A closed-ended pressure vessel is fabricated by cross winding glass filaments over a mandr...

A closed-ended pressure vessel is fabricated by cross winding glass filaments over a mandrel, so that the wall thickness t of the vessel is composed entirely of filament and an expoxy binder as shown in the figure. Consider a segment of the vessel of width w and wrapped at an angle θ. If the vessel is subjected to an internal pressure p,show that the force in the segment is pθ = σ0wt. where σ0 is the stress in the filaments. Also, show that the stresses in the hoop and longitudinal directions are σh= σ0 sin2 θ and t = σ0 cos2 θ. respectively. At what angle θ (optimum winding angle) would the filaments have to be would so that the hoop and longitudinal stresses are equivalent?