4-2 - CHAP 4 Finite Element Analysis for Beams and Frames...

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CHAP 4 Finite Element Analysis for Beams and Frames 213 2. The deflection of the simply supported beam shown in the figure is assumed as ( ) ( 1) v x cx x  , where c is a constant. A force is applied at the center of the beam. Use the following properties: EI = 1000 N-m 2 and L = 1 m. First, (a) show that the above approximate solution satisfies displacement boundary conditions, and (b) use Rayleigh-Ritz method to determine c . Solution: (a) At x = 0 and 1, v (0) = v (1) = 0. Thus, the approximate solution satisfies displacement boundary conditions. (b) The second derivative become: 2 c . Using the expression for strain energy in a beam given in Eq. (4.17) we obtain   1 2 0 2 2 EI U c dx
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.

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