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Unformatted text preview: E y E y Dissimilar material such as a composite structure: what if E and I are not constant?? assuming bending only; Mz applied; determine Iz In this cross section, the upper region has a modulus = E2 where the remainder has modulus E1 as with Euler bending, plane sections remain plane etc.... ε is axial strain E2 E1 y z NA NA ε x = − y R y the distance from the neutral (z) axis R the radius of curvature Hooke applies (although E is now dependent on y) σ x = E ⋅ε x = − E ⋅ y signs consistent with Shames 11.2 R ⌠ pure (only) bending => F x = σ x dA = = − ⌠ ( ) ⋅ y dA net axial force = 0 R ⌡ ⌡ E i suppose we define a parameter Ti such that T i = E 1 that is, a fraction of a reference modulus E1 then: − T i y ⌠ ( ) ⋅ y dA = − E 1 ⌠ ( ) ⋅ y dA R R ⌡ ⌡ "transfer" Ti to the area, in such a way that y is not affected => T i y ⋅( ( ) ⋅ dA ) = y dy ⋅( T i y ( ) ⋅ y ⋅ dA = y T i y ⋅ ( ) ⋅ dz ) which means "transfer" to dz, and in rectangular shape, equivalent to applying to z dimension, for thin walled...
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 Spring '03
 DavidBurke
 Trigraph, Second moment of area, TI, Na Na Hey Hey Kiss Him Goodbye

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