A thin-walled spherical vessel has radius r and thickness t. The pressure of fluid inside the vessel is P. Then membrane stresses for this thin-walled pressure vessel is _____

Explanation:

• Consider a thin pressure vessel having closed ends and contains a fluid under a gauge pressure p. Then the walls of the cylinder will have a longitudinal stress, circumferential stress and radial stress.
• σL =  longitudinal stress (tensile), σr = radial stress (compressive), σh = circumferential stress (tensile).

Now, we know that σ_h = hoop stress = Membrane stress

Due to the pressure inside the pressure vessel, membrane stresses i.e. hoop stresses is induced in vessel (as shown fig)

\(\begin{array}{l} {\sigma _h} \times 2\pi r \times t = P \times \pi {r^2}\\ \Rightarrow {\sigma _h} = \frac{{Pr}}{{2t}} \end{array}\)

Important Points

Longitudinal or axial stress is given as:

\({σ _L} = \frac{{pd}}{{4t}}\)

where d is the internal diameter and t is the wall thickness of the cylinder.