This calculation example demonstrates how to find the maximum principal stress, which is the largest normal stress occurring in a material. This calculation is highly important in mechanical component design to prevent failure.
An engineer needs to verify the strength of a specific point on the surface of a mechanical component under plane stress conditions. From measurement and analysis, the normal stress in the x-axis is , the normal stress in the y-axis is , and the shear stress is . Calculate the maximum principal stress () for safety evaluation.
The calculated maximum principal stress () is MPa, which is the actual maximum tensile stress occurring in the material at this point. Even though the normal stress in the x-axis is only 100 MPa, the combined effect with shear stress causes the principal direction to experience a higher stress. The engineer must compare this maximum principal stress with the material's strength limits, such as Yield Strength or Tensile Strength, according to the chosen failure theory to determine if the component is safe.