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FINITE ELEMENT ANALYSIS OF A PROPPED CANTILEVER BEAMInstructor: Professor James Sherwood Revised: Dimitri Soteropoulos Programs Utilized: ABAQUS CAE 6.9-EF1 Problem Description: This tutorial shows how to build and analyze the propped cantilever beam shown in Figure 1. The finite element model of the beam will be constructed using ABAQUS CAE. Three different loads are considered: Material: Load case 1: Load case 2: Load case 3: Steel with E=29x106 lbs/in2 Distributed Lumped Consistent

Figure 1. Schematic of Beam Dimension and Loading



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Creating the Model Geometry Go to the Start Menu and open Abaqus CAE You may be prompted with an Abaqus/CAE 6.9 Extended Functionality box (Figure 1). Close this box by clicking the X in the top right hand corner.

Figure 1. Abaqus/CAE 6.9 Extended Functionality box. Once the Extended Functionality box is exited, the ABAQUS CAE Viewport should look similar to Figure 2. (Please note the model tree is the series of functions listed on the left hand side of the viewport, while the module is the list of icons to the right of the model tree)

Model Tree

Figure 2. ABAQUS CAE Viewport



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A model of this I-Beam will be constructed using only beam elements. To create the model geometry of the steel I-beam, a sketch of the beam length must be generated. Using the left mouse button, double click Parts in the model tree and the Create Part (Figure 3a) dialog box appears. Enter a new name for the part (I-BEAM), and under the Base Feature tab choose Wire for shape and Planar for type. The Create Part dialog box should look identical to Figure 3b. Click Continue and the graphics window will change to a set of gridlines.

Figure 3a. Create Part Dialog Box

Figure 3b. Create Part Dialog Box (I-BEAM)

For the first step in generating the model geometry, a 100-in. long line must be created. Click the Create Lines: Connected icon in the module. (Remember, the module is the series of icons to the right of the model tree.) In the viewport click once with the cursor, then drag the cursor horizontally to any other place in the viewport such that you will be creating a line parallel to the bottom edge of the screen and click again. After clicking for the second time, press Esc on the keyboard to exit the Create Lines: Connected tool. Because a line of arbitrary length was drawn in the initial sketch, it will now be given the proper dimensions. Click the Add Dimension icon in the module and click the line in the sketch. After this click, the line should turn red and its corresponding dimension should appear. Move the cursor away from the horizontal line and click. At the bottom of the viewport, a New dimension: box should appear (Figure 4).Example value. Your value may be different.

Figure 4. New Dimension Box



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Enter a value of 100.0 in the New Dimension box. Hit Enter. The sketch should resize to the appropriate dimension. However, the full length of the line might not be visible in the viewport. To auto-scale the screen press F6 on the keyboard. The viewport should look identical to that in Figure 5.

Figure 5. Dimensioned Line (100 in.) Press Esc on the keyboard to exit the Add Dimension tool. Click Done in the bottom left hand corner of the viewport. Sketch mode will automatically be exited, and a grey 100-in. long beam will appear (Figure 6).



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Figure 6. Beam Model Defining Material Properties To define material properties for this model, double click on Materials in the model tree and the Edit Material dialog box will appear (Figure 7a). Enter a Name for the material (STEEL), and click the Mechanical tab, highlight Elasticity and click Elastic. Enter values of Youngs Modulus = 29E06, and Poissons Ratio = 0.32. After the material properties have been entered, the Edit Material dialog box should look identical to Figure 7b. Click OK.



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Figure 7a. Edit Material Dialog Box

Figure 7b. Edit Material Dialog Box (STEEL)

Please note there is no dropdown menu or feature in ABAQUS that sets specific units. All of the dimensions have been input in inches; therefore, the respective Youngs Modulus units should be entered in psi (lb/in2). The units chosen for the definition of the material properties should be consistent and dictate what units should be used for the dimensions of the structure. At this point in preprocessing, the model should be saved. Click File then click Save. Name the file I-Beam Tutorial. The file will save as a Model Database (*.cae*) file. It may be of interest to save the file after each section of this tutorial.

