ADS Homework 1 - Homework 1 = Π l l dx x v x q dx dx v d EI 2 2 2 2 1 1 dx l x j Sin l j v l x i Sin l i v EI j j l i i = Π ∑ ∑ ∞

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Unformatted text preview: Homework 1: ∫ ∫- = Π l l dx x v x q dx dx v d EI 2 2 2 ). ( ). ( 2 1 1 dx l x j Sin l j v l x i Sin l i v EI j j l i i - -- - = Π ∑ ∫ ∑ ∞ = ∞ = π π π π ) 1 2 ( ) 1 2 ( ) 1 2 ( ) 1 2 ( 2 2 1 2 1 2 ∑ ∞ = --- = Π 1 3 2 4 4 ) 1 2 ( 2 4 ) 1 2 ( i i i qv i l l EIv i π π 3 l x i Sin v x v i i π ) 1 2 ( ) ( 1- = ∑ ∞ = 4 Obtain Equation 3 by subsitting Equation 2 into Equation 1. Solution: Equation 1 is the potential energy expression for the system. In this expression, only the effect of bending moment is taken into account. The first part of the Equation 1 is the work done by the bending moment. The second part of the Equation 1 is the work done by the external force. The expression of the work done by the bending moment is; dx l x j Sin l x i Sin v v l j i EI i l j i j ∑ ∫ ∑ ∞ = ∞ =---- = Π 1 1 4 4 2 2 ) 1 2 ( ) 1 2 ( ) 1 2 ( )...
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This note was uploaded on 11/23/2010 for the course DEP 503E 10852 taught by Professor Prof.zekaicelep during the Fall '10 term at Istanbul Technical University.

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ADS Homework 1 - Homework 1 = Π l l dx x v x q dx dx v d EI 2 2 2 2 1 1 dx l x j Sin l j v l x i Sin l i v EI j j l i i = Π ∑ ∑ ∞

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