tocompare with the finite element results. The table below show a comparison between the FEA results and the resultspredicted by the beam calculator (which relies on classical beam theory equations).

Summary

This tutorial has given you the following skills:

1. The ability to model beam problems in ANSYS.2. The ability to generate finite element models using the direct method (i.e. defining nodes and then defining

elements linking those nodes, as opposed to taking a solid model and dividing it up into elements which wewill do in subsequent tutorials).

3. The ability to define element types, real constants and material parameters for a finite element model.



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4. The ability to apply boundary conditions and loads to specific nodes in a finite element model.5. The ability to apply distributed loads to beam elements and to specify which face of the beam they act upon.6. The ability to run a simple linear static analysis.7. The ability to list displacement and rotation results for each node in the finite element model.8. Experience in comparing the results obtained from your finite element model with other results and validating

your results against the other results.

Log Files / Input Files

Click here for the log file for Case 1



The log file for this tutorial may also be used as an input file to automatically run the analysis in ANSYS. In order touse this file as an input file save it to your working directory and then select Utility Menu > File > Read inputfrom... and select the file. You should notice ANSYS automatically building the finite element model and issuing allthe commands detailed above.

Quitting ANSYS

To quit ANSYS select Utility Menu > File > Exit... . In the dialog box that appears click on Save

Everything (assuming that you want to) and then click on Ok

Click here to return to the list of ANSYS tutorials

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ANSYS 1D Structural Beam Tutorial - Online Finite Element Analysis Consultancy Service

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