# ADS Homework 1 - Homework 1 âˆ âˆ = Î  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 = Î  âˆ‘ âˆ âˆ‘ âˆž

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Unformatted text preview: Homework 1: âˆ« âˆ«- = Î  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 - -- - = Î  âˆ‘ âˆ« âˆ‘ âˆž = âˆž = Ï€ Ï€ Ï€ Ï€ ) 1 2 ( ) 1 2 ( ) 1 2 ( ) 1 2 ( 2 2 1 2 1 2 âˆ‘ âˆž = --- = Î  1 3 2 4 4 ) 1 2 ( 2 4 ) 1 2 ( i i i qv i l l EIv i Ï€ Ï€ 3 l x i Sin v x v i i Ï€ ) 1 2 ( ) ( 1- = âˆ‘ âˆž = 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 âˆ‘ âˆ« âˆ‘ âˆž = âˆž =---- = Î  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 âˆ âˆ = Î  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 = Î  âˆ‘ âˆ âˆ‘ âˆž

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