Thin-walled Pressure Vessels (continued)

Recall Mohr’s Circle provides a convenient way to determine the normal and shear stresses
on any face of the element. Consider the following cylindrical pressure vessel of inner
radius, r, thickness, t, and with internal pressure, p.

Mohr’s Circle for a cylindrical pressure vessel for in-plane stresses on the outer surface
of the cylinder is as follows:

where σ₁ = pr/t (circumferential) and σ₂ = pr/2t (longitudinal)

Note: σ₁ and σ₂ are the in-plane principal stresses. The maximum in-plane shearing

stress is rotated 45^o from the faces of the element shown above. The value of the maximum

in-plane shearing stress for an element on the outer surface of the cylinder is just

τ _max = ( σ₂ – σ₁ ) / 2 = pr/4t

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