Buckling (with sections)

Transcription

1 roblem: An Euler column with one end fixed and one end free is to be made of an aluminum alloy (E = 71 Ga). The oss sectional area of the column is 600 mm and the column is.5 m long. Determine the column buckling load corresponding to the following shapes: a) A round tube with a 50 mm OD b) A 50 mm square tube

2 Overview Anticipated time to complete this tutorial: 30 minutes Tutorial Overview This tutorial is divided into five parts: 1) Tutorial Basics ) reprocessing 3) Solution 4) ost rocessing 5) Hand Calculations Audience This tutorial assumes familiarity of ANSYS 8.0; therefore, it does not go into step by step detail. rerequisites 1) ANSYS 8.0 in house Structural Tutorial ) Completion of all Basic Machine Design Tutorials 3) Completion of three or more Guided Machine Design Tutorials 4) Completion of Buckling of Euler Column Guided Tutorial Objectives 1) Use beam elements with section modeling to eate geometry ) Use advanced solution techniques to solve for the itical buckling load 3) Utilize the log file to re-run the model with a different oss section Outcomes 1) Explore possibilities with the graphical user interface (GUI) ) Learn how to eate and mesh simple geometries 3) Inease efficiency in problem set up and solving speed

3 In this tutorial: Instructions appear on the left. Buckling (with sections) Visual aids corresponding to the text appear on the right. Tutorial Basics All commands on the toolbars are labeled. However, only operations applicable to the tutorial are explained. The instructions should be used as follows: Bold > Example: Italics MB1 MB MB3 Text in bold are buttons, options, or selections that the user needs to click on > reprocessor > Element Type > Add/Edit/DeleteFile would mean to follow the options as shown to the right to get you to the Element Types window Text in italics are hints and notes Click on the left mouse button Click on the middle mouse button Click on the right mouse button Some basic ANSYS functions are: To rotate the models use Ctrl and MB3. To zoom use Ctrl and MB and move the mouse up and down. To translate the models use Ctrl and MB1. 3

4 1) Change the working directory, jobname, and title of your project. ) Set references to Structural. 3) Add a Beam189 element. 4) Create a Material Model. E: 71e9 RXY:.3 5) Create two Keypoints. K1: (0,0,0) K: (0,.5,0) 6) Create a Line between keypoint one and two. 7) Create a circular oss section. > reprocessor > Sections > Beam > Common Sections reprocessing Give the oss section a name (ex: Hollow Tube). Change the Subtype to the picture that shows a hollow tube. Enter the appropriate values for Ri and Ro based on the problem statement (note: Ri must be solved for by using the total oss sectional area from the problem statement). Change N to 5. If you wish to see the oss section that you just eated, click on the Meshview button. Your oss section should appear similar to the one shown to the right. ress OK. 4

5 8) Change the Number of element divisions for the line to 100. > reprocessor > Meshing > Size Cntrls > Manual Size > Lines > All Lines 9) Set the mesh attributes for the line. > reprocessor > Meshing > Mesh Attributes > All lines reprocessing Note that the section attribute for the line should be set to the name of your oss section (ex: Hollow Tube). 10) Mesh the line 11) Type the following commands into the command line: /ESHAE,1,0 /RELOT This will turn on the 3D element display. You should see your circular oss section extruded along the length of the line. Your model should look similar to the picture shown to the right: 5

6 Solution 1) Apply Structural Displacement constraint to the bottom keypoint. Constrain all of its degrees of freedom. 13) Apply a Structural Force on the top keypoint. Give it a value of 1 and put it in the negative Y direction. (i.e. a value of -1) To get the itical buckling load the solution must be done in steps. 14) > Solution > Analysis Type > New Analysis Select static and click ok. 15) Open up the unabridged menu and then open the analysis options. Select to include restresses. > Solution > Unabridged Menu then > Solution > Analysis Type > Analysis Options then next to stress stiffness or prestress select restress ON 16) Solve the model > Solution > Solve > Current LS 17) When it is done solving select Finish > Main menu > Finish 6

7 18) Setup the system to find the itical loads. > Solution > Analysis Type > New Analysis Solution Select Eigen Buckling and click ok. Close any warning message that may have appeared when you clicked New Analysis. 19) Set up the buckling options > Solution > Analysis Type > Analysis Options Select Block Lanczos and put a value of 1 for the number of modes to extract 0) Solve the model again. > Solution > Solve > Current LS 1) When it is done solving select Finish > Main menu > Finish ) Set up an expansion pass to extract the itical load data > Solution > Load Step Opts > Expansion ass > Single ass > Expand Modes put a 1 in the number of modes to expand 3) Solve the model for the last time > Solution > Solve > Current LS 7

8 4) Use the post processing tools to get the load value > General ostproc > List Results > Detailed Summary The value of the itical load for part (a) is N. ost rocessing art (b) can be easily solved by reusing the model from part (a) with a slight modification. The only thing that needs to be changed in the part (a) model is the section properties. 5) Write a log file and make any appropriate changes, including the following changes for the section properties: Old Code SECTYE, 1, BEAM, CTUBE, HollowTube, 0 SECOFFSET, CENT SECDATA,.00833,.05,5,0,0,0,0,0,0,0 New Code SECTYE, 1, BEAM, HREC, Hollow Rectangle, 0 SECOFFSET, CENT SECDATA,.050,.050, , , , ,0,0,0,0 6) Clear the current job and start a new one. 7) aste the text of the log file into the command line and press enter. The value of the itical load for part (b) is N. 8

9 Hand Calculations cπ EI = l π =.5. 5 * 71.6e9 * I a) Solve for Di, Ri, and π (.05 Di ) = D = R i i = π 4 4 I = ( ) 64 I = 1.588e 7 =.83e10 *1.588e 7 = 4453N b) Solve for a1, a, t, and a1 =.05 a = t = a1 a I = 1 I =.e 7 =.8e10 *.e 7 = 6167N 9