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Thin-walled Pressure Vessels (continued)

Next consider the case of a thin-walled cylindrical pressure vessel with wall thickness, t,
inner radius, r, and internal pressure, p, as shown below.

σ₁ = pr/t (hoop stress)

σ₂ = pr/2t (longitudinal stress)

where

σ₁ is the hoop stress on the outer surface in (psi), (N/mm²), etc

                σ₂ is the longitudinal stress on the outer surface in (psi), (N/mm²), etc
                   p is the internal pressure in (lb/in²), (lb/ft²), (N/mm²), (N/m²)
                   r   is the internal radius of the cylindrical pressure vessel in (in), (mm),etc
                   t   is the wall thickness of the cylindrical pressure vessel in (in), (mm),etc

Note: The normal stress, σ₁ and σ₂ are constant throughout the thickness.

Note further: In the case of a cylindrical pressure vessel the hoop and longitudinal stresses on outer surface of each face of are the principal stresses. However an element rotated by 45^o will carry the maximum shear stress as well as a normal stress as seen on a Mohr’s Circle.

Click here for discussion of the use of Mohr’s Circle for pressure vessels.

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