BendingComposite-10(2)

BendingComposite-10(2) - KML 7/9/09 Bending of beams made...

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KML 7/9/09 Bending of beams made of two materials (Chapter 6 in Gere) The purpose of this analysis is to transform a beam’s section of two materials into an imaginary section of one equivalent material and then calculate the bending stresses. Since the moment load supported by a material is proportional to its modulus, E, and to its width, b, for rectangular beams ( 29 ) EI /( M = κ , the effective width of a material can be imaginarily changed to represent an effective change in modulus. The stresses in the two materials can be computed with one of the two options described below. See Gere pp. 457-469 for a full derivation. ***Whichever material has its width changed will have the same factor in its stress equation*** Define the modular ratio: 1 2 E E n > 1 (by definition let 2 E denote the higher modulus of the two materials) Option 1: Transform the effective width of material two (the one with higher E) - enlarge the width of the stiffer material2 ( 1 2 E E ) by factor n ( nb b T = ) - compute the vertical centroid of transformed cross section - compute the centroidal second moment of area for the transformed
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BendingComposite-10(2) - KML 7/9/09 Bending of beams made...

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