Lab assignment – CVEN2303 Submission due by 2pm 5th of August You need to show and submit all your working solution either handwritten or typed. You can use Matlab (or other software) to invert the structural matrix or for your entire solution procedure. You need to upload a copy of your code or Excel sheet if used. If you are using Matlab, it is expected that you add some titles/subtitles and comments to the different sections of your code. It is expected to add one or two pages of handwritten or typed Flowchart of your coding or solution procedure, that will simply reflect the various stages taken in your code. For part 1.3, it will be good to include differences between the theoretical and measured results in percentages. That will prepare you to discuss the differences between the results. Introduction In this assignment students are expected to calculate axial forces of a Warren truss and a basic Roof truss using the stiffness method, and then to compare with experimental results. The test videos can be watched on moodle (might take a while to upload). A guide for using Matlab (optional) is also available on moodle. Warren Truss The Warren truss under investigation is illustrated in Figure 1, which consists of eleven 300mm long truss members that create 5 equilateral triangles as shown. The distance between the supports is 900mm. Figure 1: Warren Truss 2 The truss is simply supported with a pin support located on the left, and a roller support located on the right. For consistency, use the members numbering as shown in Figure 2. Figure 2: Reference system for Warren truss structure The pin support is located at Position L0; the roller support is located at Position L3; the vertically downwards load F is applied at Position L2. Basic Roof Truss The basic roof truss under investigation is illustrated in Figure 3, which also consists of eleven truss members as shown. The length of members 2, 6 and 10 shown below is 300mm. The distance between the supports is 900mm. The height of the truss measured from the centre of the supports to the Position U1 (Refer to Figure 4) is 259.8 mm (150√3 mm). Figure 3: Basic Roof Truss 3 Figure 4: Reference system for roof truss structure The truss is simply supported with a pin support located on the left, and a roller support located on the right. For consistency, use the members numbering as shown in Figure 4. Assume that member 3 is perpendicular to members 1 and 4 and that member 9 is perpendicular to members 8 and 11. The pin support is located at Position L0; the roller support is located at Position L3; the vertically downwards load F is applied at Position L2. Part 1.1 (70%): Calculate theoretical axial forces of the Warren and Roof trusses Use the stiffness method to calculate the axial forces of all members in the Warren truss and the Roof truss under a load that is applied at Position L2 with a magnitude of 300 N downwards. You may use any computer software to do the calculation. The material of the truss member is acrylic, and its elastic modulus is E = 2500 N/mm2. The cross-section area of each truss member is A = 250 mm2. Part 1.2 (10%): Determine experimental axial forces of the Warren and Roof trusses From the measured strains, the experimental member axial forces can be obtained using: N = EA where E is the elastic modulus of the material, A is the cross-section area, and is the measured strain which is multiplied by 106. Therefore, in order to get the actual value of you need to multiply the measured value by 10-6. Part 1.3 (20%): Results discussion Compare between the theoretical and experimental results and discuss four possible reasons for any discrepancies between the results. 4 Results of axial forces Member of truss Warren truss Basic Roof Truss Theoretical axial force (N) Measured strain ( 610 ) Experimental axial force (N) Theoretical axial force (N) Measured strain ( 610 ) Experimental axial force (N) 1 -183 -341 2 102 283 3 221 17 4 -182 -336 5 -185 -5 6 260 277 7 193 578 8 -384 -660 9 387 26 10 207 543 11 -423 -668
