EAS209 L19_UnsymmetricBending-spring 2011

EAS209 L19_UnsymmetricBending-spring 2011 - EAS 209-Spring...

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EAS 209-Spring 2010 Instructors: Christine Human 2/7/2011 1 Lecture 19- Unsymmetric Bending Lecture 19 Unsymmetric Bending Our analysis of pure bending was limited to members possessing a longitudinal plane of symmetry and supporting lateral loads acting in that plane. Consequently: The members remained symmetric and bend in the plane of symmetry The neutral axis of the cross section coincided with the axis of the couple Today’s Objectives: Understand the difference between symmetric and unsymmetric bending Calculate stresses due to unsymmetric bending Consider general case of eccentric axial loading Today’s Homework: EAS 209-Spring 2010 Instructors: Christine Human 2/7/2011 2 Lecture 19- Unsymmetric Bending Unsymmetric Bending We will now consider situations in which the bending couples do not act in a plane of symmetry. For unsymmetric bending: We cannot assume that the member will bend in the plane of the couples In general, the neutral axis of the section will not coincide with the axis of the couple.
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EAS 209-Spring 2010 Instructors: Christine Human 2/7/2011 3 Lecture 19- Unsymmetric Bending Question: For unsymmetrical section, under what conditions does the NA coincide with the axis of the couple. Return to 3 equilibrium equations containing x M dA y M dA z M dA F x z x y x x 0 0 First equation: Third equation neutral axis passes through centroid 0 or 0 xx m y F dA c ydA        or M zm m
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EAS209 L19_UnsymmetricBending-spring 2011 - EAS 209-Spring...

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