3031Closedsection_deflection

3031Closedsection_deflection - Lecture 30 Shear deformation...

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AAE 352 1 Lecture 30 Shear deformation and closed cell torsion Section 7.10
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Shear distortion AAE 352 2 ( 29 ( ) M x P L x = - x P x=L
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Energy due to bending AAE 352 3 2 0 1 2 L M U dx EI = ( 29 2 2 3 2 0 1 1 2 2 3 L P P L U L x dx EI EI = - = 3 3 2 2 3 3 bending U P L PL P EI EI δ = = =
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Shear strain energy AAE 352 4 ( 29 2 1 2 o U G τ = ( 29 ( 29 ( 29 2 2 2 1 2 1 1 2 2 o beam U U dxdydz tLds G t q Lds Lds Gt Gt = = = = ∫∫∫ 2 2 1 2 1 1 2 P U L d P Lh h h t Gt s G = =
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Shear distortion adds to the deflection AAE 352 5 2 shear U P hL P L P h Gt Gt h δ = = = 2 3 2 1 3 1 3 2 total PL E A h EI G L t  = +   x P h A A
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Shear flow in a thin wall section due to torque is constant even if we have stringers AAE 352 6 A enclosed T q(s) s t(s)
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Shear flow due to torque and shear force is different AAE 352 7 A enclosed T q(s) s t(s)
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3031Closedsection_deflection - Lecture 30 Shear deformation...

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