Burst Pressure of Thick Cylinder Calculator

For a thick-walled cylinder with internal pressure P, inner radius ri, and outer radius ro, Lamé’s stresses at the inner wall are:

• Hoop stress: σθ(ri) = P · (ro2 + ri2) / (ro2 - ri2)
• Radial stress: σr(ri) = -P
• Axial stress (closed ends): σz = P · ri2 / (ro2 - ri2)
• Axial stress (open ends): σz = 0

Burst pressure is estimated by setting a yield criterion equal to the chosen material strength:

• Tresca: max(|σ1-σ2|, |σ2-σ3|, |σ3-σ1|) = S
• von Mises: σvm = sqrt(0.5[(\sigma1-\sigma2)^2+(\sigma2-\sigma3)^2+(\sigma3-\sigma1)^2]) = S

Because stresses scale linearly with P, the calculator solves P = S / k, where k is computed for P=1 using the selected options.

1. Select a geometry mode: radii or diameters.
2. Choose length and pressure units that match your data.
3. Enter inner and outer dimensions, then material strength.
4. Pick an end condition (closed or open).
5. Select a yield criterion and a safety factor.
6. Press Calculate to display results above the form.
7. Use Download CSV or Download PDF for reports.

1) Burst Pressure in Thick Cylinders

A thick cylinder fails when the material can no longer carry the combined hoop, radial, and axial stresses created by internal pressure. This calculator estimates the burst pressure by evaluating inner-wall stresses, where the hoop stress is typically highest, then matching a selected yield criterion to a chosen strength value.

2) When Thick-Wall Theory Is Required

Thin-wall formulas assume nearly uniform hoop stress through the wall. For pressure parts with a radius-to-thickness ratio near or below about 10, stress varies strongly with radius and thin-wall methods can underpredict peak stress. Thick-wall analysis captures this gradient and provides safer screening estimates.

3) Geometry Inputs and Meaningful Ratios

The most informative geometric parameter is the ratio ro/ri. As this ratio increases, the inner-wall hoop stress factor decreases for a given pressure, which generally increases the predicted burst pressure. The tool accepts either radii or diameters and converts them consistently into meters for calculation.

4) Lamé Stresses at the Inner Wall

Lamé theory produces a radial stress that is compressive at the inner wall (-P) and approaches zero at the outer wall for an externally unpressurized cylinder. The hoop stress at the inner wall is amplified by the geometric factor (ro2+ri2)/(ro2-ri2), which can exceed 2.0 for moderately thick sections.

5) Comparing von Mises and Tresca

von Mises combines the principal stresses into an equivalent stress and is widely used for ductile metals. Tresca uses the maximum shear condition and is typically more conservative, especially when stress components differ substantially. Running both options helps bracket a reasonable design range and supports quick sensitivity checks.

6) Open Ends vs Closed Ends

End conditions influence the axial stress. With closed ends, internal pressure creates a net thrust that produces axial tension in the wall, raising the equivalent stress and lowering the predicted burst pressure. With open ends, axial stress is neglected, which can be appropriate for certain fittings or free-sliding end conditions.

7) Safety Factor and Allowable Pressure

Engineering decisions are usually based on allowable pressure rather than burst pressure. The calculator applies a user-defined safety factor by dividing burst pressure by SF. Typical screening values range from 1.5 to 4 depending on uncertainty in material data, cyclic loading, temperature, corrosion allowance, and inspection strategy.

8) Practical Use and Limitations

Use these results for early sizing, comparison of wall thickness options, or rapid checks during troubleshooting. For final design, verify against applicable pressure vessel codes, include temperature-dependent strength, residual stresses, autofrettage effects, and manufacturing tolerances. If the cylinder is brittle, fracture mechanics may govern instead of yielding.

1) What strength value should I enter?

Use yield strength for ductile design checks. Use ultimate strength only if your method or specification allows it and you understand the safety implications and failure mode.

2) Why are results different for Tresca and von Mises?

The criteria measure yielding differently. Tresca uses maximum shear and is usually more conservative. von Mises uses an energy-based equivalent stress and can predict a slightly higher burst pressure.

3) Does this include external pressure?

No. It assumes internal pressure with zero external pressure. If external pressure is relevant, the stress field changes and buckling may become important.

4) What does the end condition change?

Closed ends add axial stress from pressure thrust, increasing equivalent stress and reducing burst pressure. Open ends set axial stress to zero, which can increase the predicted burst pressure.

5) Why is radial stress negative at the inner wall?

Radial stress is compressive because pressure pushes inward on the wall. The sign convention helps combine stresses consistently in the yield equations.

6) How should I pick a safety factor?

Choose SF based on uncertainty and risk. Higher SF is common when material data is uncertain, loads are cyclic, temperatures are high, or inspection intervals are long.

7) Is this suitable for brittle materials?

Not by itself. Brittle failure may occur before yielding. Use fracture toughness, defect sizing, and code guidance for brittle materials and low-temperature service.