CEE 213—Deformable Solids The Mechanics Project Arizona State University CP 5—Multispan Beam 1 Computing Project 5 Multispan Beam The computing project Multispan Beam concerns the analysis of a multispan beam that has four spans, three intermediate supports, and either fixed, simple, slide, or free conditions at the ends. The theory needed to execute this project is contained in the set of notes (entitled CP 5—Multispan Beam) that accompany this problem statement. Those notes provide an introduction to each aspect of the computation required to solve the problem. This project is an extension of CP 4—Plane Beam, and it would be a very good idea to use your code for that project as the starting point for this one. The task in this project is to write a code that will analyze the four-span beam. We will view the task as an application of the single span governing equations and we will establish continuity conditions at the support points. The CP 5 notes describe how to set up this analysis. The general steps are as follows: 1. Develop a routine based upon Simpson’s Rule to numerically integrate the applied loading terms that produce the quantities I0, I1, I2, and I3 that are mentioned in the CP4 notes. This code segment was included in CP 4 but now you have to do the computation for four spans. 2. Develop a routine to set up and solve the system of equations that allow for the determination of the state variables (w, , M, and V) at both ends of each bar. In this task you will need to set up the equations, boundary conditions at the ends, and the continuity conditions at the supports. The CP 5 notes describe how to do this in a fairly compact way (well suited for implementation in MATLAB). 3. Develop a routine to integrate the governing equations from the left end to the right end using generalized trapezoidal rule to do the integration numerically. Store the results at each step along the axis and provide a plot of the applied load q, the transverse displacement w, the rotation of the cross section , the bending moment M, and the net shear force V as functions of x. A good way to verify this step is to CEE 213—Deformable Solids The Mechanics Project Arizona State University CP 5—Multispan Beam 2 just plot the functions and verify that they are continuous at the supports (except shear, which should jump by the amount of the reaction forces at the supports). 4. Use the code to explore the response of the system: a. What is the effect of the choice of boundary conditions at the two ends? Does it make much difference on the interior spans? b. Study what happens to the shear and moment diagrams in the neighborhood of the supports. Can you generalize any of those observations? c. Can you apply different loading functions on different spans or different magnitudes of the same loading function on different spans with your code? d. Explore any other feature of the problem that you find interesting. Write a report documenting your work and the results (in accord with the specification given in the document Guidelines for Doing Computing Projects). Post it to the Critviz website prior to the deadline. Please consult the document Evaluation of Computing Projects to see how your project will be evaluated to make sure that you can get full marks. Note that there is no peer review process for reports in this course.

CEE 213—Deformable Solids The Mechanics Project Arizona State University CP 5—Multispan Beam 1 Computing Project 5 Multispan Beam The computing project Multispan Beam concerns the analysis of a multispan beam that has four spans, three intermediate supports, and either fixed, simple, slide, or free conditions at the ends. The theory needed to execute this project is contained in the set of notes (entitled CP 5—Multispan Beam) that accompany this problem statement. Those notes provide an introduction to each aspect of the computation required to solve the problem. This project is an extension of CP 4—Plane Beam, and it would be a very good idea to use your code for that project as the starting point for this one. The task in this project is to write a code that will analyze the four-span beam. We will view the task as an application of the single span governing equations and we will establish continuity conditions at the support points. The CP 5 notes describe how to set up this analysis. The general steps are as follows: 1. Develop a routine based upon Simpson’s Rule to numerically integrate the applied loading terms that produce the quantities I0, I1, I2, and I3 that are mentioned in the CP4 notes. This code segment was included in CP 4 but now you have to do the computation for four spans. 2. Develop a routine to set up and solve the system of equations that allow for the determination of the state variables (w, , M, and V) at both ends of each bar. In this task you will need to set up the equations, boundary conditions at the ends, and the continuity conditions at the supports. The CP 5 notes describe how to do this in a fairly compact way (well suited for implementation in MATLAB). 3. Develop a routine to integrate the governing equations from the left end to the right end using generalized trapezoidal rule to do the integration numerically. Store the results at each step along the axis and provide a plot of the applied load q, the transverse displacement w, the rotation of the cross section , the bending moment M, and the net shear force V as functions of x. A good way to verify this step is to CEE 213—Deformable Solids The Mechanics Project Arizona State University CP 5—Multispan Beam 2 just plot the functions and verify that they are continuous at the supports (except shear, which should jump by the amount of the reaction forces at the supports). 4. Use the code to explore the response of the system: a. What is the effect of the choice of boundary conditions at the two ends? Does it make much difference on the interior spans? b. Study what happens to the shear and moment diagrams in the neighborhood of the supports. Can you generalize any of those observations? c. Can you apply different loading functions on different spans or different magnitudes of the same loading function on different spans with your code? d. Explore any other feature of the problem that you find interesting. Write a report documenting your work and the results (in accord with the specification given in the document Guidelines for Doing Computing Projects). Post it to the Critviz website prior to the deadline. Please consult the document Evaluation of Computing Projects to see how your project will be evaluated to make sure that you can get full marks. Note that there is no peer review process for reports in this course.

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