Figure E3-1 A plane struss structure under applied loading. Start MARC Designer. From the main menu, select STATIC STRESS ANALYSIS.

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1 Example 3 Static Stress Analysis on a Plane Truss Structure Problem Statement: In this exercise, you will use MARC Designer software to carry out a static stress analysis on a simple plane truss structure, as shown in Figure E3-1. All members of the structure are assumed to have a Young s modulus E = 29.5 x 10 6 psi and cross-sectional area A = 1.0 in 2. An external load of 20,000 lb is applied horizontally at global node 2 while another load of 25,000 lb is applied vertically at the global node 3, as shown. You are required to perform the analysis and obtain the stresses in all members of the structure and reaction forces at all supports. Figure E3-1 A plane struss structure under applied loading. Start MARC Designer. From the main menu, select STATIC STRESS ANALYSIS. I. MESH GENERATION Create four nodal points as follows: 1. Click ADD in the NODES menu (top left of the window) 2. Type in the following nodal coordinates, press Enter key after each digit: 0, 0, 0; 40, 0, 0; 40, 30, 0; 0, 30, 0 Note: the nodes are created in an ANTI-CLOCKWISE direction. Keep this order in mind every time you start creating your finite element model! Click FILL on the bottom toolbar. This command will fit the nodes into the graphics screen window. Page 20

2 We will use line(2) elements to create the model of our truss structure, as follows: 1. Click ELEMENT CLASS. In the menu, choose LINE(2). Click RETURN. 2. Click ADD in the ELEMENT menu. Select nodes at (0, 0, 0) and at (40, 0, 0), the 1 st element element is created. Next select nodes at (40, 0, 0) and (40, 30, 0), the 2 nd element is created. Next select (0, 0, 0) and (40, 30, 0), the 3 rd element is created, and finally, select nodes at (40, 30, 0) and (0, 30, 0), and the 4 th element is created. Note: It is important to follow ANTI-CLOCKWISE direction when creating elements. II. BOUNDARY CONDITIONS 1. Under the STATIC STRESS menu, click BOUNDARY CONDITIONS. 2. Click NEW; Click NAME; Type in a unique name for this boundary condition (e.g. Support). Note: Naming is an optional step since MARC Designer automatically creates a unique name when clicking NEW. Create a pinned support condition, and apply it to the two nodes on the left side of the truss structure as follows: 1. Click FIXED DISPLACEMENT; Click ON next to X DISPLACE and Y DISPLACE. This fixes the x, and y degrees of freedom since their values are 0; Click OK. 2. Click ADD next to NODES; Pick the nodes at (0, 0, 0) and (0, 30, 0); Click END LIST (#) to complete the selection. Next, specify a roller type boundary condition at node (40, 0, 0). 1. Click NEW to define a new boundary condition; Click ON next to Y DISPLACE. This fixes the y degrees of freedom at the roller support; Click OK. 2. Click ADD next to NODES; Select the node at (40, 0, 0); Click END LIST (#). Then we will create the loading of lb in the x-direction and apply it to node 2: 1. Click NEW to define a new boundary condition; Click ON next to X FORCE and then click the X FORCE button; Key in and press Enter; Click OK. 2. Click ADD next to NODES; Select the node at (40, 0, 0); Click END LIST (#). Finally, we create the loading of lb in the y-direction and apply it to node 3: 1. Click NEW to define a new boundary condition; Click ON next to Y FORCE and then click the Y FORCE button; Key in and press Enter; Click OK. 2. Click ADD next to NODES; Select the node at (40, 30, 0); Click END LIST (#). To see all the boundary conditions applied on the finite element model of the truss structure, simply click on ID APPLYS button. Figure E3-2 shows the snapshot of the finite element model with all the applied boundary conditions. Page 21

3 25,000 lb 20,000 lb Figure E3-2 Finite element model of the plane truss structure will applied boundary conditions. Note that the members of the truss structure are modeled using 1-dimensional line elements. Global node numbers are shown in pink. III. LINKS/TIES Special constraints (e.g. multi-point constraint) or special elements such as springs are defined using the LINKS/TIES menu. Since we do not have such needs for our problem, we will skip this step, and proceed to the step of inputting the material data. IV. MATERIAL PROPERTIES Define a new material description and its properties as follows: 1. Under the STATIC STRESS ANALYSIS menu, click MATERIAL PROPERTIES; Click NEW; Click NAME and give this material property set a name (e.g. steel); Press Enter. 2. Click ISOTROPIC. A menu appears where ISOTROPIC parameters can be entered; Click YOUNG'S MODULUS; Type 29.5e6 on the command line and press the Enter key; Click on POISSON'S RATIO; Type 0.3 on the command line and press the Enter key; Click OK. 3. Click MASS DENSITY; Type 1 on the command line and press the Enter key. Page 22

