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Formulas for Calculating Stress at a Point

Part of the Mechanics of Materials For Dummies Cheat Sheet

When dealing with mechanics of materials, choosing the correct formula to calculate the stress at a given point can be difficult. Normal and shear stresses come in a wide variety of applications, each stress application with its own calculation formula. The most common stress types you deal with in basic mechanics of materials fall into several major categories:

  • Axial tension: ANET is equal to the gross area of the cross section minus any holes that may exist.

    image0.jpg
  • Thin-walled pressure vessels: Two stresses exist: an axial stress along the axis of the member and a hoop (or radial) stress, which occurs tangential to the radius of the cross section. These stresses are based on the gage pressure p inside the pressure vessel.

    For cylindrical pressure vessels, use this pair of formulas:

    image1.jpg

    For spherical pressure vessels, use the following formula:

    image2.jpg image3.jpg
  • Bending stresses: For symmetric cross sections in the XY plane, use this formula:

    image4.jpg

    (moment about the x-axis)(moment about the y-axis)

  • Flexural shear stresses: Here's the formula for calculating flexural shear stress:

    image5.jpg
  • Torsional shear stress: Use this formula to find torsional shear stress:

    image6.jpg
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