Creating an I-Beam Profile To create an I-Beam profile for this model, double click Profiles in the model tree and the Create Profile dialog box will automatically appear (Figure 8a). Enter a Name for the profile (I-BEAM), and click I under the Shape option. The Create Profile dialog box should look identical to that in Figure 8b.



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Figure 8a. Create Profile Dialog Box

Figure 8b. Create Profile Dialog Box (I-BEAM)

Click Continue The Edit Profile dialog box will immediately appear (Figure 9a). This dialog box is where properties of the I-Beam will be entered. Using the properties listed in Table 1 enter the respective values into the Edit Profile dialog box. Table 1. I-Beam Properties Property Value Area 10.5 I11 20.8438 I12 0.0 I22 10.875 J 3.10051

If this description is done correctly, the Edit Profile dialog box should look identical to that in Figure 9b.



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Figure 9a. Edit Profile Dialog Box Click OK.

Figure 9b. Edit Profile Dialog Box (I-BEAM)

Creating Sections To create a beam section in ABAQUS, double click Sections in the model tree and the Create Section dialog box will appear (Figure 10a). Enter a Name for the section (BEAM), and choose Beam under the Category Tab, and Beam under the Type tab. Your Create Section dialog box should look identical to that in Figure 10b. Click Continue

Figure 10a. Create Section Dialog Box

Figure 10b. Create Section Dialog Box (BEAM)

The Edit Beam Section dialog box will immediately appear (Figure 11a). Click Before analysis under the Section integration: option. Because only one profile has been created, the dropdown options for Profile name: is set to I-BEAM. Under the Basic tab, enter a value of Youngs Modulus = 29E06 and Shear Modulus = 10.98E06. Enter 0.32 for a Section Poissons ratio. Check the box to the left of Specify section material density: and enter a value of 0.00073315. The Edit Beam Section dialog box should look similar to that in Figure 11b.



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Figure 11a. Edit Beam Section Dialog Box Click OK.

Figure 11b. Edit Beam Section Dialog Box (I-BEAM)

Assigning Sections Now that the beam section has been created, it can be assigned to the geometry. In the model tree, click the + to the left of the Parts icon, this action will further expand the model trees options. Next, click the + to the left of the part called I-BEAM, further expanding the model tree (Figure 12).

Figure 12. Model Tree Expansion (Parts) After the model tree has been expanded, double click Section Assignments. Using the cursor, draw a box around the complete geometry. If this action has been done correctly, the model will turn from a grey line to a red line (Figure 13).



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Figure 13. Assigning Beam Sections Click Done. The Edit Section Assignment dialog box will immediately appear (Figure 14). Click OK. If this action was done correctly, the model should turn a blue color.

Figure 14. Edit Section Assignment Dialog Box Assigning a Beam Section Orientation A Beam Section Orientation must be assigned. In the toolbar at the top of the Viewport, there is a dropdown menu labeled Assign. Using the left mouse button, click Assign and click Beam Section Orientation (Figure 15).



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Figure 15. Beam Section Orientation Drop down Menu Using the cursor, hold the left mouse button while dragging the cursor around the model to create a box around the entire geometry. If this drag is done correctly, the model will change color from blue to red. Click Done. Using the computer keyboard, enter (0.0,1.0,0.0) in the Enter an approximate n1 direction (tangent vectors shown) option. Hit Enter. The model should look identical to Figure 16. This step defines the orientation of the beam cross section in space. The FE modeler always wants to be sure that the beam is located properly in space for the correct application of the load direction.

Figure 16. Beam Section Orientation Click OK. Click Done. The model should turn back to a blue color.



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Creating a Mesh To create a mesh for the model geometry, double click Mesh (Empty) in the model tree. If this selection is done correctly, then the geometry should change color to pink. The first step in creating a mesh is to seed the part. Click and hold the Seed Part icon in the mesh module and six icons will appear. Hover the cursor over the Seed Edge: By Number icon and release the button on the cursor. Using the cursor, draw a box around the entire model. If this action is done correctly, the model will turn from a pink to a red color. Click Done. In


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