solution02 - Solutions to Assignment 2 (Question I) I. We...

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12 21 11 22 1 1 L L SS S S Γ + = −Γ Solutions to Assignment 2 (Question I) ( ) 11 22 12 21 22 11 L LL S S S Γ+ Γ = Γ 11 11 22 12 21 22 1 L S S S S Γ = Γ ( ) 11 11 22 12 21 22 1 L L S S S S = Γ I. We start from, It is expected that we can obtain L CR Γ− = 12 21 11 22 1 1 L L S S Γ + = Proof: (load stability circle)
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( ) * 22 * 11 11 11 2 ** 22 22 22 1 LL L L SS S S +ΔΓ ΔΓ ΔΓ = −Γ Γ + Γ () 2 11 * * 22 22 22 11 11 1 L L L L S S S S −= Γ −ΔΓ Γ − Γ + + 2 11 * 2 * 22 22 11 22 11 1 L S S S S ΔΓ− −Δ Γ 11 22 1 L L − ΔΓ = − Γ 11 22 1 L L − ΔΓ = − Γ ( )( ) ( )( ) 11 11 22 22 11 L L S S = Γ Γ
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( ) ( ) () 2 22 2 * 22 11 22 11 2 * 2 * 22 22 11 22 * 2 ** 22 11 22 22 11 1 LL L SS S S S S S −Δ − + Δ = ΔΓ Δ Δ Γ ⎡⎤ Δ Γ + ⎢⎥ ⎣⎦ ( )( ) * 2 22 11 22 11 22 11 2 * 22 22 11 1 L S S S Δ− + Δ Δ = −Δ Γ − Δ 2 22 11 2 * 2 * 22 22 11 22 * * 22 11 22 1 L S S S − = Δ Δ Γ Δ Γ
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( ) () 2 22 * 22 22 11 * * 11 22 22 11 22 11 L SS S S S −Δ Γ − Δ = +Δ − Δ − Δ ( ) 2 2 * 22 22 11 11 22 L S S S
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solution02 - Solutions to Assignment 2 (Question I) I. We...

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