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Equations for Biosolid Mechanics Final Exam

# Equations for Biosolid Mechanics Final Exam - Equations for...

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Equations for Biosolid Mechanics (BME 240) Final Exam Spring 2007 α σ α α σ α σ σ 2 2 sin cos sin 2 cos yy xy xx xx + + = α σ α α σ α σ σ 2 2 cos cos sin 2 sin yy xy xx yy + - = yx xy xx yy xy σ α σ α σ σ σ = + - = 2 cos 2 sin 2 2 2 min max/ 1 2 2 ) xy yy xx yy xx xx σ σ σ σ σ σ σ + - ± + = 2 2 min max/ 2 2 2 ) xy yy xx yy xx yy σ σ σ σ σ σ σ + - ± + = 2 2 ) 2 1 2 2 min max/ σ σ σ σ σ σ τ - ± = + - ± = xy yy xx xy m ( 29 - = - yy xx xy p σ σ σ α 2 tan 2 1 1 0 = + + + x zx yx xx g z y x ρ σ σ σ 0 = + + + y zy yy xy g z y x ρ σ σ σ 0 = + + + z zz yz xz g z y x ρ σ σ σ 0 1 = + - + + + r rr zr r rr g r z r r ρ σ σ σ θ σ σ θθ θ 0 2 1 = + + + + θ θ θ θθ θ ρ σ σ θ σ σ g r z r r r z r 0 1 = + + + + z rz zz z rz g r z r r ρ σ σ θ σ σ

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