MATH 2009: Analysis of the Shear Force and The Bending Moment - Mathematics Assignment Help

Assignment Task:

Task:

Project 1

Analysis of the shear force and the bending moment of a two-lane simply-supported bridge under the influence of moving vehicles.

Instructions for your submission

1. This project is to be in groups of two or three students.
2. Type your report using Times New Roman, Arial font or similar size 12, with line spacing at least 1.5 times that of single spacing.
3. Each group must submit the following items online (one copy per group).
a. A printed report explaining the relevant theory and the calculation procedure, and explaining your findings. Include all calculation results necessary to support your answers, except those done in
Task 1. Also include all important figures in the report. Make sure your figures have appropriate axis labels (with units), and titles. Do not use the MATLAB command “subplot”, because it produces figures that are too small.

the following: (Total: 60 marks)
1. In Task 1 we find expressions for the positions and velocities of the THREE vehicles, and the times at which these expressions change. The complete solutions will be provided and you do not need to derive them again here.
(a) Plot positions of the front axle of each vehicle (all on one graph) for t = [0, 31]. Mark and label on the graph the specific times you found in Task 1. Use this graph to complement your explanations for Questions 2—5. (4 marks)
2. Calculate the time when each vehicle leaves the bridge. That is, the time when the rear axle of each vehicle gets off the bridge. (2 marks)
3. (a) Use MATLAB to calculate the shear forces and the bending moments acting on the beam, in terms of time t and position y along the bridge, as the vehicles move across the bridge.
(b) In your report, show the explicit calculations of shear force and bending moment for the case when t = 6 seconds.
(c) Using the results of part (a), write a simulation program in MATLAB that shows how the diagrams of the shear force and the bending moment change as the vehicles move along the bridge.

 The duration of your simulation should be exactly 31 seconds, starting from the initial time t = 0. The time interval should be 0.1sec.
 The distance between the points of calculation across the bridge should be 0.5m, starting from the left endpoint y = 0 and going across to the other end of the bridge.
 In each figure, label the axes appropriately, including units, and give a title.
 In the report, include a labelled graph showing a `snapshot’ of the shear force animation at some particular moment in between t = 0 and t = 31. Do the same for bending moment.
((a)+(b)+(c) = 8+2+8 = 18)
4. In addition, use MATLAB to plot surface graphs of the shear force and of the bending moment in 3-D format (in terms of y, t, and shear force, and of y, t, and bending moment, respectively), and to generate contour plots for the shear force and for the bending moment. Label the axes appropriately, including units. Analyse the figures and discuss them briefly in your report. (8 marks)
5. Use MATLAB to find the numerical value of the maximum bending moment that occurs. When and where does it occur? (5 marks)
6. Write up your work in a report, as described above. (23 marks)
[Introduction and brief statement of problem (4 marks) Explanation (6 marks) Conclusion (2 marks)
MATLAB code in appendix, with appropriate comments (4 marks) Presentation of report (7 marks)]

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