6d. Shear Stress in Beams  (SSES Ch. 6.4)
Shear Stress
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Shear Stress
Transverse shear forces cause shear stress on a beam's cross-section at height y = y1:

  • Shear stress is zero at the top and bottom surfaces.
  • y = y-value of "cut", y = y1 (where we are finding the stress).
  • V = shear force on the cross-section.
  • A* = area on the opposite side of the "cut" from the neutral axis; i.e., area above y1.
  • y* = distance from neutral axis to the centroid of A*, NOT the distance to the cut.
  • I = moment of inertia of the entire cross-section.
  • t = width of beam at y (width of cut).
  • Q is the first moment of area of A* with respect to the neutral axis; Q = A*y*.
  • q is the shear flow; q = t   t .

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Updated: 05/24/09 DJD