What is a Thin Cylinder?

In structural engineering and mechanical design, a thin cylinder is defined as a vessel where the wall thickness is significantly smaller than its internal diameter. Specifically, if the ratio of the internal diameter to the wall thickness is greater than 20 (D/t > 20), the cylinder is categorized as "thin." Examples include water pipes, boilers, and low-pressure storage tanks.

Understanding Hoop and Longitudinal Stress

When a thin cylinder is subjected to internal pressure, it experiences two primary types of stress:

• Hoop Stress (σₕ): Also known as circumferential stress, this acts along the circumference of the cylinder. It tends to split the cylinder into two halves longitudinally. It is calculated as: σₕ = (P × D) / (2 × t).
• Longitudinal Stress (σₗ): This acts parallel to the axis of the cylinder. It tends to push the ends of the cylinder apart. It is calculated as: σₗ = (P × D) / (4 × t).

Interestingly, the hoop stress is always twice the magnitude of the longitudinal stress in thin cylinders, which is why longitudinal cracks are more common in failed pipes than transverse ones.

How to Use This Calculator

To use the Thin Cylinder Stress Calculator, simply input the internal pressure, the internal diameter of the vessel, and the wall thickness. Ensure your units are consistent. If you use MPa for pressure and mm for dimensions, your output will be in MPa (N/mm²). The calculator also provides a warning if your cylinder does not meet the "thin shell" criteria of D/t > 20.

Frequently Asked Questions

Q: Why is hoop stress greater than longitudinal stress?
A: Geometry dictates that the projected area resisting circumferential pressure is half the projected area resisting axial pressure, resulting in the hoop stress being double the longitudinal stress.

Q: Can I use this for gas tanks?
A: Yes, as long as the pressure is low enough that the cylinder remains within its elastic limit and the thickness-to-diameter ratio stays within the "thin" range.