ENGR102 Engineering Design Lab II Winter 2014

Transcription

1 ENGR 102 Engineering Design Lab II Bridge Module Week 3 Introduction to Visual Analysis Introduction For the remainder of this module, you will use Visual Analysis to determine the member forces when loading your K NEX bridge designs. You will learn how to construct and simulate the loading of a K NEX bridge in Visual Analysis. When you begin designing your K NEX bridge, you will be required to perform design iterations in Visual Analysis until the simulated results meet your design requirements. Objectives By the end of this lab today, you should: Be familiar with Visual Analysis for simulating static loading on a truss. Understand how slight geometric changes can have a large impact on the force distribution of a truss. Prelab The educational version of Visual Analysis is free to use, and is more than sufficient for our purposes in the lab. You should install and familiarize yourself with it before coming to the lab. See the course website for a download link. Review of Failure Load and Location Prediction In last week s lab, we used the method of joints analysis and the failure loads from lab 1 to determine the overall failure load and location of a truss structure. The method of joints solution gave us the mathematical relationship between the external loading put on the structure (denoted as W), and the loading experienced by each of the members (i.e., rods) of the truss structure. Using these relationships, we determined the corresponding external loading W required to cause pullout from the joints of the truss structure (excluding members in compression and having zero force). Finally, the overall failure loading and location was determined by finding the node-to-member connection with the lowest value of W to cause pullout. In this week s lab, we will be using Visual Analysis instead of the method of joints analysis to determine the relationship between the external loading and the loading experienced by each member of the truss structure. Once these relationships are known, the determination of the failure load and location is the same as in last week s lab (i.e., determining the lowest value of W to cause pullout). The approach to using Visual Analysis instead of method of joints is as follows. Revised 1/23/ Page 1

2 1. Draw the truss structure in Visual Analysis. 2. Setup the connection and loading points. 3. Set the total magnitude of the loading equal to one. 4. Run the analysis. 5. The loading found at each member represents the coefficient of the external loading W at each member Drawing a 2D Truss and Simulating Static Loading Figure 1 shows the first truss structure from Lab 2. Last week, we solved for the forces in each member of this truss by hand, in terms of the loading W. The following exercises will take you through drawing the truss of Figure 1 in Visual Analysis and setting up the loading simulation. (a) (b) Figure 1. First truss example from Lab 2. Yellow rods are 3.5 inches in length. (a) K'NEX model (b) Free body diagram 1. Open Visual Analysis. You will perform all of your analyses in 2D, so you need to first setup Visual Analysis to operate in this manner. Under the Project Manager sidebar, click the Modify tab. Expand the Project tree and select Plane Truss. 2. Under the Edit menu, select Project Units. Using the Style dropdown, select Pounds & Inches. Set the Precision dropdown to 4. Set the Length (large): dropdown to in. Select OK. 3. Find and click the Create nodes button (Figure 2). You should see a popup window titled Multiple Node Generation containing an empty table with the columns Node Name, X (in), and Y (in). Revised 1/23/ Page 2

3 Figure 2. Visual Analysis Create nodes button (circled red). 4. In the Multiple Node Generation window, begin entering all four of the coordinate pairs for the nodes relating to the truss in Figure 1. Set Node A of Figure 1b as the origin (0,0). Recall from lab 2 that yellow K NEX rods are inches in length. Assume that the distance from the rod to the center of the K NEX connector is negligible. When you are done click OK, and then Yes on the resulting popup. 5. Zoom in to the nodes you just created by selecting View Zoom Normal from the drop down menus. To add members, select Model Drawing Mode Members from the drop down menus. Then click and drag between nodes to create corresponding member connections. If you make a mistake, you can either press CTRL+Z to undo the operation, or delete the member by clicking on it and pressing DEL. When you re finished, your drawing should resemble Figure 3Figure 1. Figure 3. Finished structure of the Lab 2 truss exmaple shown in Figure To setup the constraints for the truss (i.e., the connection points), select the left-most node (i.e., Node A of Figure 1). In the Project Manager under the Modify tab, set the support Type to Pinned. Select the right-most node (i.e., Node C of Figure 1) and set the support Type to Fix Y Only. 7. To set the truss members cross-sectional shape, shift click any one of the members (this will select all of the members). In the Project Manager under the Shape tree, click the button next to the Type. In the window that appears, expand Rods, select Upset Rods, and then 0.25 Upset Rod. Press OK when finished. Revised 1/23/ Page 3

