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timer Asked: Apr 11th, 2020

Question Description

I need help with this homework/report for my mechanics class in civil engineering and this assignment requires MATLAB , I need the assignment to be typed and clear and easy to understand.

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Problem #1- 2D problem (45 points) - The frame shown in Figure 1 is made of three (3) members connected together using internal hinges at B and C. It has a distributed triangular load of 10 N/m on the vertical insertion of beam BC, a distributed load defined by the function y=x2/3 on the upper part of section BC, and a parabolic load on section CD. Section AB is a quarter circle loaded with a force F. Support A is a hinge, supports B and C are internal hinges, support D is a fixed support. Under the assumption that the radius R is equal to 8 m, the angle a is equal to 60°, and the magnitude of the force F is equal to the average of the first digit of each group member's IED number (please use the second digit of your IED number if the first one is equal to zero). Make sure to indicate the average IED number used. (i) Find the magnitude and direction of reactions at external supports A and D and the magnitude of reactions at the internal supports B and C (20 points). (ii) In the solutions, please include appropriate clear FBDs for the whole frame, the individual sub- components, and updated FBDs if the initial assumptions made for the direction of the support reactions were wrong (10 points). (iii) MATLAB: solve all of the systems of equations in MATLAB to make sure your hand-written results are correct. All other calculations should be done in MATLAB as well. In the code, you should be able to change the radius and get the corresponding changes at the external and internal supports. Be sure to submit the MATLAB files and also include them in the appendix of your report (15 points). Note: Round up to the results to three significant figures (e.g., 123.45 N = 123 N; 798.65 Nm = 799 Nm). Use at least 4 or more significant digits in intermediate calculations. 10 N/m y = x2/3 5 N/m F Parabola D B 8 m 6 m 3 m 10 N/m CL han A 8 m 4 m 4 m 9 m Figure 1. Frames with various distributed loads Problem #2-3D problem (45 points) (i) Z A 40.5 ft B 2 Х 2 ft + 2ft- (ii) The windlass is subjected to a load of 100 lb. Determine the horizontal force P needed to hold the handle in the position shown (at equilibrium), and the components of the reaction at the ball-and-socket joint A and the smooth journal bearing B. The bearing at B is in properly alignment and exerts only force reactions on the windlass (10 points). Use the equation of equilibrium (EoE) obtained in part (i) to set up a MATLAB program that will calculate the corresponding value of P after varying the load Q from 0 to 400 lb in increments of 10 lb. Make sure to plot Q against all of the other variables (Ax, Ay, Az, Bx, By and P). Plot the quantities on the same plot and use legends to annotate each one. Please show the individual points (10 points). 1 ft ft. Figure 2. Windlass with load iii) Replace the red load in Figure 2 with each object (geometry) shown below in Figure 3. Attach each geometry shown below to the winch using the red hook. Determine the location of where the hook should be position (the centroid location) so that the objects are in perfect balanced. Construct tables to record the information about each individual shape (area, ř, ſ, first moment of areas) or use integration to find the centroid location, if appropriate. Construct a separate final table that contains each one of the shapes (corresponding letter) and the ž, ], locations as shown below (15 points). Components у z а b с iv) Draw the 2D shape in MATLAB the cross-sectional area shown in the xy plane (use a similar code as Problem Set #7) and determine the location of the centroid with the centroid built-in function. Compare to the values obtained in part (iii) (10 points). a) b) c) y z у -z = (a/h)y 6 ft 3 ft EX X f T h 6 ft 8 ft 6 ft *3 ft a = 1 ft h = 2 ft Depth = 1ft Figure 3. Different shape to hang on the windlass. The depth of (b) is 1 ft into the page (negative z direction). Notes about the rubric (10 points): 5 points for organization/presentation; making things clear for the grader/reader. 2 points for including a statement of contribution that each member signs. Make sure it is clear how the work is distributed. Everyone has to contribute in order to receive credit. The statement should state how each person contributed to the project. Once someone finishes his/her part this person should arrange a time to discuss with the other members what they did to arrive at the answer and the other member should check the results. For example, if someone works on the code they need to explain the code to the rest of the group Numerical results need to be clearly indicated and showed in a box, in bold or underline (1 point). Plots need to clear and all axis must be labelled (2 points). Include a cover page that has names, group number, course number and title (1 point). . Additional items to include in the report: MATLAB file (m-files) need to be included to receive the MATLAB credits. In addition, include the scripts in the appendix of the report. Each problem has to include a couple of sentences on the procedure taken to arrive at the answers as discussed in your groups. All tables should be properly labelled and include a caption/title. Include all the data obtained from problem 2 (ii) in a table in the appendix. You can include a picture of the hand-written results but if your hand-writing is not legible please type the report. The hand-written results need to be included as pictures and labelled as a figure in the report. . .
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