L18_UnsymmetricBending-fall 10

L18_UnsymmetricBendi - EAS 209-Fall 2010 Instructors Christine Human EAS 209-Fall 2010 Instructors Christine Human Lecture 18 Unsymmetric Bending

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EAS 209-Fall 2010 Instructors: Christine Human 9/17/2010 1 Lecture 18- Unsymmetric Bending Lecture 18 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-Fall 2010 Instructors: Christine Human 9/17/2010 2 Lecture 18- 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-Fall 2010 Instructors: Christine Human 9/17/2010 3 Lecture 18- Unsymmetric Bending Arbitrary section subjected to bending Let’s first determine the conditions under which the neutral axis of a cross section of arbitrary shape does coincide with the axis of the couple as shown The resultant force and moment from the distribution of elementary forces in the section must satisfy equilibrium
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L18_UnsymmetricBendi - EAS 209-Fall 2010 Instructors Christine Human EAS 209-Fall 2010 Instructors Christine Human Lecture 18 Unsymmetric Bending

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