TABLE OF CONTENTS If the wall thickness of a cylindrical vessel is smaller than one-twentieth of the radius it is considered to be a thin-walled vessel. The hoop stress can then be calculated with the equation-- ? = PD/2t Where- P = internal pressure, Pa; D = internal diameter, meters; and t = wall thickness, meters.
Similarly, if the pressure vessel were a closed vessel, the longitudinal force acting on the cylindrical shell would equal the internal area times the pressure, and the longitudinal stress would equal--
(P D 2 ?/4)/( ? D t) = PD/4t or just half the hoop stress.
Q:
If a 750 mm diameter cylinder with a 5.00 mm thick wall is pressurized to 1.5 MPa, what is the hoop stress?
Answers
Q:
PD/2t = ? = 1.5 10 6 0.750/(2 0.005) = 112.5 MPa
Similarly the longitudinal stress equals one half the hoop stress or ? = 112.5/2 = 56.25 Mpa
These constitute the two principal stresses in the wall of the vessel. The maximum shear stress, from the diagram of Mohr's Circle in the FE Handbook, equals one-half the algebraic difference between the two principal stresses.
? max = [(112.5 - 56.25) 10 6]/2 = 28.125 Mpa
