8-16. 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 u. If the vessel is subjected to an internal pressure p , show that the force in the segment is Fu = s 0 wt , where s 0 is the stress in the filaments. Also, show that the stresses in the hoop and longitudinal directions are s h = s 0 sin 2 u and s 1 = s 0 cos 2 u, respectively. At what angle u (optimum winding angl e) would the filaments have to be would so that the hoop and longitudinal stresses are equivalent? | |
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