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Homework06

Homework06 - CE 3101 Fall 2011 Homework 06 Optimal Design...

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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 = 0 [ 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 = 0 [ 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. 4 If you ignore hints (5) and (17), you deserve the pain and frustration that you will suffer. In some societies this fate is called justice , in some child-rearing books it is called natural consequences .

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