4 Next, apply these material properties to all the elements 1. Click ADD next to ELEMENTS; Click EXIST. This is a shortcut that selects all existing elements. 2. Click END LIST (#). Alternately, click the right mouse button to end list. Note that all 4 elements are given the same material properties. V. GEOMETRIC PROPERTIES Define the geometric property by specifying the cross sectional area of each member of the structure, and apply the property to all members as follows: 1. Under the STATIC STRESS ANALYSIS menu, click the GEOMETRIC PROPERTIES; Click 3D; Click NEW; Click NAME to give this Geometric Property set a unique name (e.g. Area). 2. Click TRUSS; Click AREA; Type 1 on the command line (Cross-sectional area of each element is 1 in 2 ); Click OK. 3. Click ADD next to ELEMENTS. Designer prompts for the element list to which the material properties need to be applied to; Click EXIST; Click END LIST (#). VI. LOAD CASES Now create a Load Case definition as follows: 1. Under the STATIC STRESS ANALYSIS menu, click LOADCASES; Click MECHANICAL. The SELECT LOADS sub menu is shown; Click SELECT; Under the LOADS list, select the fixed displacements and point loads boundary conditions. 2. Verify that STATUS is SELECTED next to each boundary condition; Click OK; Click RETURN to go back to the STATIC STRESS ANALYSIS menu. VII. JOBS Create a Job description and define the job parameters as follows: 1. Under the STATIC STRESS menu, select JOBS; Select NEW; Select NAME and type in a unique name for this Job, e.g. static. 2. Select MECHANICAL; Under the LOADCASES, Press SELECT. Then, under AVAILABLE LCS, select the loadcases defined earlier, e.g. static. 3. Under the ANALYSIS DIMENSION, select 3D; Click OK. Next, define the element type as follows: 1. Select ELEMENT TYPES; Select 3D TRUSS/BEAM; Select 9; Click OK. 2. Click EXIST to apply the above element type specification to all elements in the finite element model; Click END LIST (#). Note: If an Element Type is not specified, Designer will attempt to determine an appropriate element type based on the analysis dimension set earlier. Page 23

5 VIII. SAVE YOUR DATA Before running the job, always save the model as a designer file (either formatted with an.mfd extension or a binary file with an.mud extension). 1. Select FILES from the lower toolbar. The default directory is the directory where MARC Designer was launched from (e.g. C:\Designer\Bin). 2. Select SET DIRECTORY to change to your choosen subdirectory; Type in a directory path (e.g. C:\Designer\myname\truss). 3. Select SAVE AS from under the MODEL heading; Specify a unique name for your model; Press Enter; Type yes (or just y) to confirm the file name; Press Enter. Note: Pressing Enter after specifying the filename DOES NOT create the file. You MUST answer y or yes! IX. RUN THE DESIGNER JOB Run the analysis as follows: 1. Under the STATIC STRESS... JOBS menu, select RUN JOB. The job is submitted to the program for execution. If the analysis is successful, an output file with the extension *.out and a post file with an extension of *.t16 (binary). VIII. POSTPROCESSING After a successful execution of the analysis, you can view the result by setting the postprocessing options as follows: 1. Press RETURN to go back to STATIC STRESS ANALYSIS menu; Under the STATIC STRESS menu, select RESULTS; Select OPEN DEFAULT the program will open the *.t16 binary result file. 2. Select DEF & ORIG this option allows the deformed geometry will be drawn over the undeformed geometry; Select SETTINGS; Select AUTOMATIC this option allows the deformations to be scaled up to help in displaying the results. 3. Click RETURN; Under SCALAR PLOT menu, select NUMERICS; Click SCALAR. In the SELECT POST SCALAR menu, select the result you wish to see, e.g. Displacement y; Press OK. 1. Under the FILE menu, click NEXT INC to see the deformed shape of the structure and the nodal values of the scalar you selected. You have successfully performed the analysis of a 2D truss structure and viewed the results using the post file. You should get the displacement y of in. at the node (40, 30, 0). Figure E3-3 shows the post-processing result depicting the deformed shape of the structure. Page 24

6 POST-PROCESSING RESULT Figure E3-3 Deformed shape of the plane truss structure under the applied loads. Notice that the global node 3 undergoes displacement in the negative y-direction of about in. Nazri B Kamsah, Ph.D. Department of Thermo-Fluid March 27, 2003 Page 25