Consider a cylinder 100mm outside diameter and 90mm inside diameter fixed at one end with 40 MPa internal pressure.
Tip The hoop stress and longitudinal stress are aligned with the cylindrical coordinate system. The hoop stress is in θ and the longitudinal stress in Z. The hoop stress is the same as the maximum principal stress on this occasion but this is not always the case, sometimes the maximum principal stress is at an angle to the coordinate system.
The hoop stress is calculated as follows;
The FEA Von Mises when averaged across the thickness of the cylinder is 327.8 MPa and this compares to the hand calculation of 312 MPa.