L16_Inelastic Bending- fall 10

# L16_Inelastic Bending- fall 10 - EAS 209 Fall 2010...

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EAS 209 Fall 2010 Instructor: Christine Human 9/17/2010 1 Lecture 16 – Inelastic Bending Lecture 16 Inelastic Bending Today’s Objective: Consider an elastoplastic material to understand plastic deformation Calculate M Y (maximium elastic moment) and M P (plastic moment) Today’s Homework: EAS 209 Fall 2010 Instructor: Christine Human 9/17/2010 2 Lecture 16 – Inelastic Bending Plastic Deformation Consider a rectangular section, with moment about the z-axis Provided the section remains elastic I Mc m = σ NA passes through the centroid 2 planes of symmetry y z b c c 3 3 3 2 ) 2 ( 12 1 bc I c b I = = Elastoplastic Material

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EAS 209 Fall 2010 Instructor: Christine Human 9/17/2010 3 Lecture 16 – Inelastic Bending When σ m = σ Y – top and bottom of the section reach yield M Y – maximum elastic moment Since Y Y Y bc c bc M bc I σ 2 3 3 3 2 3 / 2 3 2 = = = Once section yields, NA will shift to maintain equilibrium. However, for a section with two planes of symmetry (and same properties in
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L16_Inelastic Bending- fall 10 - EAS 209 Fall 2010...

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