Pressure End-Thrust Worked Example
Calculation of pressure end thrust on a vessel closure, bolt load in a flanged joint and support reaction at a fixed end.
Problem
A cylindrical pressure vessel with internal radius 300 mm operates at 5.0 MPa. The end closure is a bolted flange with 20 bolts. Calculate the pressure end thrust and the bolt load per bolt.
Given
- p = 5.0 MPa
- r = 300 mm
- Number of bolts = 20
Step 1 — Pressure end thrust
F = p * pi * r^2 = 5.0 * pi * 300^2 = 5.0 * 282743 = 1,413,717 N = 1414 kN
Step 2 — Bolt load per bolt (pressure only)
F_bolt = F / 20 = 1414 / 20 = 70.7 kN per bolt. This is the pressure thrust component only. The actual bolt preload must exceed this to maintain gasket compression.
Step 3 — Total bolt load with gasket residual
Assuming the gasket residual must be 30% of the pressure thrust: F_total = 1414 * 1.3 = 1838 kN. F_bolt_total = 1838 / 20 = 91.9 kN per bolt.
Result
The pressure end thrust is approximately 1414 kN. The bolt load per bolt including gasket residual is approximately 92 kN. The actual preload must be calculated using the joint stiffness ratio for the specific flange and gasket design.