1. Linear Buckling Workshop 7

2. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-2 Workshop 7 - Goals The goal in this workshop is to verify linear buckling results in ANSYS Workbench. Results will be compared to closed form calculations from a handbook. Next we will apply an expected load of 10,000 lbf to the model and determine its factor of safety. Finally we will verify that the structure will not fail structurally before buckling occurs.

3. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-3 Workshop 7 - Assumptions The model is a steel pipe that is assumed to be fixed at one end and free at the other with a purely compressive load applied to the free end. Dimensions and properties of the pipe are: OD = 4.5 in ID = 3.5 in. E = 30e6 psi, I = 12.7 in^4, L = 120 in. In this case we assume the pipe conforms to the following handbook formula where P’ is the critical load: For the case of a fixed / free beam the parameter K = 0.25.

4. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-4... Workshop 7 - Assumptions Using the formula and data from the previous page we can predict the buckling load will be:

5. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-5 Workshop 7 - Start Page From the launcher start Simulation. Choose “Geometry > From File... “ and browse to the file “Pipe.x_t”. When DS starts, close the Template menu by clicking the ‘X’ in the corner of the window.

6. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-6 Workshop 7 - Preprocessing 1.Set the working unit system to the U.S. customary system: –“Units > U.S. Customary (in, lbm, psi, F, s)”. 2.To make the material property match that of our hand calculation highlight the “Solid” branch in the tree: “Details > Material > Edit Structural Steel... ” 1 2

7. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-7... Workshop 7 - Preprocessing 3.In the field for “Young’s Modulus” type in the value “3e7”. Note, changing this property “on the fly” does not effect the stored value for Structural Steel. To save a material for future use we would “Export” the properties as a new material to the material library. Since we only need the value for this workshop we will not do that in this case. 3

8. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-8 Workshop 7 - Environment Fix one end of the pipe: 4.Highlight the Environment branch. 5.Select the surface on one end of the pipe. 6.“RMB > Insert > Fixed Support”. 6 5 4

9. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-9... Workshop 7 - Environment Add a unit force to one end of the pipe: 7.Select the surface on the free end of the pipe. 8.“RMB > Insert > Force”. 9.In the force detail change the “Define by” field to “Components”. 10.In the force detail enter 1 in the “Magnitude” field. 8 7 10 9

10. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-10 Workshop 7 - Solution Insert the buckling tool into the solution branch: 11. Highlight the solution branch. 12.“RMB > Insert > Buckling”. Solve. Notice the default setting for buckling is to find the first buckling mode. 12 11

11. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-11 Workshop 7 - Results When the solution completes review the buckling result. 13. Highlight the “1 st Buckled Mode” result object. 14. The result detail indicates a “Load Multiplier” value of 65610. Recall that we applied a unit (1) force thus the result compares well with our closed form calculation of 65648 lbf. 13 14

12. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-12... Workshop 7 - Results Change the force value to the expected load (10000 lbf). 15. Highlight the “Force” branch. 16. In the detail field for the “Z Component” enter 10000. Solve 16 15

13. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-13 When the solution completes note the “Load Multiplier” field now shows a value of 6.56. Since we now have a “real world” load applied, the load multiplier is interpreted as the buckling factor of safety for the applied load. Given that we have already calculated a buckling load of 65610 lbf, the result is obviously trivial (65610 / 10000). It is shown here only for completeness.... Workshop 7 - Results

14. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-14 Workshop 7 - Verification A final step in the buckling analysis is added here as a “best practices” exercise. We have already predicted the expected buckling load and calculated the factor of safety for our expected load. The results so far ONLY indicate results as they relate to buckling failure. To this point we can say nothing about how our expected load will affect the stresses and deflections in the structure. As a final check we will verify that the expected load (10000 lbf) will not cause excessive stresses or deflections before it is reached.

15. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-15... Workshop 7 - Verification Highlight the “Buckling” branch and delete it. 17. “RMB > Delete” 18. “RMB > Insert > Stress > Equivalent (von Mises)” 17 18

16. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-16... Workshop 7 - Verification Insert total deformation: 19. “RMB > Insert > Deformation > Total” Solve. Note, we deleted the buckling tool because it cannot be combined with other results (stress, deformation, etc.) in the same solution branch. In actual practice, it may be desirable to duplicate the environment branch and modify the duplicate. This would allow you to keep the original buckling results as well as the structural solution. 19

17. Workshop Supplement Linear Buckling August 26, 2005 Inventory #002266 WS7-17... Workshop 7 - Verification A quick check of the stress results shows the model as loaded is well within the mechanical limits of the material being used. As stated, this is not a required step in a buckling analysis but should be regarded as good engineering practice.