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# Hoop stress

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1. A pressure vessel is made of a cylindrical composite part produced by filament winding. Hoop winding is used in which the number of winding layer is 5 and the wall thickness for each layer is 1mm. The diameter of the vessel is 0.5m. The fiber material is known to be S-glass with a tensile strength of 4.5GPa, and the matrix material is polyester with a tensile strength of70MPa. The volume fraction of
fiber is 60%.
It is also known that the HOOP STRESS is the stress in a pipe wall acting circumferentially in a plane perpendicular to the longitudinal axis of the pipe and produced by the pressure of the fluid in the pipe.
S=PD/2t
S=hoop stress, in MPa
P=internal pressure, in MPa
D=outside diameter of the pipe, in mm
T=normal wall thickness, in mm

(1) If the internal pressure is 80MPa, would this pressure vessel be safe in service?

(2) If yes, how many layer of winding can be decreased so that the part will be still safe? Or if not, how many more layers needed to be added?