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L26_ General state of stress-fall 10

# L26_ General state of stress-fall 10 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 1 Lecture 26- General State of Stress Lecture 26 Effect of Third Principal Stress So far we have only determined the stresses in the xy plane, these are called the in-plane stresses. We have found that within this plane there are two principal stresses. However, there is actually a third principal stress (out-of-plane) . Today’s Objective: Consider the effect of the third principal stress Today’s Homework: EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 2 Lecture 26- General State of Stress Third Principal Stress The two principal stresses, points A and B (obtained by rotation about the z-axis) in the figure below are called the in-plane principal stresses. Remember however, that the stress element is 3- dimensional. A third principal stress exists on a plane that is perpendicular to the other two (in this case the z -axis). Consequently we know that for plane stress, the third principal stress, σ 3 =0. The third principal stress can be plotted as a point at the origin. This point can be connected to points A and B to form two additional circles.

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