Smeared Stiffener Idealisation

Smeared Stiffener Idealisation - Smeared Stiffener...

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100 Smeared Stiffener Idealisation If there are many closely spaced stiffeners then it can be assumed that their effect is distributed over the skin between the corner points. In this case, the effect of the stiffeners can be smeared over the skin and the effective thickness of the skin modified to allow for them. However, the stiffeners only carry direct stress , they do not carry any significant shear stress. This means that the idealised skin will now have two different thicknesses.
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101 Idealised Structures t s =t+ smeared stiffeners t + t t No effective thickness + = n s B L 1 t t Cross sectional area B L Case (i) t Cross sectional area =B Cross sectional area =B + t t Boom Case (ii) Case (iii)
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102
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103 dz q + dq q σ σ + δσ δ z dz Case ii The skin can now only develops shear flow due to the direct stresses in the booms
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104 Lumped Stiffener Idealisation The second form (case ii) of idealisation for including the effect of the stiffeners is to lump their area into a single point concentrated area. In this case, they have a sudden, discrete effect upon the shear flow. dz q + dq q σ σ + δσ δ z dz The discrete stiffener is usually referred to as a ‘boom’ and it will be given this name here. The area of the boom (or stiffener) is B. If there is a stress in the boom then the force is σ σ = B P Over a length of tube dz this force will change to dz dz d B B dP P σ + σ = +
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105 Considering equilibrium of the boom this gives dz q + dq q σ σ + δσ δ z dz So that But, from beam theory Hence the change in shear flow across the boom is () 0 B dz dz d B dz q dz dq q = σ σ + σ + + dz d B dq σ = x yy y xx y yy x xx S I x S I y z M I x z M I y z + = + = σ = x yy y xx S I x S I y B dq Cross sectional area B
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106 And integrating = x yy y xx S I x S I y B dq gives 0 y yy x x xx y 0 s 0 j 1 i i i yy x s 0 j 1 i i i xx y q D I S D I S q B x ds x t I S B y ds y t I S ) s ( q + + = +
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This note was uploaded on 03/24/2010 for the course AE A.213 taught by Professor S.pinhoandm.aliabadi during the Winter '09 term at Imperial College.

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Smeared Stiffener Idealisation - Smeared Stiffener...

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