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me211solution_13

# me211solution_13 - y x z 900 x = = 300 psi y = z = 0 3(1...

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x z y 900 300 3(1) x psi σ = = , 0 y z σ σ = = Generalized Hook s Law: [ ] 3 3 1 1 ( ) 300 (0 0) 0.375(10 ) 800(10 ) x x y z E ε σ ν σ σ ν = + = + = [ ] 3 3 1 1 ( ) 0 (300 0) 0.375(10 800(10 ) y y x z E ε σ ν σ σ ν = + = + = − ) ν n New length to x direction: 3 ' 6(1 ) 6(1 0.375(10 )) 6.00225 x a i ε = + = + = New length to y direction: 3 ' 3(1 ) 3(1 0.375(10 ) ) y b ε ν = + = 1 3 tan 6 θ = New angle: 1 3 ' tan 0.01 6 θ θ θ = − Δ = ° ' tan( ') ' b a θ = 3 1 3 3(1 0.375(10 ) ) tan tan 0.01 6 6.00225 ν ° = 0.164 ν =

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15-85. Plane stress: 3 0 σ = [ ] 1 1 2 1 ( ) 3 E ε σ ν σ σ = + [ ] 6 1 2 6 1 350(10 ) (0.3)( 0) 200(10 ) σ σ = + LL (1) [ ] 2 2 1 1 ( ) 3 E ε σ ν σ σ = + [ ] 6 2 1 6 1 250(10 ) (0.3)( 0) 200(10 ) σ σ = + LL (2) Solving Eqs. (1) and (2) yields: 1 60.4 MPa σ = 2 31.9 MPa σ = −