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How to Calculate Transverse Shear

A general shear stress can be calculated by dividing a parallel force by the area it is applied to. However, this supposes a uniform stress. In the case of a rectangular beam undergoing transverse shear stresses, uniformity no longer applies. These transverse shear stresses have a parabolic distribution across the beam. The top and bottom boundaries carry no longitudinal loads. They therefore experience no shear stresses. However, the beam's center experiences maximal shear stress. The aforementioned simple mathematical estimate is no longer accurate. Calculating transverse shear stress requires some different thinking and a more complex process than the general case.

Instructions

- 1
  Consider a beam with a rectangular cross section under a known applied shear force. Measure the beam's height and the width. The maximum transverse shear stress is applied along an axis located at the exact center of the beam's height. To calculate the shear stress at a different point in the beam, measure the distance between the beam's center axis and the point of interest. This is the y-distance. To calculate maximum transverse shear stress, set the y-distance equal to zero.
- 2
  Determine the height's cubed value by multiplying it by itself and then by itself again (height * height * height). Multiply this value by the width. Divide this product by 12. This calculation yields the second moment of the beam's entire area.
- 3
  Calculate the squared y-distance by multiplying it by itself (y-distance * y-distance). Calculate the squared height by multiplying the value by itself (height * height). Divide this value by 4. Subtract the squared y-distance from this quotient. Multiply the result by 6. This yields a value for the shear stress distribution factor.
- 4
  Multiply the known shear force by the distribution factor from Step 3. Divide this value by the second moment calculated in Step 2. This value is the transverse shear stress experienced by the beam at the y-distance point.

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