(Solved): can you please show working out, thank you Question A4: A thin-walled cylindrical pressure vessel is ...

Question A4: A thin-walled cylindrical pressure vessel is constructed using an alloy \( d=2 r=3 \mathrm{~m} \) and wall thickness, \( t \), of \( 30 \mathrm{~mm} \) and is known to have thumb-nail cracks of depth \( 10 \mathrm{~mm} \) oriented perpendicular to the hoop stress direction. The vessel is subjected to an increasing internal pressure for which the hoop stress is given by \( \sigma_{\theta}=\frac{p r}{t} \). The stress intensity factor for the thumb-nail cracks is given by \( K=1.26 \sigma \sqrt{a} \) (where \( a \) is the crack depth). (a) How will the pressure vessel fail? Please provide necessary solution steps. [5 marks]