equations-exam_20 323

equations-exam_20 323 - = Fn A avg = V A F.S = F fail...

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τ = G ρ d φ dx , γ = ρ d φ dx dV dx = p ( x ), dM dx = V ( x ), Δ V = P , Δ M = M 0 EIv " ( ) " = w ( x ), EIv " = M ( x ) dV dx = p ( x ) , dM dx = V ( x ) , d θ dx = 1 EI M ( x ) , dv dx = θ ( x ) V x 0 + ( ) = V x 0 ( ) + P 0 , M x 0 + ( ) = M x 0 ( ) M 0 z I y x M x y x E y x ) ( ) ( ) ( ) , ( = = ρ σ , rectangle: 3 ( ) /12 I bh = , circle: 4 ( ) / 4 I r π = , semicircle : 4 ( ) / 8 I r π = , centroid at (4 ) / (3 ) r π from diameter 2 0, i i i i I I d A = + b I y Q x V y x z ) ( ) ( ) , ( = τ , VQ q I = , ' ( ) ' ' A Q y dA y A η = = ' ' ' cos2 sin2 2 2 x y x y x xx xy xx σ σ σ σ σ θ τ θ + = + + ' ' ' cos2 sin2 2 2 x y x y y xx xy xx σ σ σ σ σ θ τ θ + = ' ' ' ' 2 cos 2 sin 2 xx xy xx y x y x θ τ θ σ σ τ + = R avg + = σ σ 1 , R avg = σ σ 2 , R = max τ + = 2 y x avg σ σ σ 2 2 ( ) 2 x y xy R σ σ τ = + , tan2 2 xy p x y τ θ σ σ = 2 tan2 x y s xy σ σ θ τ = σ = F n / A τ avg = V / A F . S . = F fail / F allow F . S . = σ fail / σ allow F . S . = τ fail / τ allow ε = ( L L 0 ) / L 0 = Δ L / L 0 γ = ( π / 2) θ σ = E ε ν = ε lat / ε long τ = G γ Δ L th = α ( Δ T ) L Δ L th = α ( Δ T ) dx 0 L ( ) ( ) ( ) 1 1 , 1 1 1 1 , , , x x y z y y x z z z x y xy xy xz xz yz yz T T E E T E G G G ε σ ν σ σ α ε σ ν σ σ
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