practice%20final%201

# practice%20final%201 - CE 215 Spring 2006 Final NAME...

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CE- 215 Spring 2006 Final NAME: _____________________ Student ID (Last four digits): ________ P A σ= L δ ε= E σ= ε ε ν=− ε b b b F A ave V A τ = G τ PL EA δ= n ii i1 NL EA = ( ) () L 0 Nx EA d x x ( ) T T ε =α Δ ( ) TT LT L δ =ε =α Δ d dx φ θ= max rd r dx φ γ= = θ max r r L φ θ = max r ρ γ=ρθ= γ max Gr τ max G r ρ τ= ρθ= τ 44 p I 23 ππ == 2 max p Tr I τ= max 3 16T d π p T GI p TL GI φ= nn i ip i i TL GI φ = ∑∑ LL p 00 Tdx d GI x ∫∫ ( ) p Txd x d GI x G τ dV q dx =− dM V dx = 1d d ds dx θ θ κ= = = ρ x y y ε =− =−κ ρ xx Ey EE y 2 A Iy d = σ= ε=− =−κ ρ A 1M EI ρ x My I σ=− 1 1 1 Mc M IS 2 2 2 Mc M 12 II S, S cc = = 32 b hb I, S 12 6 h max allow M S = σ VQ Ib 2 max Vh 3V 8I 2A = VQ f I = VQ f I = xy yx τ 1 xy y cos2 sin 2 22 σ+σ σ−σ + θ + τ θ 11 2 co σ sin s2 2 −σ τ θ y θ+τ xyx σ+ σ 1 yx y sin 2 θ τ θ xy p 2 tan2 τ σ−σ 2 2 1,2 xy σ+σ ⎛⎞ ± + τ ⎜⎟ ⎝⎠ 12xy σ +σ =σ +σ 1 p 2R 1 xy p sin2 2R τ 2 2 xy max 2 τ =+ τ 1 max 2 σ− 2 σ aver 2 pr 2t σ=σ =σ = max pr 4t τ = 1 pr 2 pr t2

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## This note was uploaded on 08/25/2011 for the course CE 215 taught by Professor Frantziskonis during the Summer '08 term at Arizona.

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practice%20final%201 - CE 215 Spring 2006 Final NAME...

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