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AA SEZC METHOD 15.2.4.3 local stability panel rotational edge fixity

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A simplified method allows for a quantified measure of the panel rotational edge stiffness, this is defined by the following expression

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AA SEZC METHOD 15.2.4.3 local stability panel rotational edge fixity

  1. 1. Abbott Aerospace – Analysis Method XL-VIKING DisplayYour Math in Excel Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures Local Stability – Compression Buckling – Panel Edge Rotational Fixity
  2. 2. Abbott Aerospace – Analysis Method XL-VIKING DisplayYour Math in Excel Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures Local Stability – Compression Buckling – Panel Edge Rotational Fixity A simplified method allows for a quantified measure of the panel rotational edge stiffness, 𝜖, this is defined by the following expression: 𝜖 = 4 ∙ 𝑆0 ∙ 𝑏 𝐷 Where: 𝑺 𝟎 Stiffness per unit length of elastic restraining medium, or moment required to rotate a unit length of elastic medium through one-fourth radian 𝑫 Flexural rigidity of panel per unit length: 𝐷 = 𝐸 ∙ 𝑡3 12 ∙ 1 − 𝜈 𝑒 2 𝒃 Width of loaded edge of Panel, in
  3. 3. Abbott Aerospace – Analysis Method XL-VIKING DisplayYour Math in Excel Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures Local Stability – Compression Buckling – Panel Edge Rotational Fixity The value of 𝜖 can be calculated by taking the following approach. This approach is taken in part from (NACA-TN-888, 1943). 4 ∙ 𝑆0 = 𝜋2 𝜆2 ∙ 𝐺 ∙ 𝐽 − 𝑓 ∙ 𝐼 𝑝 + 𝜋2 𝜆2 ∙ 𝐸𝑠 ∙ 𝐶 𝐵𝑇 When this is combined with the initial expression for 𝜖 the expression for evaluating 𝜖 becomes: 𝜀 = 𝜋2 ∙ 𝑏 𝜆2 ∙ 𝐷 ∙ 𝐺 ∙ 𝐽 − 𝑓 ∙ 𝐼 𝑝 + 𝜋2 𝜆2 ∙ 𝐸𝑠 ∙ 𝐶 𝐵𝑇 Where: 𝑪 𝑩𝑻 Torsion-bending constant of stiffener sectional area about axis of rotation at or near edge of plate (see below) and 𝝀 Half buckle wavelength, 𝑮 Material modulus of rigidity, psi 𝑱 Section torsional constant, in4
  4. 4. Abbott Aerospace – Analysis Method XL-VIKING DisplayYour Math in Excel Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures Local Stability – Compression Buckling – Panel Edge Rotational Fixity 𝐶 𝐵𝑇 is a relatively little used cross section property and (NACA-TN-888, 1943) is one of the few references that gives a method to determine this value. 𝐶 𝐵𝑇 = න 𝐴 𝑢2 𝑑𝐴 𝐶 𝐵𝑇 for common cross sections: I Beam: C Channel: Z Section: 𝐼 𝐹 ∙ ℎ2 2 𝐼 𝐹 ∙ ℎ2 2 4 − 6 ∙ 𝑒 𝑏 𝐼 𝐹 ∙ ℎ2 2 4 − 6 ∙ 𝐴 𝐹 𝐴
  5. 5. Abbott Aerospace – Analysis Method XL-VIKING DisplayYour Math in Excel Taken from: Analysis and Design of Composite and Metallic Flight Vehicle Structures Local Stability – Compression Buckling – Panel Edge Rotational Fixity Where: 𝑨 𝑭 Area of one flange 𝐴 𝐹 = 𝑏 ∙ 𝑡 𝐹 , in2 𝒃 Width of flange, in 𝒕 𝑭 Flange thickness, in 𝑨 𝑾 Area of web 𝐴 𝑊 = ℎ ∙ 𝑡 𝑊 , in2 𝒉 Height of web, in 𝒕 𝑾 Web thickness, in 𝑨 Area of cross section 𝐴 = 𝐴 𝑊 + 2 ∙ 𝐴 𝐹 , in2 𝑰 𝑭 Moment of inertia of one flange 𝐼 𝐹 = Τ𝑏3 ∙ 𝑡 𝐹 12 , in4 AA-SM-007-070 Buckling - Edge Rotational Restraint

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