02ex_1DElasticity - CEE 220 Mechanics of Materials...

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Unformatted text preview: CEE 220 Mechanics of Materials Uniaxially Loaded Rods Examples Instructor: Peter Mackenzie pmackenz@u.washington.edu Office: 121 D More Hall CEE 220- Mechanics of Materials 2 1-D Elasticity Example 1 x A, E, L b b ( x ) = b = const. d 2 u dx 2 =- b EA du dx =- b x EA + c 1 u ( x ) =- b x 2 2 EA + c 1 x + c 2 CEE 220- Mechanics of Materials 3 1-D Elasticity Example 1 Boundary Conditions u (0) = 0 =- b 2 2 EA + c 1 0 + c 2 = c 2 ( L ) = = 0 c 1 = b L EA ( L ) = E ( L ) = E du dx v v v x = L =- b L A + Ec 1 = 0 c 2 = 0 CEE 220- Mechanics of Materials 4 1-D Elasticity Example 1 u ( x ) =- b x 2 2 EA + c 1 x + c 2 u ( x ) = b L 2 2 EA p x L P b 2- p x L PB ( x ) = du ( x ) dx = b L EA b 1- p x L PB ( x ) = E ( x ) = b L A b 1- p x L PB Displacement Stress Strain CEE 220- Mechanics of Materials 5 1-D Elasticity Example 1 N ( x ) = A ( x ) = EA ( x ) = b L b 1- p x L PB Internal (axial) Force L x b L N x L u ( x ) b L 2 2 EA Displacement Function CEE 220- Mechanics of Materials...
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This note was uploaded on 04/29/2008 for the course CEE 220 taught by Professor Mackenzie during the Spring '08 term at University of Washington.

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02ex_1DElasticity - CEE 220 Mechanics of Materials...

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