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# Stress for Thin-Walled Spheres & Cylinders

Thin Walled Cylinder Stress Calculator

Summary

There are three primary mechanical stresses that can be applied to a spherical or cylindrically shaped object:

• Hoop Stress
• Axial Stress
• Radial Stress

If the object/vessel has walls with a thickness less than one-tenth of the overall diameter, then these objects can be assumed to be ‘thin-walled’ and the following equations be used to estimate the stresses:

• Cylinder Hoop Stress, $\sigma&space;=&space;\frac{P&space;*&space;r}{t}$
• Cylinder Axial Stress, $\sigma&space;=\frac{P*r}{2t}$
• Sphere Hoop Stress, $\sigma&space;=\frac{P*r}{2t}$
• Radial Stress, $\sigma&space;=\frac{-P}{2}$

In a sphere, hoop stress and axial stress have the same value.

Cylindrical Hoop Stress Calculator

 Calculate the hoop stress in a thin-walled cylinder: Formula: $\sigma&space;=&space;\frac{P&space;*&space;r}{t}$ P = pressure (+ve for internal pressure, -ve for external pressure) r = radius t = wall thickness Pressure Pa Radius m Wall thickness m Result: Pa

Cylindrical Axial / Spherical Hoop Stress Calculator

 Calculate the axial stress in a thin-walled cylinder / hoop stress in a thin-walled sphere: Formula: $\sigma&space;=\frac{P*r}{2t}$ P = pressure (+ve for internal pressure, -ve for external pressure) r = radius t = wall thickness Pressure Pa Radius m Wall thickness m Result: Pa

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