L29_ StressBeams-fall 10

# L29_ StressBeams-fall 10 - EAS 209-Fall 2010 Instructors...

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EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 1 Lecture 29- Max Stress in Beams Lecture 29-Max Stress in Beams To analyze a beam (Ch 5) we found the section with the max. bending moment, and calculated the max. bending stress using I Mc x . This occurred at the farthest distance away from the neutral axis. We then found the section with the max. shear force (Ch 6) and calculated the max. shear stress using It VQ xy . This usually occurred at the N.A. Today’s Lecture: Using the stress transformation principles (Ch 7), we will now look at the combination of normal and shear stress within a section to find the principal stresses, the maximum shear stress, and their orientation. We will look at: Narrow rectangular beams Wide flange beams Transmission shafts Today’s Homework: EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 2 Lecture 29- Max Stress in Beams Principal Stresses in Beams Consider the prismatic beam AB shown below At section C , we have both a shear force V and a bending moment M . Computed stresses Principal Stresses The elements at the top and bottom of the section are in uniaxial tension and compression respectively, while the element at the N.A. is in pure shear. M V

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EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 3 Lecture 29- Max Stress in Beams Narrow Rectangular Beam We can examine the following rectangular cantilever beam to determine the distribution of stresses throughout the beam 3 12 ) 2 ( 12 2 2 3 Ac c bh bh I   2 y c y c b y A Q Given a point distance x from the free end and distance y from N.A., we can determine stresses using the above equations. We can then find the principal stresses for the computed state of stress using Mohr’s Circle. Bending Stress 2 3 Ac Pxy I My x σ x is a function of x and y Shear Stress 2 2 1 2 3 c y A P It VQ xy τ xy is a function of y Q EAS 209-Fall 2010 Instructors: Christine Human
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L29_ StressBeams-fall 10 - EAS 209-Fall 2010 Instructors...

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