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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.... is axial strain E2 E1 y z NA NA 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) x = E x = E y signs consistent with Shames 11.2 R pure (only) bending => F x = 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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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.082 taught by Professor Davidburke during the Spring '03 term at MIT.
 Spring '03
 DavidBurke

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