32 Final Exam Equations (207)

# 32 Final Exam Equations (207) - POTENTIALLY USEFUL...

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Δ = PL/EA φ = TL/GJ σ = ± P/A τ = ± Tr/J σ = ± My/I τ = ± VQ/bI τ = ± VQ/tI I x = I y = π r 4 /4 (solid circular sections) I x = bh 3 /12 and I y = b 3 h/12 (solid rectangular sections) J = π( r o 4 - r i 4 )/2 (hollow or solid circular sections) Q = y dA = Ay MOHR’S CIRCLE of STRESS σ a = σ x = [( σ x + σ y ) + ( σ x - σ y )(cos 2 θ ) + (2 τ xy )(sin 2 θ )] / 2 σ b = σ y = [( σ x + σ y ) ( σ x - σ y )(cos 2 θ ) (2 τ xy )(sin 2 θ )] / 2 τ ab = τ x y = [- ( σ x - σ y )(sin 2 θ ) + (2 τ xy )(cos 2 θ )] / 2 c = (0.50)( σ x + σ y ) r = [(0.25)( σ x - σ y ) 2 + τ xy 2 ] 1/2 MOHR’S CIRCLE of STRAIN Replace σ with ε and τ with ½ γ in the above equations ε θ = ε x cos 2 θ + ε y sin 2 θ + γ xy cos θ sin θ GENERALIZED HOOKE’S LAW ε i = [1/E][ σ i - ν ( σ j + σ k )] γ ij = τ ij / G σ i = λ ( ε i + ε j + ε k ) + 2G ε i τ ij = G γ ij λ = ( ν E) / [(1 + ν )(1

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32 Final Exam Equations (207) - POTENTIALLY USEFUL...

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