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Unformatted text preview: MMAE 350 D. Rempfer Problem Set VIII Page 1 of 2 Due Date: December 06, 2006 1. We consider the deformation of a rod which is un- der an axial load P and a distributed transverse load f ( x ). The rod is attached to a wall at the points ( x = ,y = 0) and ( x = 1 ,y = 0) using friction- free joints, so that the moments at the end points are zero. The deformation y ( x ) in such a situation is (approximately) given by the di ff erential equa- tion P f(x) P y x d 2 y ( x ) dx 2 =- f ( x ) x (1- x ) + py, with p defined as p = P/EI , where E is the elastic modulus of the rod, and I the moment of inertia of its cross section. For the following we will assume that things have been normalized in such a way that we end up with a nondimensional form of the equation that reads d 2 y ( x ) dx 2 =- x (1- x ) 1 4- x- 1 2 2 !- y. a. What are the boundary conditions for this problem? b. Plot the load f ( x ) as a function of x ....
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