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L22_ Shearing Stresses in beams-fall 10

# L22_ Shearing Stresses in beams-fall 10 - EAS 209-Fall 2010...

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EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 1 Lecture 22- Shear Stresses in Beams Lecture 22 Chapter 6 Shearing Stresses in Beams Transverse loading applied to a beam results in both internal shear forces and bending moments. Bending moment normal stresses I My x = σ Shear force shear stresses THIS CHAPTER While the dominant criterion in the design of a beam for strength is generally the maximum value of the normal stress caused by bending moments, (Chapter 5), shear stresses can be important, particularly in the design of short, stubby beams. Today’s Objectives: Calculate shear stresses in beams Calculate forces in bolts and nails in built-up sections Today’s Homework: EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 2 Lecture 22- Shear Stresses in Beams Elementary normal and shear forces Distribution of normal and shearing stresses must satisfy equilibrium = = = = = = M dA y M dA z M dA F x z x y x x σ σ σ 0 0 We previously used the above equations to determine the distribution of normal stresses due to bending (lecture 14). Now we consider the remaining three equilibrium equations involving the shear stresses: ( ) 0 = = Σ dA z y M xy xz x τ τ symmetrical section = = Σ V dA F xy y τ xy τ must exist because V exists = = Σ 0 dA F xz z τ but we cannot conclude 0 = xz τ All 3 equations involve only σ x

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EAS 209-Fall 2010 Instructors: Christine Human 10/14/2010 3 Longitudinal Shear Stresses However, for this element we see that in addition to the shearing stresses that are exerted on the
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L22_ Shearing Stresses in beams-fall 10 - EAS 209-Fall 2010...

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