32 Final Exam Equations (207)

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online