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Unformatted text preview: CE 3101 Fall 2011 Homework 06 Optimal Design of a Non-prismatic Beam (Solving a 4th-order ordinary differential equation using the shooting method) Due Tuesday, 18 October 2011, 11:55 P.M. This is a GROUP assignment. Abstract In self-selected groups of up to three members, you will write an Excel spreadsheet program to assist in the optimal design of a non-prismatic beam with mixed end conditions and a non-uniform load. A brief letter report is required in addition to the working code. A full written report is NOT requested or required 1 . Group Evaluation and the Time Card After completing this assignment you are each required to INDIVIDUALLY complete the Homework 06 Group Evaluation , found on the course Moodle web site. Your evaluation activity must be completed by 6:00 P.M., Friday, 21 October 2011, or you risk the imposition of an egregious, 5-point, penalty 2 . 1 Background In this group assignment, you will determine the optimal 3 design for a non-prismatic beam carrying a non- uniform load. A non-prismatic beam is a beam with dimensions, shape, or materials, that change along its length. You will focus on changing dimensions specifically the height of the beam. Oh, and by the way, to complete this problem you must solve a 4th-order ordinary differential equation with mixed boundary conditions using the shooting method This problem is similar to a problem given in past semesters. However, your class has demonstrated exceptional abilities, so we made this a more challenging 4 , and we hope more interesting, version of the problem 5 . To compensate for the potential extra work, the requirements for the written report have been substantially reduced i.e. almost eliminated. 2 The Setup Consider a 40 meter long beam 6 carrying a non-uniform distributed load (see Figure 1). Define a coordinate system where the left end of the beam is at location x = [ m ] , and the right end of the beam is at x = 40 [ m ] . The positive y-axis points upward 7 , as is usually the case. The beam is simply supported 8 at the left end (at x = [ m ] ), and cantilevered 9 on the right end (at x = 40 [ m ] ). 1 Did you see that a full written report is NOT required for this assignment? 2 Did you see that there will be an individual 5-point penalty assessed for not completing the group evaluation on time? 3 For this problem, we define optimal as the minimum mass (weight) beam while meeting a set of engineering constraints. Using a cost per kilogram of fabricated steel offers a simple, and remarkably good, first-order approximation for the constructed cost. Of course, the unit cost of fabricated steel is higher than the unit cost of raw steel sitting on a shop floor....
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- Spring '11