4 8. To set the truss members material, shift click to select all members. In the Project Manager under the Materials tree, click the button. Expand and select the Special tree. The K NEX material type is not in the library by default, so you need to add it. Click Add new Material. Change the following fields, and click OK when finished. a. Set Name to K NEX (ABS-DH Plastic) b. Set E to 377,000 psi c. Set nu to 0.35 d. Set alpha to 3.90E-05 in/in/deg-f e. Set gamma to lb/in^3 f. Set Fy to 14,000 psi Select K NEX (ABS-DH Plastic) and click OK when finished. 9. In the drop down menu at the top of the screen, select the Load Case L as shown in Figure 4 (this may appear in the list as Ø: L ). Right-click the bottom point of the truss (i.e., Node D of Figure 1) and select Apply Nodal Load(s). In the window that opens, make sure that Load Case is set to L. Set the Direction as Force Y and set the Load Magnitude as -1 lb. Figure 4. Drop down menu to set Load Case to L. 10. Finally, to run the loading simulation, click Analyze Now under the Analyze drop down menu, or press CTRL+A. 11. To view the results, make sure the Results View tab is activated (if it isn t already). You can click any of the truss members to see the loading information in the Project Manager. The term Fx gives the axial loading in the selected member. Negative values indicate members which are in compression. 12. To view the overall results in a color-coded map, use the Quick Views drop down menu and select Member Fx Color. You can also drag the arrows on the color map around to highlight different aspects of the results (e.g., to only show members in tension as colored). If done correctly, you should observe the load flow results of Figure 5. Revised 1/23/ Page 4

5 Figure 5. Load flow results of the first truss from Lab 2 (i.e., Figure 1). Figure 6. Manual calculation of load flow results for the truss in Figure 1, in terms of the external loading W. Notice that the coefficients of W are the same as the values found from the load flow analysis of Figure 5. Figure 6 shows the method of joints calculations performed in the Week 2 lab. This figure tells us the tension/compression force in each truss member as a function of the applied load W. For example, if W = 1 point, the force F CD = pounds. If W = 10 pounds, F DC = 7.07 pounds. In the exercise above, we have asked Visual Analysis to calculate truss forces for us with W = 1. Compare the values shown in Figures 5 and 6 and make sure you understand how they are related. Revised 1/23/ Page 5

6 Other Common Truss Types Figure 7 through Figure 9 show a few common truss designs (i.e., Howe, Pratt, and Warren). These trusses are all the same in their general shape, however the orientation of their diagonal members is different. Recall from Lab 1 that yellow K NEX rods are approximately inches in length. Also note the location of the origin on the left of each truss. For our purposes, we will be assuming that the left-most node is pinned (i.e., has displacement fixed in the X and Y directions), whereas the right-most node is rolling (i.e., has displacement fixed in the Y direction). Furthermore, the external loading is assumed to be located at the center, top-most node of each truss. Figure 7. Example of a Howe truss. Colored K'NEX rods shown to scale. External loading location shown circled white. Figure 8. Example of a Pratt truss. Colored K'NEX rods shown to scale. External loading location shown circled white. Figure 9. Example of a Warren truss with vertical members. Colored K'NEX rods shown to scale. External loading location shown circled white. Revised 1/23/ Page 6

7 Critical Thinking Questions Perform the following exercises. Explain your findings in you lab notebook. Simulate the Howe, Pratt, and Warren trusses in Visual Analysis using an external loading of 1 lb. Assume that the vertical and horizontal distances between all nodes is the length of a yellow K NEX rod (i.e., inches) and that the left-most node is pinned and that the right-most node is rolling. Place the external loading at the center, top-most node of each truss as shown in Figure 7 through Figure 9. Using the results above, determine the failure load and location for each truss. Follow the process similar to what you have done in Lab 2. Create a table which shows the joint types of each member which is in tension, determine the corresponding value of the external loading W to produce that member s force, and locate the first member to fail. In what ways do the three truss designs produce similar and/or different load flows? Simulate a fourth truss similar to the Warren truss of Figure 9, but includes a second level (Figure 10). How does the load flow, failure load, and location change? Figure 10. Warren truss of Figure 9 with an additional level. Location of external loading shown at the top as a green arrow. Connections locations/types remain the same as in Figure 9. Closing Remarks Visual Analysis will be used to simulate the member loads in you K NEX bridges, and hence predict the failure load and location. In next week s lab, we will go through the process of determining the failure load and location of a standard K NEX bridge design. Before coming to the next lab, make sure you are comfortable with Visual Analysis as presented here. Revised 1/23/ Page 7