(Solved): A filament-wound composite pressure vessel is to be made from unidirectional AS/3501 graphite/epox ...

A filament-wound composite pressure vessel is to be made from unidirectional AS/3501 graphite/epoxy. The winding angle is \( 0^{\circ} \leq \theta \leq 90^{\circ} \). The pressure vessel has closed ends. An internal pressure \( P \), a torque \( T \) and a bending moment \( M \) are applied as shown in the figure below. The bending stress is known to be \( \sigma_{B}=5 a / 6 t \). The torque will result in a shear stress expressed as \( \tau=2 a / t \), where \( a=p d / 2=265 \mathrm{kPa}-\mathrm{m} \). The diameter \( d=0.762 \mathrm{~m} \). Determine the variation of thickness with fibre orientation \( \theta \). Do not forget to consider that the bending stress is either tensile or compressive, depending upon which circumferential position is being evaluated. Assess the failure using a) Use Tsai-Hill theory b) Use Tsai-Wu failure theory \( s_{L}^{+}=1448 \mathrm{MPa}, s_{L}^{-}=1172 \mathrm{MPa}, s_{T}^{+}=48.3 \mathrm{MPa}, s_{L}^{-}=248 \mathrm{MPa}, s_{L T}=62.1 \mathrm{MPa} \)