practice final 2

practice final 2 - CE 215 Spring 2007 Final NAME Student...

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CE- 215 Spring 2007 Final NAME: _____________________ Student ID (Last four digits): ________ P A σ = L δ ε = E σ = ε ε ν = − ε b b b F A σ = ave V A τ = G τ = γ PL EA δ = n i i i 1 i i N L E A = δ = ( ) ( ) L 0 N x EA δ = dx x ( ) T T ε = α Δ ( ) T T L T L δ = ε = α Δ d dx φ θ = max rd r dx φ γ = = θ max r r L φ γ = θ = max r ρ γ = ρθ = γ max Gr τ = θ max G r ρ τ = ρθ = τ 4 4 p r d I 2 3 π π = = 2 max p Tr I τ = max 3 16T d τ = π p T GI θ = p TL GI φ = n n i i i i 1 i 1 i pii TL G I = = φ = φ = ( ) L L p 0 0 Tdx d GI x φ = φ = ( ) ( ) L L p 0 0 T x dx d GI x φ = φ = G τ γ = dV q dx = − dM V dx = 1 d d ds dx θ θ κ = = = ρ x y y ε = − = −κ ρ x x Ey E E y σ = ε = − = − κ ρ 2 A I y d = A 1 M EI κ = = ρ x My I σ = − 1 1 1 Mc M I S σ = − = − 2 2 2 Mc M I S σ = − = − 1 2 1 2 I I S , S c c = = 3 2 bh bh I , S 12 6 = = max allow M S = σ VQ Ib τ = 2 max Vh 3V 8I 2A τ = = VQ f I = VQ f I = xy yx τ = τ 1 x y x y x x sin2 θ + τ θ y cos2 2 2 σ + σ σ − σ σ = + 1 1 x y τ = − x y xy sin2 cos2 2 σ − σ θ + τ θ 1 1 x y x y σ + σ = σ + σ 1 σ + σ = x y x y y x cos2 2 2 σ σ − σ θ − τ y θ sin2 xy p x y 2 tan2 τ θ = σ − σ 2 x y x y 2 1,2 xy 2 2 σ + σ σ − σ σ = ± + τ 1 2 x y σ + σ = σ + σ 1 x y p cos2 2R σ − σ θ = 1 xy p sin2 2R τ θ = 2 x y 2 xy max 2
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