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Lect2.pdf - Lecture 2 Potential Energy Approach Potential...

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Lecture 2 Potential Energy Approach
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Potential Energy Approach 1/17/18 2 Strain Energy is the capacity of internal forces (or stresses) to do work through deformations (strains) in the structure.
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Potential Energy Approach 1/17/18 3 The differential internal work (or strain energy ) in the spring for a small change in length of the spring is the internal force multiplied by the change in displacement through which the force moves, given by F x x+dx dU k
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Potential Energy Approach 1/17/18 4
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Potential Energy Approach 1/17/18 5
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Potential Energy Approach (Single Spring Example) 1/17/18 6
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Potential Energy Approach (Spring Assembly Example) 1/17/18 7
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Potential Energy Approach (Spring Assembly Example) In matrix form… Using nodal force equilibrium 1/17/18 8 ï ï þ ï ï ý ü ï ï î ï ï í ì + + = ï ï þ ï ï ý ü ï ï î ï ï í ì ú ú ú ú û ù ê ê ê ê ë é + - - - + - - - ) 3 ( 4 ) 2 ( 4 ) 2 ( 3 ) 1 ( 3 ) 3 ( 2 ) 1 ( 1 4 3 2 1 3 2 2 3 2 2 1 1 3 3 1 1 0 0 0 0 0 0 x x x x x x x x x x f f f f f f d d d d k k k k k k k k k k k k ï ï þ ï ï ý ü ï ï î ï ï í ì = ï ï þ ï ï ý ü ï ï î ï ï í ì
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